1
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Kwon S, Jung H, Lee S, Cho GY, Kong K, Won C, Cheong SW, Yeom HW. Dual Higgs modes entangled into a soliton lattice in CuTe. Nat Commun 2024; 15:984. [PMID: 38302482 PMCID: PMC10834594 DOI: 10.1038/s41467-024-45354-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2023] [Accepted: 01/18/2024] [Indexed: 02/03/2024] Open
Abstract
Recently discovered Higgs particle is a key element in the standard model of elementary particles and its analogue in materials, massive Higgs mode, has elucidated intriguing collective phenomena in a wide range of materials with spontaneous symmetry breaking such as antiferromagnets, cold atoms, superconductors, superfluids, and charge density waves (CDW). As a straightforward extension beyond the standard model, multiple Higgs particles have been considered theoretically but not yet for Higgs modes. Here, we report the real-space observations, which suggest two Higgs modes coupled together with a soliton lattice in a solid. Our scanning tunneling microscopy reveals the 1D CDW state of an anisotropic transition metal monochalcogenide crystal CuTe is composed of two distinct but degenerate CDW structures by the layer inversion symmetry broken. More importantly, the amplitudes of each CDW structure oscillate in an out-of-phase fashion to result in a regular array of alternating domains with repeating phase-shift domain walls. This unusual finding is explained by the extra degeneracy in CDWs within the standard Landau theory of the free energy. The multiple and entangled Higgs modes demonstrate how novel collective modes can emerge in systems with distinct symmetries broken simultaneously.
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Affiliation(s)
- SeongJin Kwon
- Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science, Pohang, 37673, Korea
- Department of Physics, Pohang University of Science and Technology, Pohang, 37673, Korea
| | - Hyunjin Jung
- Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science, Pohang, 37673, Korea
- Department of Physics, Pohang University of Science and Technology, Pohang, 37673, Korea
| | - SangJin Lee
- Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science, Pohang, 37673, Korea
- Department of Physics, Pohang University of Science and Technology, Pohang, 37673, Korea
| | - Gil Young Cho
- Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science, Pohang, 37673, Korea
- Department of Physics, Pohang University of Science and Technology, Pohang, 37673, Korea
| | - KiJeong Kong
- Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science, Pohang, 37673, Korea
| | - ChoongJae Won
- Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science, Pohang, 37673, Korea
- Laboatory for Pohang Emergent Materials, POSTECH, Pohang, 37673, Korea
- MPPC-CPM, Max Planck POSTECH/Korea Research Initiative, Pohang, 37673, Korea
| | - Sang-Wook Cheong
- Laboatory for Pohang Emergent Materials, POSTECH, Pohang, 37673, Korea
- MPPC-CPM, Max Planck POSTECH/Korea Research Initiative, Pohang, 37673, Korea
- Rutgers Center for Emergent Materials and Department of Physics and Astronomy, Piscataway, NJ, 08854, USA
| | - Han Woong Yeom
- Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science, Pohang, 37673, Korea.
- Department of Physics, Pohang University of Science and Technology, Pohang, 37673, Korea.
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2
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Barresi A, Boulet A, Wlazłowski G, Magierski P. Generation and decay of Higgs mode in a strongly interacting Fermi gas. Sci Rep 2023; 13:11285. [PMID: 37438452 DOI: 10.1038/s41598-023-38176-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2023] [Accepted: 07/04/2023] [Indexed: 07/14/2023] Open
Abstract
We investigate the life cycle of the large amplitude Higgs mode in strongly interacting superfluid Fermi gas. Through numerical simulations with time-dependent density functional theory and the technique of the interaction quench, we verify the previous theoretical predictions on the mode's frequency. Next, we demonstrate that the mode is dynamically unstable against external perturbation and qualitatively examine the emerging state after the mode decays. The post-decay state is characterized by spatial fluctuations of the order parameter and density at scales comparable to the superfluid coherence length scale. We identify similarities with FFLO states, which become more prominent at higher dimensionalities and nonzero spin imbalances.
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Affiliation(s)
- Andrea Barresi
- Faculty of Physics, Warsaw University of Technology, Ulica Koszykowa 75, 00-662, Warsaw, Poland
| | - Antoine Boulet
- Faculty of Physics, Warsaw University of Technology, Ulica Koszykowa 75, 00-662, Warsaw, Poland
- ISMANS CESI, 44 Avenue Frédéric Auguste Bartholdi, 72000, Le Mans, France
| | - Gabriel Wlazłowski
- Faculty of Physics, Warsaw University of Technology, Ulica Koszykowa 75, 00-662, Warsaw, Poland.
- Department of Physics, University of Washington, Seattle, WA, 98195-1560, USA.
| | - Piotr Magierski
- Faculty of Physics, Warsaw University of Technology, Ulica Koszykowa 75, 00-662, Warsaw, Poland
- Department of Physics, University of Washington, Seattle, WA, 98195-1560, USA
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3
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Dong T, Zhang SJ, Wang NL. Recent Development of Ultrafast Optical Characterizations for Quantum Materials. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2022:e2110068. [PMID: 35853841 DOI: 10.1002/adma.202110068] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2021] [Revised: 06/09/2022] [Indexed: 06/15/2023]
Abstract
The advent of intense ultrashort optical pulses spanning a frequency range from terahertz to the visible has opened a new era in the experimental investigation and manipulation of quantum materials. The generation of strong optical field in an ultrashort time scale enables the steering of quantum materials nonadiabatically, inducing novel phenomenon or creating new phases which may not have an equilibrium counterpart. Ultrafast time-resolved optical techniques have provided rich information and played an important role in characterization of the nonequilibrium and nonlinear properties of solid systems. Here, some of the recent progress of ultrafast optical techniques and their applications to the detection and manipulation of physical properties in selected quantum materials are reviewed. Specifically, the new development in the detection of the Higgs mode and photoinduced nonequilibrium response in the study of superconductors by time-resolved terahertz spectroscopy are discussed.
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Affiliation(s)
- Tao Dong
- International Center for Quantum Materials, School of Physics, Peking University, Beijing, 100871, China
| | - Si-Jie Zhang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing, 100871, China
| | - Nan-Lin Wang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing, 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing, 100871, China
- Beijing Academy of Quantum Information Sciences, Beijing, 100913, China
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4
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Yamamoto K, Nakagawa M, Tsuji N, Ueda M, Kawakami N. Collective Excitations and Nonequilibrium Phase Transition in Dissipative Fermionic Superfluids. PHYSICAL REVIEW LETTERS 2021; 127:055301. [PMID: 34397242 DOI: 10.1103/physrevlett.127.055301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2020] [Accepted: 06/17/2021] [Indexed: 06/13/2023]
Abstract
We predict a new mechanism to induce collective excitations and a nonequilibrium phase transition of fermionic superfluids via a sudden switch on of two-body loss, for which we extend the BCS theory to fully incorporate a change in particle number. We find that a sudden switch on of dissipation induces an amplitude oscillation of the superfluid order parameter accompanied by a chirped phase rotation as a consequence of particle loss. We demonstrate that when dissipation is introduced to one of the two superfluids coupled via a Josephson junction, it gives rise to a nonequilibrium dynamical phase transition characterized by the vanishing dc Josephson current. The dissipation-induced collective modes and nonequilibrium phase transition can be realized with ultracold fermionic atoms subject to inelastic collisions.
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Affiliation(s)
- Kazuki Yamamoto
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
| | - Masaya Nakagawa
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Tokyo 113-0033, Japan
| | - Naoto Tsuji
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Tokyo 113-0033, Japan
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
| | - Masahito Ueda
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Tokyo 113-0033, Japan
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
- Institute for Physics of Intelligence, University of Tokyo, 7-3-1 Hongo, Tokyo 113-0033, Japan
| | - Norio Kawakami
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
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5
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Vaswani C, Kang JH, Mootz M, Luo L, Yang X, Sundahl C, Cheng D, Huang C, Kim RHJ, Liu Z, Collantes YG, Hellstrom EE, Perakis IE, Eom CB, Wang J. Light quantum control of persisting Higgs modes in iron-based superconductors. Nat Commun 2021; 12:258. [PMID: 33431843 PMCID: PMC7801641 DOI: 10.1038/s41467-020-20350-6] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2020] [Accepted: 11/30/2020] [Indexed: 11/28/2022] Open
Abstract
The Higgs mechanism, i.e., spontaneous symmetry breaking of the quantum vacuum, is a cross-disciplinary principle, universal for understanding dark energy, antimatter and quantum materials, from superconductivity to magnetism. Unlike one-band superconductors (SCs), a conceptually distinct Higgs amplitude mode can arise in multi-band, unconventional superconductors via strong interband Coulomb interaction, but is yet to be accessed. Here we discover such hybrid Higgs mode and demonstrate its quantum control by light in iron-based high-temperature SCs. Using terahertz (THz) two-pulse coherent spectroscopy, we observe a tunable amplitude mode coherent oscillation of the complex order parameter from coupled lower and upper bands. The nonlinear dependence of the hybrid Higgs mode on the THz driving fields is distinct from any known SC results: we observe a large reversible modulation of resonance strength, yet with a persisting mode frequency. Together with quantum kinetic modeling of a hybrid Higgs mechanism, distinct from charge-density fluctuations and without invoking phonons or disorder, our result provides compelling evidence for a light-controlled coupling between the electron and hole amplitude modes assisted by strong interband quantum entanglement. Such light-control of Higgs hybridization can be extended to probe many-body entanglement and hidden symmetries in other complex systems. A collective excitation called Higgs mode may arise in multi-band superconductors via strong interband interaction, but it is yet to be accessed. Here, the authors observe a tunable coherent amplitude oscillation of the order parameter in Ba(Fe1−xCox)2As2, suggesting appearance and control of the Higgs mode by light tuning interband interaction.
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Affiliation(s)
- C Vaswani
- Department of Physics and Astronomy, Iowa State University, and Ames Laboratory, Ames, IA, 50011, USA
| | - J H Kang
- Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, WI, 53706, USA
| | - M Mootz
- Department of Physics, University of Alabama at Birmingham, Birmingham, AL, 35294-1170, USA
| | - L Luo
- Department of Physics and Astronomy, Iowa State University, and Ames Laboratory, Ames, IA, 50011, USA
| | - X Yang
- Department of Physics and Astronomy, Iowa State University, and Ames Laboratory, Ames, IA, 50011, USA
| | - C Sundahl
- Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, WI, 53706, USA
| | - D Cheng
- Department of Physics and Astronomy, Iowa State University, and Ames Laboratory, Ames, IA, 50011, USA
| | - C Huang
- Department of Physics and Astronomy, Iowa State University, and Ames Laboratory, Ames, IA, 50011, USA
| | - R H J Kim
- Department of Physics and Astronomy, Iowa State University, and Ames Laboratory, Ames, IA, 50011, USA
| | - Z Liu
- Department of Physics and Astronomy, Iowa State University, and Ames Laboratory, Ames, IA, 50011, USA
| | - Y G Collantes
- Applied Superconductivity Center, National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL, 32310, USA
| | - E E Hellstrom
- Applied Superconductivity Center, National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL, 32310, USA
| | - I E Perakis
- Department of Physics, University of Alabama at Birmingham, Birmingham, AL, 35294-1170, USA
| | - C B Eom
- Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, WI, 53706, USA
| | - J Wang
- Department of Physics and Astronomy, Iowa State University, and Ames Laboratory, Ames, IA, 50011, USA.
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6
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Vaswani C, Mootz M, Sundahl C, Mudiyanselage DH, Kang JH, Yang X, Cheng D, Huang C, Kim RHJ, Liu Z, Luo L, Perakis IE, Eom CB, Wang J. Terahertz Second-Harmonic Generation from Lightwave Acceleration of Symmetry-Breaking Nonlinear Supercurrents. PHYSICAL REVIEW LETTERS 2020; 124:207003. [PMID: 32501057 DOI: 10.1103/physrevlett.124.207003] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2019] [Revised: 03/29/2020] [Accepted: 04/23/2020] [Indexed: 06/11/2023]
Abstract
We report terahertz (THz) light-induced second harmonic generation, in superconductors with inversion symmetry that forbid even-order nonlinearities. The THz second harmonic emission vanishes above the superconductor critical temperature and arises from precession of twisted Anderson pseudospins at a multicycle, THz driving frequency that is not allowed by equilibrium symmetry. We explain the microscopic physics by a dynamical symmetry breaking principle at sub-THz-cycle by using quantum kinetic modeling of the interplay between strong THz-lightwave nonlinearity and pulse propagation. The resulting nonzero integrated pulse area inside the superconductor leads to light-induced nonlinear supercurrents due to subcycle Cooper pair acceleration, in contrast to dc-biased superconductors, which can be controlled by the band structure and THz driving field below the superconducting gap.
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Affiliation(s)
- C Vaswani
- Department of Physics and Astronomy and Ames Laboratory-U.S. DOE, Iowa State University, Ames, Iowa 50011, USA
| | - M Mootz
- Department of Physics, University of Alabama at Birmingham, Birmingham, Alabama 35294-1170, USA
| | - C Sundahl
- Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | - D H Mudiyanselage
- Department of Physics and Astronomy and Ames Laboratory-U.S. DOE, Iowa State University, Ames, Iowa 50011, USA
| | - J H Kang
- Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | - X Yang
- Department of Physics and Astronomy and Ames Laboratory-U.S. DOE, Iowa State University, Ames, Iowa 50011, USA
| | - D Cheng
- Department of Physics and Astronomy and Ames Laboratory-U.S. DOE, Iowa State University, Ames, Iowa 50011, USA
| | - C Huang
- Department of Physics and Astronomy and Ames Laboratory-U.S. DOE, Iowa State University, Ames, Iowa 50011, USA
| | - R H J Kim
- Department of Physics and Astronomy and Ames Laboratory-U.S. DOE, Iowa State University, Ames, Iowa 50011, USA
| | - Z Liu
- Department of Physics and Astronomy and Ames Laboratory-U.S. DOE, Iowa State University, Ames, Iowa 50011, USA
| | - L Luo
- Department of Physics and Astronomy and Ames Laboratory-U.S. DOE, Iowa State University, Ames, Iowa 50011, USA
| | - I E Perakis
- Department of Physics, University of Alabama at Birmingham, Birmingham, Alabama 35294-1170, USA
| | - C B Eom
- Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | - J Wang
- Department of Physics and Astronomy and Ames Laboratory-U.S. DOE, Iowa State University, Ames, Iowa 50011, USA
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7
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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] [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.
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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.
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8
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Classification and characterization of nonequilibrium Higgs modes in unconventional superconductors. Nat Commun 2020; 11:287. [PMID: 31941881 PMCID: PMC6962398 DOI: 10.1038/s41467-019-13763-5] [Citation(s) in RCA: 38] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2018] [Accepted: 11/26/2019] [Indexed: 11/17/2022] Open
Abstract
Recent findings of new Higgs modes in unconventional superconductors require a classification and characterization of the modes allowed by nontrivial gap symmetry. Here we develop a theory for a tailored nonequilibrium quantum quench to excite all possible oscillation symmetries of a superconducting condensate. We show that both a finite momentum transfer and quench symmetry allow for an identification of the resulting Higgs oscillations. These serve as a fingerprint for the ground state gap symmetry. We provide a classification scheme of these oscillations and the quench symmetry based on group theory for the underlying lattice point group. For characterization, analytic calculations as well as full scale numeric simulations of the transient optical response resulting from an excitation by a realistic laser pulse are performed. Our classification of Higgs oscillations allows us to distinguish between different symmetries of the superconducting condensate. The lately reported Higgs modes in unconventional superconductors require a classification and characterization allowed by nontrivial symmetry of the gap and the quench pulses. Here, the authors provide a classification scheme of Higgs oscillations with their excitation processes allowing them to distinguish between different symmetries of the superconducting condensate.
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9
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Nakamura S, Iida Y, Murotani Y, Matsunaga R, Terai H, Shimano R. Infrared Activation of the Higgs Mode by Supercurrent Injection in Superconducting NbN. PHYSICAL REVIEW LETTERS 2019; 122:257001. [PMID: 31347872 DOI: 10.1103/physrevlett.122.257001] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2018] [Revised: 02/07/2019] [Indexed: 06/10/2023]
Abstract
The Higgs mode in superconductors, i.e., the collective amplitude mode of the order parameter, does not associate with charge nor spin fluctuations, therefore it does not couple to the electromagnetic field in the linear response regime. Contrary to this common understanding, here, we demonstrate that if the dc supercurrent is introduced into the superconductor, the Higgs mode becomes infrared active and is directly observed in the linear optical conductivity measurement. We observed a sharp resonant peak at ω=2Δ in the optical conductivity spectrum of a thin-film NbN in the presence of dc supercurrent, showing a reasonable agreement with the recent theoretical prediction. The method as proven by this work opens a new pathway to study the Higgs mode in a wide variety of superconductors.
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Affiliation(s)
- Sachiko Nakamura
- Cryogenic Research Center, the University of Tokyo, Yayoi, Tokyo, 113-0032, Japan
| | - Yudai Iida
- Department of Physics, the University of Tokyo, Hongo, Tokyo, 113-0033, Japan
| | - Yuta Murotani
- Department of Physics, the University of Tokyo, Hongo, Tokyo, 113-0033, Japan
| | - Ryusuke Matsunaga
- The Institute for Solid State Physics, the University of Tokyo, Kashiwa, Chiba 277-8581, Japan
| | - Hirotaka Terai
- National Institute of Information and Communications Technology, 588-2 Iwaoka, Nishi-ku, Kobe 651-2492, Japan
| | - Ryo Shimano
- Cryogenic Research Center, the University of Tokyo, Yayoi, Tokyo, 113-0032, Japan
- Department of Physics, the University of Tokyo, Hongo, Tokyo, 113-0033, Japan
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10
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Li J, Strand HUR, Werner P, Eckstein M. Theory of photoinduced ultrafast switching to a spin-orbital ordered hidden phase. Nat Commun 2018; 9:4581. [PMID: 30389918 PMCID: PMC6214932 DOI: 10.1038/s41467-018-07051-x] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2018] [Accepted: 10/06/2018] [Indexed: 11/09/2022] Open
Abstract
Photo-induced hidden phases are often observed in materials with intertwined orders. Understanding the formation of these non-thermal phases is challenging and requires a resolution of the cooperative interplay between different orders on the ultra-short timescale. In this work, we demonstrate that non-equilibrium photo-excitations can induce a state with spin-orbital orders entirely different from the equilibrium state in the three-quarter-filled two-band Hubbard model. We identify a general mechanism governing the transition to the hidden state, which relies on a non-thermal partial melting of the intertwined orders mediated by photoinduced charge excitations in the presence of strong spin-orbital exchange interactions. Our study theoretically confirms the crucial role played by orbital degrees of freedom in the light-induced dynamics of strongly correlated materials and it shows that the switching to hidden states can be controlled already on the fs timescale of the electron dynamics. Ultrafast excitation of materials can cause the formation of hidden phases that are not accessible in thermal equilibrium. Li et al. identify and investigate theoretically a hidden phase that can be accessed in systems with intertwined spin and orbital-ordering such as KCuF3.
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Affiliation(s)
- Jiajun Li
- Department of Physics, University Erlangen-Nürnberg, 91058, Erlangen, Germany.
| | - Hugo U R Strand
- Center for Computational Quantum Physics, Flatiron Institute, 162 Fifth Avenue, New York, NY, 10010, USA.,Department of Quantum Matter Physics, University of Geneva, 24 Quai Ernest-Ansermet, 1211, Geneva 4, Switzerland.,Department of Physics, University of Fribourg, 1700, Fribourg, Switzerland
| | - Philipp Werner
- Department of Physics, University of Fribourg, 1700, Fribourg, Switzerland
| | - Martin Eckstein
- Department of Physics, University Erlangen-Nürnberg, 91058, Erlangen, Germany
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Hage FS, Nicholls RJ, Yates JR, McCulloch DG, Lovejoy TC, Dellby N, Krivanek OL, Refson K, Ramasse QM. Nanoscale momentum-resolved vibrational spectroscopy. SCIENCE ADVANCES 2018; 4:eaar7495. [PMID: 29951584 PMCID: PMC6018998 DOI: 10.1126/sciadv.aar7495] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2017] [Accepted: 05/01/2018] [Indexed: 05/21/2023]
Abstract
Vibrational modes affect fundamental physical properties such as the conduction of sound and heat and can be sensitive to nano- and atomic-scale structure. Probing the momentum transfer dependence of vibrational modes provides a wealth of information about a materials system; however, experimental work has been limited to essentially bulk and averaged surface approaches or to small wave vectors. We demonstrate a combined experimental and theoretical methodology for nanoscale mapping of optical and acoustic phonons across the first Brillouin zone, in the electron microscope, probing a volume ~1010 to 1020 times smaller than that of comparable bulk and surface techniques. In combination with more conventional electron microscopy techniques, the presented methodology should allow for direct correlation of nanoscale vibrational mode dispersions with atomic-scale structure and chemistry.
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Affiliation(s)
- Fredrik S. Hage
- SuperSTEM Laboratory, SciTech Daresbury Campus, Keckwick Lane, Daresbury WA4 4AD, UK
- Corresponding author. (Q.M.R.); (F.S.H.)
| | - Rebecca J. Nicholls
- Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, UK
| | - Jonathan R. Yates
- Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, UK
| | - Dougal G. McCulloch
- Physics, School of Science, RMIT University, Melbourne, Victoria 3001, Australia
| | | | - Niklas Dellby
- Nion Company, 11511 NE 118th Street, Kirkland, WA 98034, USA
| | - Ondrej L. Krivanek
- Nion Company, 11511 NE 118th Street, Kirkland, WA 98034, USA
- Department of Physics, Arizona State University, Tempe, AZ 85287, USA
| | - Keith Refson
- STFC (Science & Technology Facilities Council) Rutherford Appleton Laboratory, Harwell Science and Innovation Campus, Didcot OX11 0QX, UK
- Department of Physics, Royal Holloway, University of London, Egham TW20 0EX, UK
| | - Quentin M. Ramasse
- SuperSTEM Laboratory, SciTech Daresbury Campus, Keckwick Lane, Daresbury WA4 4AD, UK
- School of Physics, University of Leeds, Leeds LS2 9JT, UK
- School of Chemical and Process Engineering, University of Leeds, Leeds LS2 9JT, UK
- Corresponding author. (Q.M.R.); (F.S.H.)
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12
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Katsumi K, Tsuji N, Hamada YI, Matsunaga R, Schneeloch J, Zhong RD, Gu GD, Aoki H, Gallais Y, Shimano R. Higgs Mode in the d-Wave Superconductor Bi_{2}Sr_{2}CaCu_{2}O_{8+x} Driven by an Intense Terahertz Pulse. PHYSICAL REVIEW LETTERS 2018; 120:117001. [PMID: 29601772 DOI: 10.1103/physrevlett.120.117001] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2017] [Revised: 02/05/2018] [Indexed: 06/08/2023]
Abstract
We investigate the terahertz (THz)-pulse-driven nonlinear response in the d-wave cuprate superconductor Bi_{2}Sr_{2}CaCu_{2}O_{8+x} (Bi2212) using a THz pump near-infrared probe scheme in the time domain. We observe an oscillatory behavior of the optical reflectivity that follows the THz electric field squared and is markedly enhanced below T_{c}. The corresponding third-order nonlinear effect exhibits both A_{1g} and B_{1g} symmetry components, which are decomposed from polarization-resolved measurements. A comparison with a BCS calculation of the nonlinear susceptibility indicates that the A_{1g} component is associated with the Higgs mode of the d-wave order parameter.
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Affiliation(s)
- Kota Katsumi
- Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan
| | - Naoto Tsuji
- RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan
| | - Yuki I Hamada
- Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan
| | - Ryusuke Matsunaga
- Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan
- JST, PRESTO, Kawaguchi 332-0012, Japan
| | | | | | - Genda D Gu
- Brookhaven National Lab, Upton, New York 11973, USA
| | - Hideo Aoki
- Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan
- Department of Physics, ETH Zürich, 8093 Zürich, Switzerland
- National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba 305-8568, Japan
| | - Yann Gallais
- Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan
- MPQ CNRS, Université Paris Diderot, Bâtiment Condorcet, 75205 Paris Cedex 13, France
- Cryogenic Research Center, The University of Tokyo, Tokyo 113-0032, Japan
| | - Ryo Shimano
- Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan
- Cryogenic Research Center, The University of Tokyo, Tokyo 113-0032, Japan
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Sentef MA, Tokuno A, Georges A, Kollath C. Theory of Laser-Controlled Competing Superconducting and Charge Orders. PHYSICAL REVIEW LETTERS 2017; 118:087002. [PMID: 28282212 DOI: 10.1103/physrevlett.118.087002] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2016] [Indexed: 06/06/2023]
Abstract
We investigate the nonequilibrium dynamics of competing coexisting superconducting (SC) and charge-density wave (CDW) orders in an attractive Hubbard model. A time-periodic laser field A[over →](t) lifts the SC-CDW degeneracy, since the CDW couples linearly to the field (A[over →]), whereas SC couples in second order (A[over →]^{2}) due to gauge invariance. This leads to a striking resonance: When the photon energy is red detuned compared to the equilibrium single-particle energy gap, CDW is enhanced and SC is suppressed, while this behavior is reversed for blue detuning. Both orders oscillate with an emergent slow frequency, which is controlled by the small amplitude of a third induced order, namely η pairing, given by the commutator of the two primary orders. The induced η pairing is shown to control the enhancement and suppression of the dominant orders. Finally, we demonstrate that light-induced superconductivity is possible starting from a predominantly CDW initial state.
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Affiliation(s)
- M A Sentef
- Max Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, 22761 Hamburg, Germany
| | - A Tokuno
- Centre de Physique Théorique, École Polytechnique, CNRS, 91128 Palaiseau Cedex, France
- Collège de France, 11 place Marcelin Berthelot, 75005 Paris, France
| | - A Georges
- Centre de Physique Théorique, École Polytechnique, CNRS, 91128 Palaiseau Cedex, France
- Collège de France, 11 place Marcelin Berthelot, 75005 Paris, France
- Department of Quantum Matter Physics, University of Geneva, 24 Quai Ernest-Ansermet, 1211 Geneva 4, Switzerland
| | - C Kollath
- HISKP, University of Bonn, Nussallee 14-16, D-53115 Bonn, Germany
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