1
|
Yuan J, Shi L, Yue L, Li B, Wang Z, Xu S, Xu T, Wang Y, Gan Z, Chen F, Lin Z, Wang X, Jin K, Wang X, Luo J, Zhang S, Wu Q, Liu Q, Hu T, Li R, Zhou X, Wu D, Dong T, Wang N. Dynamical interplay between superconductivity and pseudogap in cuprates as revealed by terahertz third-harmonic generation spectroscopy. Sci Adv 2024; 10:eadg9211. [PMID: 38335284 PMCID: PMC10857425 DOI: 10.1126/sciadv.adg9211] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/02/2023] [Accepted: 01/10/2024] [Indexed: 02/12/2024]
Abstract
We report on nonlinear terahertz third-harmonic generation (THG) measurements on YBa2Cu3O6+x thin films. Different from conventional superconductors, the THG signal starts to appear in the normal state, which is consistent with the crossover temperature T* of pseudogap over broad doping levels. Upon lowering the temperature, the THG signal shows an anomaly just below Tc in the optimally doped sample. Notably, we observe a beat pattern directly in the measured real-time waveform of the THG signal. We elaborate that the Higgs mode, which develops below Tc, couples to the mode already developed below T*, resulting in an energy level splitting. However, this coupling effect is not evident in underdoped samples. We explore different potential explanations for the observed phenomena. Our research offers valuable insight into the interplay between superconductivity and pseudogap.
Collapse
Affiliation(s)
- Jiayu Yuan
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Liyu Shi
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Li Yue
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Bohan Li
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Zixiao Wang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Shuxiang Xu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Tiequan Xu
- Applied Superconductivity Center and State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
| | - Yue Wang
- Applied Superconductivity Center and State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
- Peking University Yangtze Delta Institute of Optoelectronics, Nantong, Jiangsu, China
| | - Zizhao Gan
- Applied Superconductivity Center and State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
- Peking University Yangtze Delta Institute of Optoelectronics, Nantong, Jiangsu, China
| | - Fucong Chen
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Zefeng Lin
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Xu Wang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Kui Jin
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Xinbo Wang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Jianlin Luo
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Sijie Zhang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Qiong Wu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Qiaomei Liu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Tianchen Hu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Rongsheng Li
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Xinyu Zhou
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Dong Wu
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Tao Dong
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Nanlin Wang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
- Collaborative Innovation Center of Quantum Matter, Beijing, China
| |
Collapse
|
2
|
El Hage R, Sánchez-Manzano D, Humbert V, Carreira S, Rouco V, Sander A, Cuellar F, Seurre K, Lagarrigue A, Mesoraca S, Briatico J, Trastoy J, Santamaría J, Villegas JE. Disentangling Photodoping, Photoconductivity, and Photosuperconductivity in the Cuprates. Phys Rev Lett 2024; 132:066001. [PMID: 38394577 DOI: 10.1103/physrevlett.132.066001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2023] [Accepted: 01/02/2024] [Indexed: 02/25/2024]
Abstract
The normal-state conductivity and superconducting critical temperature of oxygen-deficient YBa_{2}Cu_{3}O_{7-δ} can be persistently enhanced by illumination. Strongly debated for years, the origin of those effects-termed persistent photoconductivity and photosuperconductivity (PPS)-has remained an unsolved critical problem, whose comprehension may provide key insights to harness the origin of high-temperature superconductivity itself. Here, we make essential steps toward understanding PPS. While the models proposed so far assume that it is caused by a carrier-density increase (photodoping) observed concomitantly, our experiments contradict such conventional belief: we demonstrate that it is instead linked to a photo-induced decrease of the electronic scattering rate. Furthermore, we find that the latter effect and photodoping are completely disconnected and originate from different microscopic mechanisms, since they present different wavelength and oxygen-content dependences as well as strikingly different relaxation dynamics. Besides helping disentangle photodoping, persistent photoconductivity, and PPS, our results provide new evidence for the intimate relation between critical temperature and scattering rate, a key ingredient in modern theories on high-temperature superconductivity.
Collapse
Affiliation(s)
- R El Hage
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
| | - D Sánchez-Manzano
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
| | - V Humbert
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
| | - S Carreira
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
| | - V Rouco
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
| | - A Sander
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
| | - F Cuellar
- GFMC, Departamento de Física de Materiales, Universidad de Ciencias Físicas, Facultad Complutense de Madrid, 28040 Madrid, Spain
| | - K Seurre
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
| | - A Lagarrigue
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
| | - S Mesoraca
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
| | - J Briatico
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
| | - J Trastoy
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
| | - J Santamaría
- GFMC, Departamento de Física de Materiales, Universidad de Ciencias Físicas, Facultad Complutense de Madrid, 28040 Madrid, Spain
| | - Javier E Villegas
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
| |
Collapse
|
3
|
Arpaia R, Martinelli L, Sala MM, Caprara S, Nag A, Brookes NB, Camisa P, Li Q, Gao Q, Zhou X, Garcia-Fernandez M, Zhou KJ, Schierle E, Bauch T, Peng YY, Di Castro C, Grilli M, Lombardi F, Braicovich L, Ghiringhelli G. Signature of quantum criticality in cuprates by charge density fluctuations. Nat Commun 2023; 14:7198. [PMID: 37938250 PMCID: PMC10632404 DOI: 10.1038/s41467-023-42961-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2022] [Accepted: 10/25/2023] [Indexed: 11/09/2023] Open
Abstract
The universality of the strange metal phase in many quantum materials is often attributed to the presence of a quantum critical point (QCP), a zero-temperature phase transition ruled by quantum fluctuations. In cuprates, where superconductivity hinders direct QCP observation, indirect evidence comes from the identification of fluctuations compatible with the strange metal phase. Here we show that the recently discovered charge density fluctuations (CDF) possess the right properties to be associated to a quantum phase transition. Using resonant x-ray scattering, we studied the CDF in two families of cuprate superconductors across a wide doping range (up to p = 0.22). At p* ≈ 0.19, the putative QCP, the CDF intensity peaks, and the characteristic energy Δ is minimum, marking a wedge-shaped region in the phase diagram indicative of a quantum critical behavior, albeit with anomalies. These findings strengthen the role of charge order in explaining strange metal phenomenology and provide insights into high-temperature superconductivity.
Collapse
Affiliation(s)
- Riccardo Arpaia
- Quantum Device Physics Laboratory, Department of Microtechnology and Nanoscience, Chalmers University of Technology, SE-41296, Göteborg, Sweden.
| | - Leonardo Martinelli
- Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133, Milano, Italy
| | - Marco Moretti Sala
- Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133, Milano, Italy
| | - Sergio Caprara
- Dipartimento di Fisica, Università di Roma "La Sapienza", P.le Aldo Moro 5, I-00185, Roma, Italy
- CNR-ISC, via dei Taurini 19, I-00185, Roma, Italy
| | - Abhishek Nag
- Diamond Light Source, Harwell Campus, Didcot, OX11 0DE, United Kingdom
| | - Nicholas B Brookes
- ESRF, The European Synchrotron, 71 Avenue des Martyrs, F-38000, Grenoble, France
| | - Pietro Camisa
- Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133, Milano, Italy
| | - Qizhi Li
- International Center for Quantum Materials, School of Physics, Peking University, CN-100871, Beijing, China
| | - Qiang Gao
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, CN-100190, Beijing, China
| | - Xingjiang Zhou
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, CN-100190, Beijing, China
| | | | - Ke-Jin Zhou
- Diamond Light Source, Harwell Campus, Didcot, OX11 0DE, United Kingdom
| | - Enrico Schierle
- Helmholtz-Zentrum Berlin für Materialien und Energie, Albert-Einstein-Straße 15, D-12489, Berlin, Germany
| | - Thilo Bauch
- Quantum Device Physics Laboratory, Department of Microtechnology and Nanoscience, Chalmers University of Technology, SE-41296, Göteborg, Sweden
| | - Ying Ying Peng
- International Center for Quantum Materials, School of Physics, Peking University, CN-100871, Beijing, China
| | - Carlo Di Castro
- Dipartimento di Fisica, Università di Roma "La Sapienza", P.le Aldo Moro 5, I-00185, Roma, Italy
| | - Marco Grilli
- Dipartimento di Fisica, Università di Roma "La Sapienza", P.le Aldo Moro 5, I-00185, Roma, Italy
- CNR-ISC, via dei Taurini 19, I-00185, Roma, Italy
| | - Floriana Lombardi
- Quantum Device Physics Laboratory, Department of Microtechnology and Nanoscience, Chalmers University of Technology, SE-41296, Göteborg, Sweden
| | - Lucio Braicovich
- Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133, Milano, Italy
- ESRF, The European Synchrotron, 71 Avenue des Martyrs, F-38000, Grenoble, France
| | - Giacomo Ghiringhelli
- Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133, Milano, Italy.
- CNR-SPIN, Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133, Milano, Italy.
| |
Collapse
|
4
|
Li Q, Huang HY, Ren T, Weschke E, Ju L, Zou C, Zhang S, Qiu Q, Liu J, Ding S, Singh A, Prokhnenko O, Huang DJ, Esterlis I, Wang Y, Xie Y, Peng Y. Prevailing Charge Order in Overdoped La_{2-x}Sr_{x}CuO_{4} beyond the Superconducting Dome. Phys Rev Lett 2023; 131:116002. [PMID: 37774302 DOI: 10.1103/physrevlett.131.116002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2022] [Revised: 04/03/2023] [Accepted: 08/24/2023] [Indexed: 10/01/2023]
Abstract
The extremely overdoped cuprates are generally considered to be Fermi liquid metals without exotic orders, whereas the underdoped cuprates harbor intertwined states. Contrary to this conventional wisdom, using Cu L_{3}-edge and O K-edge resonant x-ray scattering, we reveal a charge order (CO) correlation in overdoped La_{2-x}Sr_{x}CuO_{4} (0.35≤x≤0.6) beyond the superconducting dome. This CO has a periodicity of ∼6 lattice units with correlation lengths of ∼20 lattice units. It shows similar in-plane momentum and polarization dependence and dispersive excitations as the CO of underdoped cuprates, but its maximum intensity differs along the c direction and persists up to 300 K. This CO correlation cannot be explained by the Fermi surface instability and its origin remains to be understood. Our results suggest that CO is prevailing in the overdoped metallic regime and requires a reassessment of the picture of overdoped cuprates as weakly correlated Fermi liquids.
Collapse
Affiliation(s)
- Qizhi Li
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Hsiao-Yu Huang
- National Synchrotron Radiation Research Center, Hsinchu 30076, Taiwan
| | - Tianshuang Ren
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Eugen Weschke
- Helmholtz-Zentrum Berlin für Materialien und Energie, Berlin 14109, Germany
| | - Lele Ju
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Changwei Zou
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Shilong Zhang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Qingzheng Qiu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Jiarui Liu
- Department of Physics and Astronomy, Clemson University, Clemson, South Carolina 29631, USA
| | - Shuhan Ding
- Department of Physics and Astronomy, Clemson University, Clemson, South Carolina 29631, USA
| | - Amol Singh
- National Synchrotron Radiation Research Center, Hsinchu 30076, Taiwan
| | | | - Di-Jing Huang
- National Synchrotron Radiation Research Center, Hsinchu 30076, Taiwan
| | - Ilya Esterlis
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Yao Wang
- Department of Physics and Astronomy, Clemson University, Clemson, South Carolina 29631, USA
- Department of Chemistry, Emory University, Atlanta, Georgia 30322, USA
| | - Yanwu Xie
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Yingying Peng
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| |
Collapse
|
5
|
Scott K, Kisiel E, Boyle TJ, Basak R, Jargot G, Das S, Agrestini S, Garcia-Fernandez M, Choi J, Pelliciari J, Li J, Chuang YD, Zhong R, Schneeloch JA, Gu G, Légaré F, Kemper AF, Zhou KJ, Bisogni V, Blanco-Canosa S, Frano A, Boschini F, da Silva Neto EH. Low-energy quasi-circular electron correlations with charge order wavelength in Bi 2Sr 2CaCu 2O 8+δ. Sci Adv 2023; 9:eadg3710. [PMID: 37467326 DOI: 10.1126/sciadv.adg3710] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/24/2022] [Accepted: 06/16/2023] [Indexed: 07/21/2023]
Abstract
Most resonant inelastic x-ray scattering (RIXS) studies of dynamic charge order correlations in the cuprates have focused on the high-symmetry directions of the copper oxide plane. However, scattering along other in-plane directions should not be ignored as it may help understand, for example, the origin of charge order correlations or the isotropic scattering resulting in strange metal behavior. Our RIXS experiments reveal dynamic charge correlations over the qx-qy scattering plane in underdoped Bi2Sr2CaCu2O8+δ. Tracking the softening of the RIXS-measured bond-stretching phonon, we show that these dynamic correlations exist at energies below approximately 70 meV and are centered around a quasi-circular manifold in the qx-qy scattering plane with radius equal to the magnitude of the charge order wave vector, qCO. This phonon-tracking procedure also allows us to rule out fluctuations of short-range directional charge order (i.e., centered around [qx = ±qCO, qy = 0] and [qx = 0, qy = ±qCO]) as the origin of the observed correlations.
Collapse
Affiliation(s)
- Kirsty Scott
- Department of Physics, Yale University, New Haven, CT 06520, USA
- Energy Sciences Institute, Yale University, West Haven, CT 06516, USA
| | - Elliot Kisiel
- Department of Physics, University of California San Diego, La Jolla, CA 92093, USA
| | - Timothy J Boyle
- Department of Physics, Yale University, New Haven, CT 06520, USA
- Energy Sciences Institute, Yale University, West Haven, CT 06516, USA
- Department of Physics and Astronomy, University of California, Davis, CA 95616, USA
| | - Rourav Basak
- Department of Physics, University of California San Diego, La Jolla, CA 92093, USA
| | - Gaëtan Jargot
- Centre Énergie Matériaux Télécommunications, Institut National de la Recherche Scientifique, Varennes, Québec J3X 1S2, Canada
| | - Sarmistha Das
- Department of Physics, University of California San Diego, La Jolla, CA 92093, USA
| | | | | | - Jaewon Choi
- Diamond Light Source, Harwell Campus, Didcot OX11 0DE, UK
| | - Jonathan Pelliciari
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, NY 11973, USA
| | - Jiemin Li
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, NY 11973, USA
| | - Yi-De Chuang
- Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
| | - Ruidan Zhong
- Condensed Matter Physics and Materials Science, Brookhaven National Laboratory, Upton, NY 11973, USA
| | - John A Schneeloch
- Condensed Matter Physics and Materials Science, Brookhaven National Laboratory, Upton, NY 11973, USA
| | - Genda Gu
- Condensed Matter Physics and Materials Science, Brookhaven National Laboratory, Upton, NY 11973, USA
| | - François Légaré
- Centre Énergie Matériaux Télécommunications, Institut National de la Recherche Scientifique, Varennes, Québec J3X 1S2, Canada
| | - Alexander F Kemper
- Department of Physics, North Carolina State University, Raleigh, NC 27695, USA
| | - Ke-Jin Zhou
- Diamond Light Source, Harwell Campus, Didcot OX11 0DE, UK
| | - Valentina Bisogni
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, NY 11973, USA
| | - Santiago Blanco-Canosa
- Donostia International Physics Center (DIPC), 20018 Donostia-San Sebastian, Basque Country, Spain
- IKERBASQUE, Basque Foundation for Science, 48013 Bilbao, Spain
| | - Alex Frano
- Department of Physics, University of California San Diego, La Jolla, CA 92093, USA
- Canadian Institute for Advanced Research, Toronto, ON M5G 1M1, Canada
| | - Fabio Boschini
- Centre Énergie Matériaux Télécommunications, Institut National de la Recherche Scientifique, Varennes, Québec J3X 1S2, Canada
- Quantum Matter Institute, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
| | - Eduardo H da Silva Neto
- Department of Physics, Yale University, New Haven, CT 06520, USA
- Energy Sciences Institute, Yale University, West Haven, CT 06516, USA
- Department of Physics and Astronomy, University of California, Davis, CA 95616, USA
- Department of Applied Physics, Yale University, New Haven, CT 06520, USA
| |
Collapse
|
6
|
Song CL, Main EJ, Simmons F, Liu S, Phillabaum B, Dahmen KA, Hudson EW, Hoffman JE, Carlson EW. Critical nematic correlations throughout the superconducting doping range in Bi 2-zPb zSr 2-yLa yCuO 6+x. Nat Commun 2023; 14:2622. [PMID: 37147296 PMCID: PMC10162959 DOI: 10.1038/s41467-023-38249-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2022] [Accepted: 04/17/2023] [Indexed: 05/07/2023] Open
Abstract
Charge modulations have been widely observed in cuprates, suggesting their centrality for understanding the high-Tc superconductivity in these materials. However, the dimensionality of these modulations remains controversial, including whether their wavevector is unidirectional or bidirectional, and also whether they extend seamlessly from the surface of the material into the bulk. Material disorder presents severe challenges to understanding the charge modulations through bulk scattering techniques. We use a local technique, scanning tunneling microscopy, to image the static charge modulations on Bi2-zPbzSr2-yLayCuO6+x. The ratio of the phase correlation length ξCDW to the orientation correlation length ξorient points to unidirectional charge modulations. By computing new critical exponents at free surfaces including that of the pair connectivity correlation function, we show that these locally 1D charge modulations are actually a bulk effect resulting from classical 3D criticality of the random field Ising model throughout the entire superconducting doping range.
Collapse
Affiliation(s)
- Can-Li Song
- Department of Physics, Harvard University, Cambridge, MA, 02138, USA
| | - Elizabeth J Main
- Department of Physics, Harvard University, Cambridge, MA, 02138, USA
| | - Forrest Simmons
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA
- Purdue Quantum Science and Engineering Institute, West Lafayette, IN, 47907, USA
| | - Shuo Liu
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA
| | - Benjamin Phillabaum
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA
| | - Karin A Dahmen
- Department of Physics, University of Illinois, Urbana-Champaign, IL, 61801, USA
| | - Eric W Hudson
- Department of Physics, The Pennsylvania State University, University Park, PA, 16802, USA
| | | | - Erica W Carlson
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA.
- Purdue Quantum Science and Engineering Institute, West Lafayette, IN, 47907, USA.
| |
Collapse
|
7
|
Disa AS, Curtis J, Fechner M, Liu A, von Hoegen A, Först M, Nova TF, Narang P, Maljuk A, Boris AV, Keimer B, Cavalleri A. Photo-induced high-temperature ferromagnetism in YTiO 3. Nature 2023; 617:73-78. [PMID: 37138109 PMCID: PMC10156606 DOI: 10.1038/s41586-023-05853-8] [Citation(s) in RCA: 10] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2021] [Accepted: 02/16/2023] [Indexed: 05/05/2023]
Abstract
In quantum materials, degeneracies and frustrated interactions can have a profound impact on the emergence of long-range order, often driving strong fluctuations that suppress functionally relevant electronic or magnetic phases1-7. Engineering the atomic structure in the bulk or at heterointerfaces has been an important research strategy to lift these degeneracies, but these equilibrium methods are limited by thermodynamic, elastic and chemical constraints8. Here we show that all-optical, mode-selective manipulation of the crystal lattice can be used to enhance and stabilize high-temperature ferromagnetism in YTiO3, a material that shows only partial orbital polarization, an unsaturated low-temperature magnetic moment and a suppressed Curie temperature, Tc = 27 K (refs. 9-13). The enhancement is largest when exciting a 9 THz oxygen rotation mode, for which complete magnetic saturation is achieved at low temperatures and transient ferromagnetism is realized up to Tneq > 80 K, nearly three times the thermodynamic transition temperature. We interpret these effects as a consequence of the light-induced dynamical changes to the quasi-degenerate Ti t2g orbitals, which affect the magnetic phase competition and fluctuations found in the equilibrium state14-20. Notably, the light-induced high-temperature ferromagnetism discovered in our work is metastable over many nanoseconds, underscoring the ability to dynamically engineer practically useful non-equilibrium functionalities.
Collapse
Affiliation(s)
- A S Disa
- Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany.
- School of Applied and Engineering Physics, Cornell University, Ithaca, NY, USA.
| | - J Curtis
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
- College of Letters and Science, University of California, Los Angeles, CA, USA
| | - M Fechner
- Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany
| | - A Liu
- Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany
| | - A von Hoegen
- Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany
| | - M Först
- Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany
| | - T F Nova
- Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany
| | - P Narang
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
- College of Letters and Science, University of California, Los Angeles, CA, USA
| | - A Maljuk
- Leibniz Institute for Solid State and Materials Research Dresden, Dresden, Germany
| | - A V Boris
- Max Planck Institute for Solid State Research, Stuttgart, Germany
| | - B Keimer
- Max Planck Institute for Solid State Research, Stuttgart, Germany
| | - A Cavalleri
- Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany.
- Clarendon Laboratory, Department of Physics, Oxford University, Oxford, UK.
| |
Collapse
|
8
|
Adamus P, Xu B, Marsik P, Dubroka A, Barabasová P, Růžičková H, Puphal P, Pomjakushina E, Tallon JL, Mathis YL, Munzar D, Bernhard C. Analogies of phonon anomalies and electronic gap features in the infrared response of Sr14-xCa xCu 24O 41and underdoped YBa 2Cu 3O6+x. Rep Prog Phys 2023; 86:044502. [PMID: 36821858 DOI: 10.1088/1361-6633/acbe4f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2022] [Accepted: 02/23/2023] [Indexed: 06/18/2023]
Abstract
We present an experimental and theoretical study which compares the phonon anomalies and the electronic gap features in the infrared response of the weakly coupled two-leg-ladders in Sr14-xCaxCu24O41(SCCO) with those of the underdoped high-Tcsuperconductor YBa2Cu3O6+x(YBCO) and thereby reveals some surprising analogies. Specifically, we present a phenomenological model that describes the anomalous doping- and temperature-dependence of some of the phonon features in thea-axis response (field along the rungs of the ladders) of SCCO. It assumes that the phonons are coupled to charge oscillations within the ladders. Their changes with decreasing temperature reveal the formation of a crystal (density wave) of hole pairs that are oriented along the rungs. We also discuss the analogy to a similar model that was previously used to explain the phonon anomalies and an electronic plasma mode in thec-axis response (field perpendicular to the CuO2planes) of YBCO. We further confirm that an insulator-like pseudogap develops in thea-axis conductivity of SCCO which closely resembles that in thec-axis conductivity of YBCO. Most surprisingly, we find that thec-axis conductivity (field along the legs of the ladders) of SCCO is strikingly similar to the in-plane one (field parallel to the CuO2planes) of YBCO. Notably, in both cases a dip feature develops in the normal state spectra that is connected with a spectral weight shift toward low frequencies and can thus be associated with precursor superconducting pairing correlations that are lacking macroscopic phase coherence. This SCCO-YBCO analogy indicates that collective degrees of freedom contribute to the low-energy response of underdoped highTccuprates and it even suggests that the charges in the CuO2planes tend to segregate forming quasi-one-dimensional structures similar to the two-leg ladders, as predicted for the stripe-scenario or certain intertwinned states.
Collapse
Affiliation(s)
- Petr Adamus
- Department of Condensed Matter Physics, Faculty of Science, Masaryk University, Kotlářská 2, 61137 Brno, Czech Republic
| | - Bing Xu
- University of Fribourg, Department of Physics, Chemin du Musée 3, CH-1700 Fribourg, Switzerland
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
| | - Premysl Marsik
- University of Fribourg, Department of Physics, Chemin du Musée 3, CH-1700 Fribourg, Switzerland
| | - Adam Dubroka
- Department of Condensed Matter Physics, Faculty of Science, Masaryk University, Kotlářská 2, 61137 Brno, Czech Republic
| | - Paulína Barabasová
- Department of Condensed Matter Physics, Faculty of Science, Masaryk University, Kotlářská 2, 61137 Brno, Czech Republic
| | - Hana Růžičková
- Department of Condensed Matter Physics, Faculty of Science, Masaryk University, Kotlářská 2, 61137 Brno, Czech Republic
| | - Pascal Puphal
- Laboratory for Multiscale Materials Experiments, PSI, 5232 Villigen, Switzerland
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | | | - Jeffery L Tallon
- Victoria University of Wellington, Robinson Research Institute, POB 33436, Lower Hutt 5046, New Zealand
| | - Yves-Laurent Mathis
- Karlsruhe Institute of Technology, Institute for Beam Physics and Technology, Hermann-von-Helmhotz-Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany
| | - Dominik Munzar
- Department of Condensed Matter Physics, Faculty of Science, Masaryk University, Kotlářská 2, 61137 Brno, Czech Republic
| | - Christian Bernhard
- University of Fribourg, Department of Physics, Chemin du Musée 3, CH-1700 Fribourg, Switzerland
| |
Collapse
|
9
|
Jiang C, Beneduce E, Baggioli M, Setty C, Zaccone A. Possible enhancement of the superconductingTcdue to sharp Kohn-like soft phonon anomalies. J Phys Condens Matter 2023; 35:164003. [PMID: 36808073 DOI: 10.1088/1361-648x/acbd0a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/25/2022] [Accepted: 02/17/2023] [Indexed: 06/18/2023]
Abstract
Phonon softening is a ubiquitous phenomenon in condensed matter systems which is often associated with charge density wave (CDW) instabilities and anharmonicity. The interplay between phonon softening, CDW and superconductivity is a topic of intense debate. In this work, the effects of anomalous soft phonon instabilities on superconductivity are studied based on a recently developed theoretical framework that accounts for phonon damping and softening within the Migdal-Eliashberg theory. Model calculations show that the phonon softening in the form of a sharp dip in the phonon dispersion relation, either acoustic or optical (including the case of Kohn-type anomalies typically associated with CDW), can cause a manifold increase of the electron-phonon coupling constantλ. This, under certain conditions, which are consistent with the concept of optimal frequency introduced by Bergmann and Rainer, can produce a large increase of the superconducting transition temperatureTc. In summary, our results suggest the possibility of reaching high-temperature superconductivity by exploiting soft phonon anomalies restricted in momentum space.
Collapse
Affiliation(s)
- Cunyuan Jiang
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China
| | - Enrico Beneduce
- Department of Physics "A. Pontremoli", University of Milan, via Celoria 16, 20133 Milan, Italy
| | - Matteo Baggioli
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China
- Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, People's Republic of China
| | - Chandan Setty
- Department of Physics and Astronomy, Rice Center for Quantum Materials, Rice University, Houston, TX 77005, United States of America
| | - Alessio Zaccone
- Department of Physics "A. Pontremoli", University of Milan, via Celoria 16, 20133 Milan, Italy
| |
Collapse
|
10
|
Grilli M, Di Castro C, Mirarchi G, Seibold G, Caprara S. Dissipative Quantum Criticality as a Source of Strange Metal Behavior. Symmetry (Basel) 2023; 15:569. [DOI: 10.3390/sym15030569] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/24/2023] Open
Abstract
The strange metal behavior, usually characterized by a linear-in-temperature (T) resistivity, is a still unsolved mystery in solid-state physics. It is often associated with the proximity to a quantum critical point (a second order transition at temperature T=0, leading to a broken symmetry phase) focusing on the related divergent order parameter correlation length. Here, we propose a paradigmatic shift, focusing on a divergent characteristic time scale due to a divergent dissipation acting on the fluctuating critical modes while their correlation length stays finite. To achieve a divergent dissipation, we propose a mechanism based on the coupling between a local order parameter fluctuation and electron density diffusive modes that accounts both for the linear-in-T resistivity and for the logarithmic specific heat versus temperature ratio CV/T∼log(1/T), down to low temperatures.
Collapse
|
11
|
Wen JJ, He W, Jang H, Nojiri H, Matsuzawa S, Song S, Chollet M, Zhu D, Liu YJ, Fujita M, Jiang JM, Rotundu CR, Kao CC, Jiang HC, Lee JS, Lee YS. Enhanced charge density wave with mobile superconducting vortices in La(1.885)Sr(0.115)CuO(4). Nat Commun 2023; 14:733. [PMID: 36759612 DOI: 10.1038/s41467-023-36203-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2022] [Accepted: 01/17/2023] [Indexed: 02/11/2023] Open
Abstract
Superconductivity in the cuprates is found to be intertwined with charge and spin density waves. Determining the interactions between the different types of order is crucial for understanding these important materials. Here, we elucidate the role of the charge density wave (CDW) in the prototypical cuprate La1.885Sr0.115CuO4, by studying the effects of large magnetic fields (H) up to 24 Tesla. At low temperatures (T), the observed CDW peaks reveal two distinct regions in the material: a majority phase with short-range CDW coexisting with superconductivity, and a minority phase with longer-range CDW coexisting with static spin density wave (SDW). With increasing magnetic field, the CDW first grows smoothly in a manner similar to the SDW. However, at high fields we discover a sudden increase in the CDW amplitude upon entering the vortex-liquid state. Our results signify strong coupling of the CDW to mobile superconducting vortices and link enhanced CDW amplitude with local superconducting pairing across the H - T phase diagram.
Collapse
|
12
|
von Arx K, Wang Q, Mustafi S, Mazzone DG, Horio M, Mukkattukavil DJ, Pomjakushina E, Pyon S, Takayama T, Takagi H, Kurosawa T, Momono N, Oda M, Brookes NB, Betto D, Zhang W, Asmara TC, Tseng Y, Schmitt T, Sassa Y, Chang J. Fate of charge order in overdoped La-based cuprates. NPJ Quantum Mater 2023; 8:7. [PMID: 38666240 PMCID: PMC11041719 DOI: 10.1038/s41535-023-00539-w] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/23/2022] [Accepted: 01/09/2023] [Indexed: 04/28/2024]
Abstract
In high-temperature cuprate superconductors, stripe order refers broadly to a coupled spin and charge modulation with a commensuration of eight and four lattice units, respectively. How this stripe order evolves across optimal doping remains a controversial question. Here we present a systematic resonant inelastic x-ray scattering study of weak charge correlations in La2-xSrxCuO4 and La1.8-xEu0.2SrxCuO4. Ultra high energy resolution experiments demonstrate the importance of the separation of inelastic and elastic scattering processes. Long-range temperature-dependent stripe order is only found below optimal doping. At higher doping, short-range temperature-independent correlations are present up to the highest doping measured. This transformation is distinct from and preempts the pseudogap critical doping. We argue that the doping and temperature-independent short-range correlations originate from unresolved electron-phonon coupling that broadly peaks at the stripe ordering vector. In La2-xSrxCuO4, long-range static stripe order vanishes around optimal doping and we discuss both quantum critical and crossover scenarios.
Collapse
Affiliation(s)
- K. von Arx
- Physik-Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
- Department of Physics, Chalmers University of Technology, SE-412 96 Göteborg, Sweden
| | - Qisi Wang
- Physik-Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - S. Mustafi
- Physik-Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - D. G. Mazzone
- Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institut, CH-5232 Villigen, PSI Switzerland
| | - M. Horio
- Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581 Japan
| | - D. John Mukkattukavil
- Department of Physics and Astronomy, Uppsala University, Box 516, 751 20 Uppsala, Sweden
| | | | - S. Pyon
- Department of Applied Physics, The University of Tokyo, Tokyo, 113-8646 Japan
| | - T. Takayama
- Max Planck Institute for Solid State Research, 70569 Stuttgart, Germany
| | - H. Takagi
- Max Planck Institute for Solid State Research, 70569 Stuttgart, Germany
- Department of Physics, The University of Tokyo, Tokyo, 113-0033 Japan
| | - T. Kurosawa
- Department of Physics, Hokkaido University, Sapporo, 060-0810 Japan
| | - N. Momono
- Department of Physics, Hokkaido University, Sapporo, 060-0810 Japan
- Department of Applied Sciences, Muroran Institute of Technology, Muroran, 050-8585 Japan
| | - M. Oda
- Department of Physics, Hokkaido University, Sapporo, 060-0810 Japan
| | - N. B. Brookes
- European Synchrotron Radiation Facility, B.P. 220, 38043 Grenoble, France
| | - D. Betto
- European Synchrotron Radiation Facility, B.P. 220, 38043 Grenoble, France
| | - W. Zhang
- Swiss Light Source, Photon Science Division, Paul Scherrer Institut, CH-5232 Villigen, PSI Switzerland
| | - T. C. Asmara
- Swiss Light Source, Photon Science Division, Paul Scherrer Institut, CH-5232 Villigen, PSI Switzerland
| | - Y. Tseng
- Swiss Light Source, Photon Science Division, Paul Scherrer Institut, CH-5232 Villigen, PSI Switzerland
| | - T. Schmitt
- Swiss Light Source, Photon Science Division, Paul Scherrer Institut, CH-5232 Villigen, PSI Switzerland
| | - Y. Sassa
- Department of Physics, Chalmers University of Technology, SE-412 96 Göteborg, Sweden
| | - J. Chang
- Physik-Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| |
Collapse
|
13
|
Klose C, Büttner F, Hu W, Mazzoli C, Litzius K, Battistelli R, Lemesh I, Bartell JM, Huang M, Günther CM, Schneider M, Barbour A, Wilkins SB, Beach GSD, Eisebitt S, Pfau B. Coherent correlation imaging for resolving fluctuating states of matter. Nature 2023; 614:256-61. [PMID: 36653456 DOI: 10.1038/s41586-022-05537-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2021] [Accepted: 11/08/2022] [Indexed: 01/19/2023]
Abstract
Fluctuations and stochastic transitions are ubiquitous in nanometre-scale systems, especially in the presence of disorder. However, their direct observation has so far been impeded by a seemingly fundamental, signal-limited compromise between spatial and temporal resolution. Here we develop coherent correlation imaging (CCI) to overcome this dilemma. Our method begins by classifying recorded camera frames in Fourier space. Contrast and spatial resolution emerge by averaging selectively over same-state frames. Temporal resolution down to the acquisition time of a single frame arises independently from an exceptionally low misclassification rate, which we achieve by combining a correlation-based similarity metric1,2 with a modified, iterative hierarchical clustering algorithm3,4. We apply CCI to study previously inaccessible magnetic fluctuations in a highly degenerate magnetic stripe domain state with nanometre-scale resolution. We uncover an intricate network of transitions between more than 30 discrete states. Our spatiotemporal data enable us to reconstruct the pinning energy landscape and to thereby explain the dynamics observed on a microscopic level. CCI massively expands the potential of emerging high-coherence X-ray sources and paves the way for addressing large fundamental questions such as the contribution of pinning5-8 and topology9-12 in phase transitions and the role of spin and charge order fluctuations in high-temperature superconductivity13,14.
Collapse
|
14
|
Ruiz A, Gunn B, Lu Y, Sasmal K, Moir CM, Basak R, Huang H, Lee JS, Rodolakis F, Boyle TJ, Walker M, He Y, Blanco-Canosa S, da Silva Neto EH, Maple MB, Frano A. Stabilization of three-dimensional charge order through interplanar orbital hybridization in Pr xY 1-xBa 2Cu 3O 6+δ. Nat Commun 2022; 13:6197. [PMID: 36261435 DOI: 10.1038/s41467-022-33607-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2022] [Accepted: 09/23/2022] [Indexed: 11/09/2022] Open
Abstract
The shape of 3d-orbitals often governs the electronic and magnetic properties of correlated transition metal oxides. In the superconducting cuprates, the planar confinement of the \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$${d}_{{x}^{2}-{y}^{2}}$$\end{document}dx2−y2 orbital dictates the two-dimensional nature of the unconventional superconductivity and a competing charge order. Achieving orbital-specific control of the electronic structure to allow coupling pathways across adjacent planes would enable direct assessment of the role of dimensionality in the intertwined orders. Using Cu L3 and Pr M5 resonant x-ray scattering and first-principles calculations, we report a highly correlated three-dimensional charge order in Pr-substituted YBa2Cu3O7, where the Pr f-electrons create a direct orbital bridge between CuO2 planes. With this we demonstrate that interplanar orbital engineering can be used to surgically control electronic phases in correlated oxides and other layered materials. External perturbations can induce 3D charge order in cuprates, but the 3D correlation length is limited and the mechanism is not well understood. Ruiz et al. show that Pr substitution in YBa2Cu3O7 enhances interplanar orbital coupling and stabilizes coherent 3D charge order that coexists with superconductivity.
Collapse
|
15
|
Tam CC, Choi J, Ding X, Agrestini S, Nag A, Wu M, Huang B, Luo H, Gao P, García-Fernández M, Qiao L, Zhou KJ. Charge density waves in infinite-layer NdNiO 2 nickelates. Nat Mater 2022; 21:1116-1120. [PMID: 35982306 DOI: 10.1038/s41563-022-01330-1] [Citation(s) in RCA: 21] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2021] [Accepted: 07/07/2022] [Indexed: 06/15/2023]
Abstract
In materials science, much effort has been devoted to the reproduction of superconductivity in chemical compositions, analogous to cuprate superconductors since their discovery over 30 years ago. This approach was recently successful in realising superconductivity in infinite-layer nickelates1-6. Although differing from cuprates in electronic and magnetic properties, strong Coulomb interactions suggest that infinite-layer nickelates have a propensity towards various symmetry-breaking orders that populate cuprates7-10. Here we report the observation of charge density waves (CDWs) in infinite-layer NdNiO2 films using Ni L3 resonant X-ray scattering. Remarkably, CDWs form in Nd 5d and Ni 3d orbitals at the same commensurate wavevector (0.333, 0) reciprocal lattice units, with non-negligible out-of-plane dependence and an in-plane correlation length of up to ~60 Å. Spectroscopic studies reveal a strong connection between CDWs and Nd 5d-Ni 3d orbital hybridization. Upon entering the superconducting state at 20% Sr doping, the CDWs disappear. Our work demonstrates the existence of CDWs in infinite-layer nickelates with a multiorbital character distinct from cuprates, which establishes their low-energy physics.
Collapse
Affiliation(s)
- Charles C Tam
- Diamond Light Source, Didcot, United Kingdom
- H. H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom
| | - Jaewon Choi
- Diamond Light Source, Didcot, United Kingdom
| | - Xiang Ding
- School of Physics, University of Electronic Science and Technology of China, Chengdu, China
| | | | - Abhishek Nag
- Diamond Light Source, Didcot, United Kingdom
- Laboratory for Non-linear Optics, Paul Scherrer Institut, Villigen, PSI, Switzerland
| | - Mei Wu
- International Center for Quantum Materials and Electron Microscopy Laboratory, School of Physics, Peking University, Beijing, China
| | - Bing Huang
- Beijing Computational Science Research Center, Beijing, China
| | - Huiqian Luo
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong, China
| | - Peng Gao
- International Center for Quantum Materials and Electron Microscopy Laboratory, School of Physics, Peking University, Beijing, China
| | | | - Liang Qiao
- School of Physics, University of Electronic Science and Technology of China, Chengdu, China.
| | - Ke-Jin Zhou
- Diamond Light Source, Didcot, United Kingdom.
| |
Collapse
|
16
|
Campi G, Bianconi A, Joseph B, Mishra SK, Müller L, Zozulya A, Nugroho AA, Roy S, Sprung M, Ricci A. Nanoscale inhomogeneity of charge density waves dynamics in La2−xSrxNiO4. Sci Rep 2022; 12. [PMID: 36153400 PMCID: PMC9509336 DOI: 10.1038/s41598-022-18925-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2022] [Accepted: 08/22/2022] [Indexed: 11/09/2022] Open
Abstract
AbstractWhile stripe phases with broken rotational symmetry of charge density are known to emerge in doped strongly correlated perovskites, the dynamics and heterogeneity of spatial ordering remain elusive. Here we shed light on the temperature dependent lattice motion and the spatial nanoscale phase separation of charge density wave order in the archetypal striped phase in La2−xSrxNiO4+y (LSNO) perovskite using X-ray photon correlation spectroscopy (XPCS) joint with scanning micro X-ray diffraction (SµXRD). While it is known that the CDW in 1/8 doped cuprates shows a remarkable stability we report the CDW motion dynamics by XPCS in nickelates with an anomalous quantum glass regime at low temperature, T < 65 K, and the expected thermal melting at higher temperature 65 < T < 120 K. The nanoscale CDW puddles with a shorter correlation length are more mobile than CDW puddles with a longer correlation length. The direct imaging of nanoscale spatial inhomogeneity of CDW by scanning micro X-ray diffraction (SµXRD) shows a nanoscale landscape of percolating short range dynamic CDW puddles competing with large quasi-static CDW puddles giving rise to a novel form of nanoscale phase separation of the incommensurate stripes order landscape.
Collapse
|
17
|
Chen W, Ren W, Kennedy N, Hamidian MH, Uchida S, Eisaki H, Johnson PD, O'Mahony SM, Davis JCS. Identification of a nematic pair density wave state in Bi(2)Sr(2)CaCu(2)O(8+x). Proc Natl Acad Sci U S A 2022; 119:e2206481119. [PMID: 35895680 DOI: 10.1073/pnas.2206481119] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Abstract
Electron-pair density wave (PDW) states are now an intense focus of research in the field of cuprate correlated superconductivity. PDWs exhibit periodically modulating superconductive electron pairing that can be visualized directly using scanned Josephson tunneling microscopy (SJTM). Although from theory, intertwining the d-wave superconducting (DSC) and PDW order parameters allows a plethora of global electron-pair orders to appear, which one actually occurs in the various cuprates is unknown. Here, we use SJTM to visualize the interplay of PDW and DSC states in Bi2Sr2CaCu2O8+x at a carrier density where the charge density wave modulations are virtually nonexistent. Simultaneous visualization of their amplitudes reveals that the intertwined PDW and DSC are mutually attractive states. Then, by separately imaging the electron-pair density modulations of the two orthogonal PDWs, we discover a robust nematic PDW state. Its spatial arrangement entails Ising domains of opposite nematicity, each consisting primarily of unidirectional and lattice commensurate electron-pair density modulations. Further, we demonstrate by direct imaging that the scattering resonances identifying Zn impurity atom sites occur predominantly within boundaries between these domains. This implies that the nematic PDW state is pinned by Zn atoms, as was recently proposed [Lozano et al., Phys. Rev. B 103, L020502 (2021)]. Taken in combination, these data indicate that the PDW in Bi2Sr2CaCu2O8+x is a vestigial nematic pair density wave state [Agterberg et al. Phys. Rev. B 91, 054502 (2015); Wardh and Granath arXiv:2203.08250].
Collapse
|
18
|
Krieger G, Martinelli L, Zeng S, Chow LE, Kummer K, Arpaia R, Moretti Sala M, Brookes NB, Ariando A, Viart N, Salluzzo M, Ghiringhelli G, Preziosi D. Charge and Spin Order Dichotomy in NdNiO_{2} Driven by the Capping Layer. Phys Rev Lett 2022; 129:027002. [PMID: 35867432 DOI: 10.1103/physrevlett.129.027002] [Citation(s) in RCA: 20] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2021] [Accepted: 06/03/2022] [Indexed: 06/15/2023]
Abstract
Superconductivity in infinite-layer nickelates holds exciting analogies with that of cuprates, with similar structures and 3d-electron count. Using resonant inelastic x-ray scattering, we studied electronic and magnetic excitations and charge density correlations in Nd_{1-x}Sr_{x}NiO_{2} thin films with and without an SrTiO_{3} capping layer. We observe dispersing magnons only in the capped samples, progressively dampened at higher doping. We detect an elastic resonant scattering peak in the uncapped x=0 compound at wave vector (∼⅓,0), remindful of the charge order signal in hole doped cuprates. The peak weakens at x=0.05 and disappears in the superconducting x=0.20 film. The role of the capping on the electronic reconstruction far from the interface remains to be understood.
Collapse
Affiliation(s)
- G Krieger
- Université de Strasbourg, CNRS, IPCMS UMR 7504, F-67034 Strasbourg, France
| | - L Martinelli
- Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy
| | - S Zeng
- Department of Physics, Faculty of Science, National University of Singapore, 117551 Singapore, Singapore
| | - L E Chow
- Department of Physics, Faculty of Science, National University of Singapore, 117551 Singapore, Singapore
| | - K Kummer
- ESRF, The European Synchrotron, 71 Avenue des Martyrs, F-38043 Grenoble, France
| | - R Arpaia
- Quantum Device Physics Laboratory, Department of Microtechnology and Nanoscience, Chalmers University of Technology, SE-41296 Göteborg, Sweden
| | - M Moretti Sala
- Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy
| | - N B Brookes
- ESRF, The European Synchrotron, 71 Avenue des Martyrs, F-38043 Grenoble, France
| | - A Ariando
- Department of Physics, Faculty of Science, National University of Singapore, 117551 Singapore, Singapore
| | - N Viart
- Université de Strasbourg, CNRS, IPCMS UMR 7504, F-67034 Strasbourg, France
| | - M Salluzzo
- CNR-SPIN Complesso di Monte S. Angelo, via Cinthia-I-80126 Napoli, Italy
| | - G Ghiringhelli
- Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy
- CNR-SPIN, Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy
| | - D Preziosi
- Université de Strasbourg, CNRS, IPCMS UMR 7504, F-67034 Strasbourg, France
| |
Collapse
|
19
|
Wandel S, Boschini F, da Silva Neto EH, Shen L, Na MX, Zohar S, Wang Y, Welch SB, Seaberg MH, Koralek JD, Dakovski GL, Hettel W, Lin MF, Moeller SP, Schlotter WF, Reid AH, Minitti MP, Boyle T, He F, Sutarto R, Liang R, Bonn D, Hardy W, Kaindl RA, Hawthorn DG, Lee JS, Kemper AF, Damascelli A, Giannetti C, Turner JJ, Coslovich G. Enhanced charge density wave coherence in a light-quenched, high-temperature superconductor. Science 2022; 376:860-864. [PMID: 35587968 DOI: 10.1126/science.abd7213] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Superconductivity and charge density waves (CDWs) are competitive, yet coexisting, orders in cuprate superconductors. To understand their microscopic interdependence, a probe capable of discerning their interaction on its natural length and time scale is necessary. We use ultrafast resonant soft x-ray scattering to track the transient evolution of CDW correlations in YBa2Cu3O6+x after the quench of superconductivity by an infrared laser pulse. We observe a nonthermal response of the CDW order characterized by a near doubling of the correlation length within ≈1 picosecond of the superconducting quench. Our results are consistent with a model in which the interaction between superconductivity and CDWs manifests inhomogeneously through disruption of spatial coherence, with superconductivity playing the dominant role in stabilizing CDW topological defects, such as discommensurations.
Collapse
Affiliation(s)
- S Wandel
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
| | - F Boschini
- Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada.,Quantum Matter Institute, University of British Columbia, Vancouver, BC V6T 1Z4, Canada.,Centre Énergie Matériaux Télécommunications, Institut National de la Recherche Scientifique, Varennes, QC J3X 1S2, Canada
| | - E H da Silva Neto
- Department of Physics, Yale University, New Haven, CT 06520, USA.,Energy Sciences Institute, Yale University, New Haven, CT 06516, USA.,Department of Physics, University of California, Davis, CA 95616, USA
| | - L Shen
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA.,Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, CA 94025, USA
| | - M X Na
- Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada.,Quantum Matter Institute, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
| | - S Zohar
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
| | - Y Wang
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
| | - S B Welch
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
| | - M H Seaberg
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
| | - J D Koralek
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
| | - G L Dakovski
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
| | - W Hettel
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
| | - M-F Lin
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
| | - S P Moeller
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
| | - W F Schlotter
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
| | - A H Reid
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
| | - M P Minitti
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
| | - T Boyle
- Department of Physics, Yale University, New Haven, CT 06520, USA.,Energy Sciences Institute, Yale University, New Haven, CT 06516, USA.,Department of Physics, University of California, Davis, CA 95616, USA
| | - F He
- Canadian Light Source, Saskatoon, SK S7N 2V3, Canada
| | - R Sutarto
- Canadian Light Source, Saskatoon, SK S7N 2V3, Canada
| | - R Liang
- Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada.,Quantum Matter Institute, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
| | - D Bonn
- Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada.,Quantum Matter Institute, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
| | - W Hardy
- Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada.,Quantum Matter Institute, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
| | - R A Kaindl
- Department of Physics, Arizona State University, Tempe, AZ 85287, USA.,Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
| | - D G Hawthorn
- Department of Physics and Astronomy, University of Waterloo, Waterloo, ON N2L 3G1, Canada
| | - J-S Lee
- Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
| | - A F Kemper
- Department of Physics, North Carolina State University, Raleigh, NC 27695, USA
| | - A Damascelli
- Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada.,Quantum Matter Institute, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
| | - C Giannetti
- Department of Mathematics and Physics, Università Cattolica del Sacro Cuore, Brescia, BS I-25121, Italy
| | - J J Turner
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA.,Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, CA 94025, USA
| | - G Coslovich
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
| |
Collapse
|
20
|
Abstract
Recent resonant X-ray scattering experiments on cuprates allowed to identify a new kind of collective excitations, known as charge density fluctuations, which have finite characteristic wave vector, short correlation length and small characteristic energy. It was then shown that these fluctuations provide a microscopic scattering mechanism that accounts for the anomalous transport properties of cuprates in the so-called strange-metal phase and are a source of anomalies in the specific heat. In this work, we retrace the main steps that led us to attributing a central role to charge density fluctuations in the strange-metal phase of cuprates, discuss the state of the art on the issue and provide an in-depth analysis of the contribution of charge density fluctuations to the specific heat.
Collapse
|
21
|
Tam CC, Zhu M, Ayres J, Kummer K, Yakhou-Harris F, Cooper JR, Carrington A, Hayden SM. Charge density waves and Fermi surface reconstruction in the clean overdoped cuprate superconductor Tl 2Ba 2CuO 6+δ. Nat Commun 2022; 13:570. [PMID: 35091572 PMCID: PMC8799688 DOI: 10.1038/s41467-022-28124-y] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2021] [Accepted: 01/10/2022] [Indexed: 12/03/2022] Open
Abstract
Hall effect and quantum oscillation measurements on high temperature cuprate superconductors show that underdoped compositions have small Fermi surface pockets whereas when heavily overdoped, a single much larger pocket is found. The origin of this change in electronic structure has been unclear, but may be related to the high temperature superconductivity. Here we show that the clean overdoped single-layer cuprate Tl2Ba2CuO6+δ (Tl2201) displays CDW order with a remarkably long correlation length ξ ≈ 200 Å which disappears above a hole doping of pCDW ≈ 0.265. We show that the evolution of the electronic properties of Tl2201 as the doping is lowered may be explained by a Fermi surface reconstruction which accompanies the emergence of the CDW below pCDW. Our results demonstrate importance of CDW correlations in understanding the electronic properties of overdoped cuprates. The origin of the Fermi surface reconstruction that occurs in cuprate superconductors as hole doping increases remains unclear. Here, the authors observe long range charge density wave (CDW) order in the overdoped single-layer cuprate Tl2Ba2CuO6+δ, which then disappears above a hole concentration 0.265, suggesting a correlation between Fermi surface reconstruction and the emergence of the CDW.
Collapse
Affiliation(s)
- C C Tam
- H. H. Wills Physics Laboratory, University of Bristol, Bristol, BS8 1TL, United Kingdom.,Diamond Light Source, Harwell Campus, Didcot, OX11 0DE, United Kingdom
| | - M Zhu
- H. H. Wills Physics Laboratory, University of Bristol, Bristol, BS8 1TL, United Kingdom
| | - J Ayres
- H. H. Wills Physics Laboratory, University of Bristol, Bristol, BS8 1TL, United Kingdom
| | - K Kummer
- ESRF, The European Synchrotron, 71 Avenue des Martyrs, CS40220, 38043, Grenoble Cedex 9, France
| | - F Yakhou-Harris
- ESRF, The European Synchrotron, 71 Avenue des Martyrs, CS40220, 38043, Grenoble Cedex 9, France
| | - J R Cooper
- Department of Physics, University of Cambridge, Madingley Road, Cambridge, CB3 0HE, United Kingdom
| | - A Carrington
- H. H. Wills Physics Laboratory, University of Bristol, Bristol, BS8 1TL, United Kingdom.
| | - S M Hayden
- H. H. Wills Physics Laboratory, University of Bristol, Bristol, BS8 1TL, United Kingdom.
| |
Collapse
|
22
|
Wahlberg E, Arpaia R, Seibold G, Rossi M, Fumagalli R, Trabaldo E, Brookes NB, Braicovich L, Caprara S, Gran U, Ghiringhelli G, Bauch T, Lombardi F. Restored strange metal phase through suppression of charge density waves in underdoped YBa 2Cu 3O 7-δ. Science 2021; 373:1506-1510. [PMID: 34554788 DOI: 10.1126/science.abc8372] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
[Figure: see text].
Collapse
Affiliation(s)
- Eric Wahlberg
- Quantum Device Physics Laboratory, Department of Microtechnology and Nanoscience, Chalmers University of Technology, SE-41296 Göteborg, Sweden
| | - Riccardo Arpaia
- Quantum Device Physics Laboratory, Department of Microtechnology and Nanoscience, Chalmers University of Technology, SE-41296 Göteborg, Sweden.,Dipartimento di Fisica, Politecnico di Milano, I-20133 Milano, Italy
| | - Götz Seibold
- Institut für Physik, BTU Cottbus-Senftenberg, D-03013 Cottbus, Germany
| | - Matteo Rossi
- Dipartimento di Fisica, Politecnico di Milano, I-20133 Milano, Italy
| | - Roberto Fumagalli
- Dipartimento di Fisica, Politecnico di Milano, I-20133 Milano, Italy
| | - Edoardo Trabaldo
- Quantum Device Physics Laboratory, Department of Microtechnology and Nanoscience, Chalmers University of Technology, SE-41296 Göteborg, Sweden
| | | | - Lucio Braicovich
- Dipartimento di Fisica, Politecnico di Milano, I-20133 Milano, Italy.,ESRF, European Synchrotron, F-38043 Grenoble, France
| | - Sergio Caprara
- Dipartimento di Fisica, Università di Roma "La Sapienza," I-00185 Roma, Italy.,CNR-ISC, I-00185 Roma, Italy
| | - Ulf Gran
- Division of Subatomic, High-Energy and Plasma Physics, Chalmers University of Technology, SE-41296 Göteborg, Sweden
| | - Giacomo Ghiringhelli
- Dipartimento di Fisica, Politecnico di Milano, I-20133 Milano, Italy.,CNR-SPIN, Dipartimento di Fisica, Politecnico di Milano, I-20133 Milano, Italy
| | - Thilo Bauch
- Quantum Device Physics Laboratory, Department of Microtechnology and Nanoscience, Chalmers University of Technology, SE-41296 Göteborg, Sweden
| | - Floriana Lombardi
- Quantum Device Physics Laboratory, Department of Microtechnology and Nanoscience, Chalmers University of Technology, SE-41296 Göteborg, Sweden
| |
Collapse
|
23
|
Vinograd I, Zhou R, Hirata M, Wu T, Mayaffre H, Krämer S, Liang R, Hardy WN, Bonn DA, Julien MH. Locally commensurate charge-density wave with three-unit-cell periodicity in YBa 2Cu 3O y. Nat Commun 2021; 12:3274. [PMID: 34075033 PMCID: PMC8169916 DOI: 10.1038/s41467-021-23140-w] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2021] [Accepted: 04/16/2021] [Indexed: 11/20/2022] Open
Abstract
In order to identify the mechanism responsible for the formation of charge-density waves (CDW) in cuprate superconductors, it is important to understand which aspects of the CDW's microscopic structure are generic and which are material-dependent. Here, we show that, at the local scale probed by NMR, long-range CDW order in YBa2Cu3Oy is unidirectional with a commensurate period of three unit cells (λ = 3b), implying that the incommensurability found in X-ray scattering is ensured by phase slips (discommensurations). Furthermore, NMR spectra reveal a predominant oxygen character of the CDW with an out-of-phase relationship between certain lattice sites but no specific signature of a secondary CDW with λ = 6b associated with a putative pair-density wave. These results shed light on universal aspects of the cuprate CDW. In particular, its spatial profile appears to generically result from the interplay between an incommensurate tendency at long length scales, possibly related to properties of the Fermi surface, and local commensuration effects, due to electron-electron interactions or lock-in to the lattice.
Collapse
Affiliation(s)
- Igor Vinograd
- Univ. Grenoble Alpes, INSA Toulouse, Univ. Toulouse Paul Sabatier, EMFL, CNRS, LNCMI, Grenoble, France.
| | - Rui Zhou
- Univ. Grenoble Alpes, INSA Toulouse, Univ. Toulouse Paul Sabatier, EMFL, CNRS, LNCMI, Grenoble, France
- Institute of Physics, Chinese Academy of Sciences, and Beijing National Laboratory for Condensed Matter Physics, Beijing, China
| | - Michihiro Hirata
- Univ. Grenoble Alpes, INSA Toulouse, Univ. Toulouse Paul Sabatier, EMFL, CNRS, LNCMI, Grenoble, France
- MPA-Q, Los Alamos National Laboratory, Los Alamos, NM, USA
| | - Tao Wu
- Univ. Grenoble Alpes, INSA Toulouse, Univ. Toulouse Paul Sabatier, EMFL, CNRS, LNCMI, Grenoble, France
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui, China
| | - Hadrien Mayaffre
- Univ. Grenoble Alpes, INSA Toulouse, Univ. Toulouse Paul Sabatier, EMFL, CNRS, LNCMI, Grenoble, France
| | - Steffen Krämer
- Univ. Grenoble Alpes, INSA Toulouse, Univ. Toulouse Paul Sabatier, EMFL, CNRS, LNCMI, Grenoble, France
| | - Ruixing Liang
- Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, Canada
- Canadian Institute for Advanced Research, Toronto, Canada
| | - W N Hardy
- Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, Canada
- Canadian Institute for Advanced Research, Toronto, Canada
| | - D A Bonn
- Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, Canada
- Canadian Institute for Advanced Research, Toronto, Canada
| | - Marc-Henri Julien
- Univ. Grenoble Alpes, INSA Toulouse, Univ. Toulouse Paul Sabatier, EMFL, CNRS, LNCMI, Grenoble, France.
| |
Collapse
|
24
|
Diego J, Said AH, Mahatha SK, Bianco R, Monacelli L, Calandra M, Mauri F, Rossnagel K, Errea I, Blanco-Canosa S. van der Waals driven anharmonic melting of the 3D charge density wave in VSe 2. Nat Commun 2021; 12:598. [PMID: 33500397 DOI: 10.1038/s41467-020-20829-2] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2020] [Accepted: 12/22/2020] [Indexed: 11/24/2022] Open
Abstract
Understanding of charge-density wave (CDW) phases is a main challenge in condensed matter due to their presence in high-Tc superconductors or transition metal dichalcogenides (TMDs). Among TMDs, the origin of the CDW in VSe2 remains highly debated. Here, by means of inelastic x-ray scattering and first-principles calculations, we show that the CDW transition is driven by the collapse at 110 K of an acoustic mode at qCDW = (2.25 0 0.7) r.l.u. The softening starts below 225 K and expands over a wide region of the Brillouin zone, identifying the electron-phonon interaction as the driving force of the CDW. This is supported by our calculations that determine a large momentum-dependence of the electron-phonon matrix-elements that peak at the CDW wave vector. Our first-principles anharmonic calculations reproduce the temperature dependence of the soft mode and the TCDW onset only when considering the out-of-plane van der Waals interactions, which reveal crucial for the melting of the CDW phase. The nature of the charge density wave transition in VSe2 is still debated. Here, the authors demonstrate that the transition is mainly driven by electron-phonon interactions, despite the presence of the Fermi-surface nesting, and that Wan-der-Waals forces are responsible for melting of the charge density wave order.
Collapse
|
25
|
Boschini F, Minola M, Sutarto R, Schierle E, Bluschke M, Das S, Yang Y, Michiardi M, Shao YC, Feng X, Ono S, Zhong RD, Schneeloch JA, Gu GD, Weschke E, He F, Chuang YD, Keimer B, Damascelli A, Frano A, da Silva Neto EH. Dynamic electron correlations with charge order wavelength along all directions in the copper oxide plane. Nat Commun 2021; 12:597. [PMID: 33500415 DOI: 10.1038/s41467-020-20824-7] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2020] [Accepted: 12/21/2020] [Indexed: 11/08/2022] Open
Abstract
In strongly correlated systems the strength of Coulomb interactions between electrons, relative to their kinetic energy, plays a central role in determining their emergent quantum mechanical phases. We perform resonant x-ray scattering on Bi2Sr2CaCu2O8+δ, a prototypical cuprate superconductor, to probe electronic correlations within the CuO2 plane. We discover a dynamic quasi-circular pattern in the x-y scattering plane with a radius that matches the wave vector magnitude of the well-known static charge order. Along with doping- and temperature-dependent measurements, our experiments reveal a picture of charge order competing with superconductivity where short-range domains along x and y can dynamically rotate into any other in-plane direction. This quasi-circular spectrum, a hallmark of Brazovskii-type fluctuations, has immediate consequences to our understanding of rotational and translational symmetry breaking in the cuprates. We discuss how the combination of short- and long-range Coulomb interactions results in an effective non-monotonic potential that may determine the quasi-circular pattern. Knowledge of effective Coulomb interactions is central to understand emergent quantum phases in strongly correlated systems. Here, Boschini et al. report a dynamic quasi-circular spectrum of charge density wave fluctuations in the CuO2 plane of Bi2Sr2CaCu2O8+δ, shedding a light on understanding how Coulomb interactions can lead to rotational and translational symmetry breaking in the cuprates.
Collapse
|
26
|
Bagrov AA, Danilov M, Brener S, Harland M, Lichtenstein AI, Katsnelson MI. Detecting quantum critical points in the t-[Formula: see text] Fermi-Hubbard model via complex network theory. Sci Rep 2020; 10:20470. [PMID: 33235259 PMCID: PMC7686386 DOI: 10.1038/s41598-020-77513-0] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2020] [Accepted: 10/27/2020] [Indexed: 11/25/2022] Open
Abstract
A considerable success in phenomenological description of [Formula: see text] superconductors has been achieved within the paradigm of Quantum Critical Point (QCP)-a parental state of a variety of exotic phases that is characterized by dense entanglement and absence of well-defined quasiparticles. However, the microscopic origin of the critical regime in real materials remains an open question. On the other hand, there is a popular view that a single-band t-[Formula: see text] Hubbard model is the minimal model to catch the main relevant physics of superconducting compounds. Here, we suggest that emergence of the QCP is tightly connected with entanglement in real space and identify its location on the phase diagram of the hole-doped t-[Formula: see text] Hubbard model. To detect the QCP we study a weighted graph of inter-site quantum mutual information within a four-by-four plaquette that is solved by exact diagonalization. We demonstrate that some quantitative characteristics of such a graph, viewed as a complex network, exhibit peculiar behavior around a certain submanifold in the parametric space of the model. This method allows us to overcome difficulties caused by finite size effects and to identify precursors of the transition point even on a small lattice, where long-range asymptotics of correlation functions cannot be accessed.
Collapse
Affiliation(s)
- Andrey A. Bagrov
- Department of Physics and Astronomy, Uppsala University, Box 516, 75120 Uppsala, Sweden
- Institute for Molecules and Materials, Radboud University, 6525AJ Nijmegen, The Netherlands
- Theoretical Physics and Applied Mathematics Department, Ural Federal University, 620002 Yekaterinburg, Russia
| | - Mikhail Danilov
- Institute of Theoretical Physics, University of Hamburg, 20355 Hamburg, Germany
| | - Sergey Brener
- Institute of Theoretical Physics, University of Hamburg, 20355 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Malte Harland
- Institute of Theoretical Physics, University of Hamburg, 20355 Hamburg, Germany
| | - Alexander I. Lichtenstein
- Theoretical Physics and Applied Mathematics Department, Ural Federal University, 620002 Yekaterinburg, Russia
- Institute of Theoretical Physics, University of Hamburg, 20355 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Mikhail I. Katsnelson
- Institute for Molecules and Materials, Radboud University, 6525AJ Nijmegen, The Netherlands
- Theoretical Physics and Applied Mathematics Department, Ural Federal University, 620002 Yekaterinburg, Russia
| |
Collapse
|
27
|
Di Castro C. Revival of Charge Density Waves and Charge Density Fluctuations in Cuprate High-Temperature Superconductors. Condensed Matter 2020; 5:70. [DOI: 10.3390/condmat5040070] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
I present here a short memory of my scientific contacts with K.A. Müller starting from the Interlaken Conference (1988), Erice (1992 and 1993), and Cottbus (1994) on the initial studies on phase separation (PS) and charge inhomogeneity in cuprates carried out against the view of the majority of the scientific community at that time. Going over the years and passing through the charge density wave (CDW) instability of the correlated Fermi liquid (FL) and to the consequences of charge density fluctuations (CDFs), I end with a presentation of my current research activity on CDWs and the related two-dimensional charge density fluctuations (2D-CDFs). A scenario follows of the physics of cuprates, which includes the solution of the decades-long problem of the strange metal (SM) state.
Collapse
|
28
|
Zhou KJ, Matsuyama S, Strocov VN. hv 2-concept breaks the photon-count limit of RIXS instrumentation. J Synchrotron Radiat 2020; 27:1235-1239. [PMID: 32876598 PMCID: PMC7467335 DOI: 10.1107/s1600577520008607] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/31/2020] [Accepted: 06/26/2020] [Indexed: 06/11/2023]
Abstract
Upon progressive refinement of energy resolution, the conventional resonant inelastic X-ray scattering (RIXS) instrumentation reaches the limit where the bandwidth of incident photons becomes insufficient to deliver an acceptable photon-count rate. Here it is shown that RIXS spectra as a function of energy loss are essentially invariant to their integration over incident energies within the core-hole lifetime. This fact permits RIXS instrumentation based on the hv2-concept to utilize incident synchrotron radiation over the whole core-hole lifetime window without any compromise on the much finer energy-loss resolution, thereby breaking the photon-count limit.
Collapse
Affiliation(s)
- Ke-Jin Zhou
- Diamond Light Source, Harwell Campus, Didcot OX11 0DE, United Kingdom
| | - Satoshi Matsuyama
- Department of Precision Science and Technology, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka, Japan
| | | |
Collapse
|
29
|
Peng YY, Husain AA, Mitrano M, Sun SXL, Johnson TA, Zakrzewski AV, MacDougall GJ, Barbour A, Jarrige I, Bisogni V, Abbamonte P. Enhanced Electron-Phonon Coupling for Charge-Density-Wave Formation in La_{1.8-x}Eu_{0.2}Sr_{x}CuO_{4+δ}. Phys Rev Lett 2020; 125:097002. [PMID: 32915627 DOI: 10.1103/physrevlett.125.097002] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2019] [Revised: 03/04/2020] [Accepted: 07/30/2020] [Indexed: 06/11/2023]
Abstract
Charge density wave (CDW) correlations are prevalent in all copper-oxide superconductors. While CDWs in conventional metals are driven by coupling between lattice vibrations and electrons, the role of the electron-phonon coupling (EPC) in cuprate CDWs is strongly debated. Using Cu L_{3} edge resonant inelastic x-ray scattering, we study the CDW and Cu-O bond-stretching phonons in the stripe-ordered cuprate La_{1.8-x}Eu_{0.2}Sr_{x}CuO_{4+δ}. We investigate the interplay between charge order and EPC as a function of doping and temperature and find that the EPC is enhanced in a narrow momentum region around the CDW ordering vector. By detuning the incident photon energy from the absorption resonance, we extract an EPC matrix element at the CDW ordering vector of M≃0.36 eV, which decreases to M≃0.30 eV at high temperature in the absence of the CDW. Our results suggest a feedback mechanism in which the CDW enhances the EPC which, in turn, further stabilizes the CDW.
Collapse
Affiliation(s)
- Y Y Peng
- Department of Physics and Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - A A Husain
- Department of Physics and Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
| | - M Mitrano
- Department of Physics and Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - S X-L Sun
- Department of Physics and Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
| | - T A Johnson
- Department of Physics and Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
| | - A V Zakrzewski
- Department of Physics and Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
| | - G J MacDougall
- Department of Physics and Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
| | - A Barbour
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - I Jarrige
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - V Bisogni
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - P Abbamonte
- Department of Physics and Materials Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
| |
Collapse
|
30
|
Li J, Nag A, Pelliciari J, Robarts H, Walters A, Garcia-Fernandez M, Eisaki H, Song D, Ding H, Johnston S, Comin R, Zhou KJ. Multiorbital charge-density wave excitations and concomitant phonon anomalies in Bi 2Sr 2LaCuO 6+δ. Proc Natl Acad Sci U S A 2020; 117:16219-25. [PMID: 32586955 DOI: 10.1073/pnas.2001755117] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Charge-density waves (CDWs) are a ubiquitous form of electron density modulation in cuprate superconductors. Unveiling the nature of quasistatic CDWs and their dynamical excitations is crucial for understanding their origin––similar to the study of antiferromagnetism in cuprates. However, dynamical CDW excitations remain largely unexplored due to the limited availability of suitable experimental probes. Here, using resonant inelastic X-ray scattering, we observe dynamical CDW excitations in Bi2Sr2LaCuO6+δ (Bi2201) superconductors through its interference with the lattice. The distinct anomalies of the bond-buckling and the bond-stretching phonons allow us to draw a clear picture of funnel-shaped dynamical CDW excitations in Bi2201. Our results of the interplay between CDWs and the phonon anomalies shed light on the nature of CDWs in cuprates. Charge-density waves (CDWs) are ubiquitous in underdoped cuprate superconductors. As a modulation of the valence electron density, CDWs in hole-doped cuprates possess both Cu-3d and O-2p orbital character owing to the strong hybridization of these orbitals near the Fermi level. Here, we investigate underdoped Bi2Sr1.4La0.6CuO6+δ using resonant inelastic X-ray scattering (RIXS) and find that a short-range CDW exists at both Cu and O sublattices in the copper-oxide (CuO2) planes with a comparable periodicity and correlation length. Furthermore, we uncover bond-stretching and bond-buckling phonon anomalies concomitant to the CDWs. Comparing to slightly overdoped Bi2Sr1.8La0.2CuO6+δ, where neither CDWs nor phonon anomalies appear, we highlight that a sharp intensity anomaly is induced in the proximity of the CDW wavevector (QCDW) for the bond-buckling phonon, in concert with the diffused intensity enhancement of the bond-stretching phonon at wavevectors much greater than QCDW. Our results provide a comprehensive picture of the quasistatic CDWs, their dispersive excitations, and associated electron-phonon anomalies, which are key for understanding the competing electronic instabilities in cuprates.
Collapse
|
31
|
Frano A, Blanco-Canosa S, Keimer B, Birgeneau RJ. Charge ordering in superconducting copper oxides. J Phys Condens Matter 2020; 32:374005. [PMID: 31829986 DOI: 10.1088/1361-648x/ab6140] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2019] [Accepted: 12/12/2019] [Indexed: 06/10/2023]
Abstract
Charge order has recently been identified as a leading competitor of high-temperature superconductivity in moderately doped cuprates. We provide a survey of universal and materials-specific aspects of this phenomenon, with emphasis on results obtained by scattering methods. In particular, we discuss the structure, periodicity, and stability range of the charge-ordered state, its response to various external perturbations, the influence of disorder, the coexistence and competition with superconductivity, as well as collective charge dynamics. In the context of this journal issue which honors Roger Cowley's legacy, we also discuss the connection of charge ordering with lattice vibrations and the central-peak phenomenon. We end the review with an outlook on research opportunities offered by new synthesis methods and experimental platforms, including cuprate thin films and superlattices.
Collapse
Affiliation(s)
- Alex Frano
- Department of Physics, University of California, San Diego, CA 92093, United States of America
| | - Santiago Blanco-Canosa
- Donostia International Physics Center, DIPC, 20018 Donostia-San Sebastian, Basque Country, Spain
- IKERBASQUE, Basque Foundation for Science, 48013 Bilbao, Basque Country, Spain
| | - Bernhard Keimer
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
| | - Robert J Birgeneau
- Department of Physics, University of California, Berkeley, CA 94720, United States of America
- Department of Materials Science and Engineering, University of California Berkeley, Berkeley, CA 94720, United States of America
| |
Collapse
|
32
|
Lin JQ, Miao H, Mazzone DG, Gu GD, Nag A, Walters AC, García-Fernández M, Barbour A, Pelliciari J, Jarrige I, Oda M, Kurosawa K, Momono N, Zhou KJ, Bisogni V, Liu X, Dean MPM. Strongly Correlated Charge Density Wave in La_{2-x}Sr_{x}CuO_{4} Evidenced by Doping-Dependent Phonon Anomaly. Phys Rev Lett 2020; 124:207005. [PMID: 32501068 DOI: 10.1103/physrevlett.124.207005] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2020] [Accepted: 03/25/2020] [Indexed: 06/11/2023]
Abstract
The discovery of charge-density-wave-related effects in the resonant inelastic x-ray scattering spectra of cuprates holds the tantalizing promise of clarifying the interactions that stabilize the electronic order. Here, we report a comprehensive resonant inelastic x-ray scattering study of La_{2-x}Sr_{x}CuO_{4} finding that charge-density wave effects persist up to a remarkably high doping level of x=0.21 before disappearing at x=0.25. The inelastic excitation spectra remain essentially unchanged with doping despite crossing a topological transition in the Fermi surface. This indicates that the spectra contain little or no direct coupling to electronic excitations near the Fermi surface, rather they are dominated by the resonant cross section for phonons and charge-density-wave-induced phonon softening. We interpret our results in terms of a charge-density wave that is generated by strong correlations and a phonon response that is driven by the charge-density-wave-induced modification of the lattice.
Collapse
Affiliation(s)
- J Q Lin
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - H Miao
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - D G Mazzone
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - G D Gu
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - A Nag
- Diamond Light Source, Harwell Campus, Didcot, Oxfordshire OX11 0DE, United Kingdom
| | - A C Walters
- Diamond Light Source, Harwell Campus, Didcot, Oxfordshire OX11 0DE, United Kingdom
| | - M García-Fernández
- Diamond Light Source, Harwell Campus, Didcot, Oxfordshire OX11 0DE, United Kingdom
| | - A Barbour
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - J Pelliciari
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - I Jarrige
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - M Oda
- Department of Physics, Hokkaido University, Sapporo 060-0810, Japan
| | - K Kurosawa
- Department of Physics, Hokkaido University, Sapporo 060-0810, Japan
| | - N Momono
- Department of Sciences and Informatics, Muroran Institute of Technology, Muroran 050-8585, Japan
| | - Ke-Jin Zhou
- Diamond Light Source, Harwell Campus, Didcot, Oxfordshire OX11 0DE, United Kingdom
| | - V Bisogni
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - X Liu
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
| | - M P M Dean
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
| |
Collapse
|
33
|
Wang Q, Horio M, von Arx K, Shen Y, John Mukkattukavil D, Sassa Y, Ivashko O, Matt CE, Pyon S, Takayama T, Takagi H, Kurosawa T, Momono N, Oda M, Adachi T, Haidar SM, Koike Y, Tseng Y, Zhang W, Zhao J, Kummer K, Garcia-Fernandez M, Zhou KJ, Christensen NB, Rønnow HM, Schmitt T, Chang J. High-Temperature Charge-Stripe Correlations in La_{1.675}Eu_{0.2}Sr_{0.125}CuO_{4}. Phys Rev Lett 2020; 124:187002. [PMID: 32441965 DOI: 10.1103/physrevlett.124.187002] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2019] [Revised: 03/02/2020] [Accepted: 04/14/2020] [Indexed: 06/11/2023]
Abstract
We use resonant inelastic x-ray scattering to investigate charge-stripe correlations in La_{1.675}Eu_{0.2}Sr_{0.125}CuO_{4}. By differentiating elastic from inelastic scattering, it is demonstrated that charge-stripe correlations precede both the structural low-temperature tetragonal phase and the transport-defined pseudogap onset. The scattering peak amplitude from charge stripes decays approximately as T^{-2} towards our detection limit. The in-plane integrated intensity, however, remains roughly temperature independent. Therefore, although the incommensurability shows a remarkably large increase at high temperature, our results are interpreted via a single scattering constituent. In fact, direct comparison to other stripe-ordered compounds (La_{1.875}Ba_{0.125}CuO_{4}, La_{1.475}Nd_{0.4}Sr_{0.125}CuO_{4}, and La_{1.875}Sr_{0.125}CuO_{4}) suggests a roughly constant integrated scattering intensity across all these compounds. Our results therefore provide a unifying picture for the charge-stripe ordering in La-based cuprates. As charge correlations in La_{1.675}Eu_{0.2}Sr_{0.125}CuO_{4} extend beyond the low-temperature tetragonal and pseudogap phase, their emergence heralds a spontaneous symmetry breaking in this compound.
Collapse
Affiliation(s)
- Qisi Wang
- Physik-Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - M Horio
- Physik-Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - K von Arx
- Physik-Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - Y Shen
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
| | - D John Mukkattukavil
- Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20 Uppsala, Sweden
| | - Y Sassa
- Department of Physics, Chalmers University of Technology, SE-412 96 Göteborg, Sweden
| | - O Ivashko
- Physik-Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - C E Matt
- Physik-Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
- Swiss Light Source, Photon Science Division, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
| | - S Pyon
- Department of Advanced Materials, University of Tokyo, Kashiwa 277-8561, Japan
| | - T Takayama
- Department of Advanced Materials, University of Tokyo, Kashiwa 277-8561, Japan
| | - H Takagi
- Department of Advanced Materials, University of Tokyo, Kashiwa 277-8561, Japan
| | - T Kurosawa
- Department of Physics, Hokkaido University, Sapporo 060-0810, Japan
| | - N Momono
- Department of Physics, Hokkaido University, Sapporo 060-0810, Japan
- Department of Applied Sciences, Muroran Institute of Technology, Muroran 050-8585, Japan
| | - M Oda
- Department of Physics, Hokkaido University, Sapporo 060-0810, Japan
| | - T Adachi
- Department of Engineering and Applied Sciences, Sophia University, Tokyo 102-8554, Japan
| | - S M Haidar
- Department of Applied Physics, Tohoku University, Sendai 980-8579, Japan
| | - Y Koike
- Department of Applied Physics, Tohoku University, Sendai 980-8579, Japan
| | - Y Tseng
- Swiss Light Source, Photon Science Division, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
| | - W Zhang
- Swiss Light Source, Photon Science Division, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
| | - J Zhao
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China
| | - K Kummer
- European Synchrotron Radiation Facility, 71 Avenue des Martyrs, 38043 Grenoble, France
| | - M Garcia-Fernandez
- Diamond Light Source, Harwell Campus, Didcot, Oxfordshire OX11 0DE, United Kingdom
| | - Ke-Jin Zhou
- Diamond Light Source, Harwell Campus, Didcot, Oxfordshire OX11 0DE, United Kingdom
| | - N B Christensen
- Department of Physics, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
| | - H M Rønnow
- Institute of Physics, École Polytechnique Fedérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - T Schmitt
- Swiss Light Source, Photon Science Division, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
| | - J Chang
- Physik-Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| |
Collapse
|
34
|
Chu H, Kim MJ, Katsumi K, Kovalev S, Dawson RD, Schwarz L, Yoshikawa N, Kim G, Putzky D, Li ZZ, Raffy H, Germanskiy S, Deinert JC, Awari N, Ilyakov I, Green B, Chen M, Bawatna M, Cristiani G, Logvenov G, Gallais Y, Boris AV, Keimer B, Schnyder AP, Manske D, Gensch M, Wang Z, Shimano R, Kaiser S. Phase-resolved Higgs response in superconducting cuprates. Nat Commun 2020; 11:1793. [PMID: 32286291 PMCID: PMC7156672 DOI: 10.1038/s41467-020-15613-1] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2019] [Accepted: 03/02/2020] [Indexed: 11/29/2022] Open
Abstract
In high-energy physics, the Higgs field couples to gauge bosons and fermions and gives mass to their elementary excitations. Experimentally, such couplings can be inferred from the decay product of the Higgs boson, i.e., the scalar (amplitude) excitation of the Higgs field. In superconductors, Cooper pairs bear a close analogy to the Higgs field. Interaction between the Cooper pairs and other degrees of freedom provides dissipation channels for the amplitude mode, which may reveal important information about the microscopic pairing mechanism. To this end, we investigate the Higgs (amplitude) mode of several cuprate thin films using phase-resolved terahertz third harmonic generation (THG). In addition to the heavily damped Higgs mode itself, we observe a universal jump in the phase of the driven Higgs oscillation as well as a non-vanishing THG above Tc. These findings indicate coupling of the Higgs mode to other collective modes and potentially a nonzero pairing amplitude above Tc. Interaction between Cooper pairs and other collective excitations may reveal important information about the pairing mechanism. Here, the authors observe a universal jump in the phase of the driven Higgs oscillations in cuprate thin films, indicating the presence of a coupled collective mode, as well as a nonvanishing Higgs-like response at high temperatures, suggesting a potential nonzero pairing amplitude above Tc.
Collapse
Affiliation(s)
- Hao Chu
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569, Stuttgart, Germany.,4th Physics Institute, University of Stuttgart, 70569, Stuttgart, Germany.,Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, BC, V6T 1Z4, Canada
| | - Min-Jae Kim
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569, Stuttgart, Germany.,4th Physics Institute, University of Stuttgart, 70569, Stuttgart, Germany
| | - Kota Katsumi
- Department of Physics, University of Tokyo, Hongo, Tokyo, 113-0033, Japan
| | - Sergey Kovalev
- Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstr. 400, 01328, Dresden, Germany
| | - Robert David Dawson
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569, Stuttgart, Germany
| | - Lukas Schwarz
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569, Stuttgart, Germany
| | - Naotaka Yoshikawa
- Department of Physics, University of Tokyo, Hongo, Tokyo, 113-0033, Japan
| | - Gideok Kim
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569, Stuttgart, Germany
| | - Daniel Putzky
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569, Stuttgart, Germany
| | - Zhi Zhong Li
- Laboratoire de Physique des Solides (CNRS UMR 8502), Bâtiment 510, Université Paris-Saclay, 91405, Orsay, France
| | - Hélène Raffy
- Laboratoire de Physique des Solides (CNRS UMR 8502), Bâtiment 510, Université Paris-Saclay, 91405, Orsay, France
| | - Semyon Germanskiy
- Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstr. 400, 01328, Dresden, Germany
| | - Jan-Christoph Deinert
- Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstr. 400, 01328, Dresden, Germany
| | - Nilesh Awari
- Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstr. 400, 01328, Dresden, Germany.,University of Groningen, 9747 AG, Groningen, Netherlands
| | - Igor Ilyakov
- Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstr. 400, 01328, Dresden, Germany
| | - Bertram Green
- Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstr. 400, 01328, Dresden, Germany
| | - Min Chen
- Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstr. 400, 01328, Dresden, Germany.,Technische Universität Berlin, Institut für Optik und Atomare Physik, Strasse des 17. Juni 135, 10623, Berlin, Germany
| | - Mohammed Bawatna
- Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstr. 400, 01328, Dresden, Germany
| | - Georg Cristiani
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569, Stuttgart, Germany
| | - Gennady Logvenov
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569, Stuttgart, Germany
| | - Yann Gallais
- Laboratoire Matériaux et Phénomènes Quantiques (UMR 7162 CNRS), Université de Paris, Bâtiment Condorcet, 75205, Paris Cedex 13, France
| | - Alexander V Boris
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569, Stuttgart, Germany
| | - Bernhard Keimer
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569, Stuttgart, Germany
| | - Andreas P Schnyder
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569, Stuttgart, Germany
| | - Dirk Manske
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569, Stuttgart, Germany
| | - Michael Gensch
- Technische Universität Berlin, Institut für Optik und Atomare Physik, Strasse des 17. Juni 135, 10623, Berlin, Germany.,German Aerospace Center (DLR), Institute of Optical Sensor Systems, Rutherfordstrasse 2, 12489, Berlin, Germany
| | - Zhe Wang
- Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstr. 400, 01328, Dresden, Germany. .,Institute of Physics II, University of Cologne, 50937, Cologne, Germany.
| | - Ryo Shimano
- Department of Physics, University of Tokyo, Hongo, Tokyo, 113-0033, Japan. .,Cryogenic Research Center, University of Tokyo, Hongo, Tokyo, 113-0032, Japan.
| | - Stefan Kaiser
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569, Stuttgart, Germany. .,4th Physics Institute, University of Stuttgart, 70569, Stuttgart, Germany.
| |
Collapse
|
35
|
Arpaia R, Caprara S, Fumagalli R, De Vecchi G, Peng YY, Andersson E, Betto D, De Luca GM, Brookes NB, Lombardi F, Salluzzo M, Braicovich L, Di Castro C, Grilli M, Ghiringhelli G. Dynamical charge density fluctuations pervading the phase diagram of a Cu-based high- T c superconductor. Science 2020; 365:906-910. [PMID: 31467219 DOI: 10.1126/science.aav1315] [Citation(s) in RCA: 78] [Impact Index Per Article: 19.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2018] [Accepted: 07/30/2019] [Indexed: 11/02/2022]
Abstract
Charge density modulations have been observed in all families of high-critical temperature (T c) superconducting cuprates. Although they are consistently found in the underdoped region of the phase diagram and at relatively low temperatures, it is still unclear to what extent they influence the unusual properties of these systems. Using resonant x-ray scattering, we carefully determined the temperature dependence of charge density modulations in YBa2Cu3O7-δ and Nd1+ x Ba2- x Cu3O7-δ for several doping levels. We isolated short-range dynamical charge density fluctuations in addition to the previously known quasi-critical charge density waves. They persist up to well above the pseudogap temperature T*, are characterized by energies of a few milli-electron volts, and pervade a large area of the phase diagram.
Collapse
Affiliation(s)
- R Arpaia
- Dipartimento di Fisica, Politecnico di Milano, I-20133 Milano, Italy. .,Quantum Device Physics Laboratory, Department of Microtechnology and Nanoscience, Chalmers University of Technology, SE-41296 Göteborg, Sweden
| | - S Caprara
- Dipartimento di Fisica, Università di Roma "La Sapienza," I-00185 Roma, Italy.,CNR-ISC, I-00185 Roma, Italy
| | - R Fumagalli
- Dipartimento di Fisica, Politecnico di Milano, I-20133 Milano, Italy
| | - G De Vecchi
- Dipartimento di Fisica, Politecnico di Milano, I-20133 Milano, Italy
| | - Y Y Peng
- Dipartimento di Fisica, Politecnico di Milano, I-20133 Milano, Italy
| | - E Andersson
- Quantum Device Physics Laboratory, Department of Microtechnology and Nanoscience, Chalmers University of Technology, SE-41296 Göteborg, Sweden
| | - D Betto
- ESRF, European Synchrotron, F-38043 Grenoble, France
| | - G M De Luca
- Dipartimento di Fisica "E. Pancini," Università di Napoli Federico II, Complesso Monte Sant'Angelo, I-80126 Napoli, Italy.,CNR-SPIN, Complesso Monte Sant'Angelo, I-80126 Napoli, Italy
| | - N B Brookes
- ESRF, European Synchrotron, F-38043 Grenoble, France
| | - F Lombardi
- Quantum Device Physics Laboratory, Department of Microtechnology and Nanoscience, Chalmers University of Technology, SE-41296 Göteborg, Sweden
| | - M Salluzzo
- CNR-SPIN, Complesso Monte Sant'Angelo, I-80126 Napoli, Italy
| | - L Braicovich
- Dipartimento di Fisica, Politecnico di Milano, I-20133 Milano, Italy.,ESRF, European Synchrotron, F-38043 Grenoble, France
| | - C Di Castro
- Dipartimento di Fisica, Università di Roma "La Sapienza," I-00185 Roma, Italy.,CNR-ISC, I-00185 Roma, Italy
| | - M Grilli
- Dipartimento di Fisica, Università di Roma "La Sapienza," I-00185 Roma, Italy.,CNR-ISC, I-00185 Roma, Italy
| | - G Ghiringhelli
- Dipartimento di Fisica, Politecnico di Milano, I-20133 Milano, Italy. .,CNR-SPIN, Dipartimento di Fisica, Politecnico di Milano, I-20133 Milano, Italy
| |
Collapse
|
36
|
Amoretti A, Areán D, Goutéraux B, Musso D. Universal Relaxation in a Holographic Metallic Density Wave Phase. Phys Rev Lett 2019; 123:211602. [PMID: 31809185 DOI: 10.1103/physrevlett.123.211602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2019] [Revised: 09/04/2019] [Indexed: 06/10/2023]
Abstract
In this Letter, we uncover a universal relaxation mechanism of pinned density waves, combining gauge-gravity duality and effective field theory techniques. Upon breaking translations spontaneously, new gapless collective modes emerge, the Nambu-Goldstone bosons of broken translations. When translations are also weakly broken (e.g., by disorder or lattice effects), these phonons are pinned with a mass m and damped at a rate Ω, which we explicitly compute. This contribution to Ω is distinct from that of topological defects. We show that Ω≃Gm^{2}Ξ, where G is the shear modulus and Ξ is related to a diffusivity of the purely spontaneous state. This result follows from the smallness of the bulk and shear moduli, as would be the case in a phase with fluctuating translational order. At low temperatures, the collective modes relax quickly into the heat current, so that late time transport is dominated by the thermal diffusivity. In this regime, the resistivity in our model is linear in temperature and the ac conductivity displays a significant rearranging of the degrees of freedom, as spectral weight is shifted from an off-axis, pinning peak to a Drude-like peak. These results could shed light on transport properties in cuprate high T_{c} superconductors, where quantum critical behavior and translational order occur over large parts of the phase diagram and transport shows qualitatively similar features.
Collapse
Affiliation(s)
- Andrea Amoretti
- Dipartimento di Fisica, Università di Genova, via Dodecaneso 33, I-16146 Genova, Italy and I.N.F.N.-Sezione di Genova and Physique Théorique et Mathématique and International Solvay Institutes Université Libre de Bruxelles, C.P. 231, 1050 Brussels, Belgium
| | - Daniel Areán
- Instituto de Física Teórica UAM/CSIC, Calle Nicolás Cabrera 13-15, Cantoblanco, 28049 Madrid, Spain
| | - Blaise Goutéraux
- CPHT, CNRS, Ecole polytechnique, IP Paris, F-91128 Palaiseau, France and Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden
| | - Daniele Musso
- Departamento de Física de Partículas, Universidade de Santiago de Compostela and Instituto Galego de Física de Altas Enerxías (IGFAE), Santiago de Compostela, 15705, Spain
| |
Collapse
|
37
|
Auvray N, Loret B, Benhabib S, Cazayous M, Zhong RD, Schneeloch J, Gu GD, Forget A, Colson D, Paul I, Sacuto A, Gallais Y. Nematic fluctuations in the cuprate superconductor Bi 2Sr 2CaCu 2O 8+δ. Nat Commun 2019; 10:5209. [PMID: 31729372 PMCID: PMC6858346 DOI: 10.1038/s41467-019-12940-w] [Citation(s) in RCA: 30] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2019] [Accepted: 10/11/2019] [Indexed: 11/25/2022] Open
Abstract
Establishing the presence and the nature of a quantum critical point in their phase diagram is a central enigma of the high-temperature superconducting cuprates. It could explain their pseudogap and strange metal phases, and ultimately their high superconducting temperatures. Yet, while solid evidences exist in several unconventional superconductors of ubiquitous critical fluctuations associated to a quantum critical point, in the cuprates they remain undetected until now. Here using symmetry-resolved electronic Raman scattering in the cuprate \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta}$$\end{document}Bi2Sr2CaCu2O8+δ, we report the observation of enhanced electronic nematic fluctuations near the endpoint of the pseudogap phase. While our data hint at the possible presence of an incipient nematic quantum critical point, the doping dependence of the nematic fluctuations deviates significantly from a canonical quantum critical scenario. The observed nematic instability rather appears to be tied to the presence of a van Hove singularity in the band structure. Solid evidence of quantum fluctuations associated to a quantum critical point in cuprate superconductors remains elusive. Here, Auvray et al. report Raman scattering evidence of enhanced electronic nematic fluctuations near the endpoint of the pseudogap phase in Bi\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$${}_{2}$$\end{document}2Sr\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$${}_{2}$$\end{document}2CaCu\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$${}_{2}$$\end{document}2O\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$${}_{8+\delta }$$\end{document}8+δ.
Collapse
Affiliation(s)
- N Auvray
- Université de Paris, Matériaux et Phénomènes Quantiques, CNRS UMR 7162, F-75205, Paris, France
| | - B Loret
- Université de Paris, Matériaux et Phénomènes Quantiques, CNRS UMR 7162, F-75205, Paris, France
| | - S Benhabib
- Université de Paris, Matériaux et Phénomènes Quantiques, CNRS UMR 7162, F-75205, Paris, France
| | - M Cazayous
- Université de Paris, Matériaux et Phénomènes Quantiques, CNRS UMR 7162, F-75205, Paris, France
| | - R D Zhong
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY, 11973, USA
| | - J Schneeloch
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY, 11973, USA
| | - G D Gu
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY, 11973, USA
| | - A Forget
- Service de Physique de lÉtat Condensé, DRF/IRAMIS/SPEC (UMR 3680 CNRS), CEA Saclay, 91191, Gif-sur-Yvette cedex, France
| | - D Colson
- Service de Physique de lÉtat Condensé, DRF/IRAMIS/SPEC (UMR 3680 CNRS), CEA Saclay, 91191, Gif-sur-Yvette cedex, France
| | - I Paul
- Université de Paris, Matériaux et Phénomènes Quantiques, CNRS UMR 7162, F-75205, Paris, France
| | - A Sacuto
- Université de Paris, Matériaux et Phénomènes Quantiques, CNRS UMR 7162, F-75205, Paris, France
| | - Y Gallais
- Université de Paris, Matériaux et Phénomènes Quantiques, CNRS UMR 7162, F-75205, Paris, France.
| |
Collapse
|