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Herrera E, Guillamón I, Barrena V, Herrera WJ, Galvis JA, Yeyati AL, Rusz J, Oppeneer PM, Knebel G, Brison JP, Flouquet J, Aoki D, Suderow H. Quantum-well states at the surface of a heavy-fermion superconductor. Nature 2023; 616:465-469. [PMID: 36949204 PMCID: PMC10115632 DOI: 10.1038/s41586-023-05830-1] [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] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2022] [Accepted: 02/13/2023] [Indexed: 03/24/2023]
Abstract
Two-dimensional electronic states at surfaces are often observed in simple wide-band metals such as Cu or Ag (refs. 1-4). Confinement by closed geometries at the nanometre scale, such as surface terraces, leads to quantized energy levels formed from the surface band, in stark contrast to the continuous energy dependence of bulk electron bands2,5-10. Their energy-level separation is typically hundreds of meV (refs. 3,6,11). In a distinct class of materials, strong electronic correlations lead to so-called heavy fermions with a strongly reduced bandwidth and exotic bulk ground states12,13. Quantum-well states in two-dimensional heavy fermions (2DHFs) remain, however, notoriously difficult to observe because of their tiny energy separation. Here we use millikelvin scanning tunnelling microscopy (STM) to study atomically flat terraces on U-terminated surfaces of the heavy-fermion superconductor URu2Si2, which exhibits a mysterious hidden-order (HO) state below 17.5 K (ref. 14). We observe 2DHFs made of 5f electrons with an effective mass 17 times the free electron mass. The 2DHFs form quantized states separated by a fraction of a meV and their level width is set by the interaction with correlated bulk states. Edge states on steps between terraces appear along one of the two in-plane directions, suggesting electronic symmetry breaking at the surface. Our results propose a new route to realize quantum-well states in strongly correlated quantum materials and to explore how these connect to the electronic environment.
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Affiliation(s)
- Edwin Herrera
- Facultad de Ingeniería y Ciencias Básicas, Universidad Central, Bogotá, Colombia.
- Departamento de Física, Universidad Nacional de Colombia, Bogotá, Colombia.
- Laboratorio de Bajas Temperaturas y Altos Campos Magnéticos, Unidad Asociada UAM/CSIC, Departamento de Física de la Materia Condensada, Instituto Nicolás Cabrera and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid, Spain.
| | - Isabel Guillamón
- Laboratorio de Bajas Temperaturas y Altos Campos Magnéticos, Unidad Asociada UAM/CSIC, Departamento de Física de la Materia Condensada, Instituto Nicolás Cabrera and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid, Spain
| | - Víctor Barrena
- Laboratorio de Bajas Temperaturas y Altos Campos Magnéticos, Unidad Asociada UAM/CSIC, Departamento de Física de la Materia Condensada, Instituto Nicolás Cabrera and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid, Spain
| | - William J Herrera
- Departamento de Física, Universidad Nacional de Colombia, Bogotá, Colombia
| | - Jose Augusto Galvis
- Facultad de Ingeniería y Ciencias Básicas, Universidad Central, Bogotá, Colombia
- School of Engineering, Science and Technology, Universidad del Rosario, Bogotá, Colombia
| | - Alfredo Levy Yeyati
- Departamento de Física Teórica de la Materia Condensada, Instituto Nicolás Cabrera and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid, Spain
| | - Ján Rusz
- Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden
| | - Peter M Oppeneer
- Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden
| | - Georg Knebel
- University Grenoble Alpes, CEA, Grenoble-INP, IRIG, PHELIQS, Grenoble, France
| | - Jean Pascal Brison
- University Grenoble Alpes, CEA, Grenoble-INP, IRIG, PHELIQS, Grenoble, France
| | - Jacques Flouquet
- University Grenoble Alpes, CEA, Grenoble-INP, IRIG, PHELIQS, Grenoble, France
| | - Dai Aoki
- Institute for Materials Research (IMR), Tohoku University, Oarai, Japan
| | - Hermann Suderow
- Laboratorio de Bajas Temperaturas y Altos Campos Magnéticos, Unidad Asociada UAM/CSIC, Departamento de Física de la Materia Condensada, Instituto Nicolás Cabrera and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid, Spain.
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Mydosh JA, Oppeneer PM, Riseborough PS. Hidden order and beyond: an experimental-theoretical overview of the multifaceted behavior of URu 2Si 2. J Phys Condens Matter 2020; 32:143002. [PMID: 31801118 DOI: 10.1088/1361-648x/ab5eba] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
This topical review describes the multitude of unconventional behaviors in the hidden order, heavy fermion, antiferromagnetic and superconducting phases of the intermetallic compound URu2Si2 when tuned with pressure, magnetic field, and substitutions for all three elements. Such 'perturbations' result in a variety of new phases beyond the mysterious hidden order that are only now being slowly understood through a series of state-of-the-science experimentation, along with an array of novel theoretical approaches. Despite all these efforts spanning more than 30 years, hidden order (HO) remains puzzling and non-clarified, and the search continues in 2019 into a fourth decade for its final resolution. Here we attempt to update the present situation of URu2Si2 importing the latest experimental results and theoretical proposals. First, let us consider the pristine compound as a function of temperature and report the recent measurements and models relating to its heavy Fermi liquid crossover, its HO and superconductivity (SC). Recent experiments and theories are surmized that address four-fold symmetry breaking (or nematicity), Isingness and unconventional excitation modes. Second, we review the pressure dependence of URu2Si2 and its transformation to antiferromagnetic long-range order. Next we confront the dramatic high magnetic-field phases requiring fields above 40 T. And finally, we attempt to answer how does random substitutions of other 5f elements for U, and 3d, 4d, and 5d elements for Ru, and even P for Si affect and transform the HO. Commensurately, recent theoretical models are summarized and then related to the intriguing experimental behavior.
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Affiliation(s)
- J A Mydosh
- Institute Lorentz and Kamerlingh Onnes Laboratory, Leiden University, NL-2300 RA Leiden, The Netherlands
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Hattori T, Sakai H, Tokunaga Y, Kambe S, Matsuda TD, Haga Y. Evidence for Spin Singlet Pairing with Strong Uniaxial Anisotropy in URu_{2}Si_{2} Using Nuclear Magnetic Resonance. Phys Rev Lett 2018; 120:027001. [PMID: 29376726 DOI: 10.1103/physrevlett.120.027001] [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: 07/12/2017] [Indexed: 06/07/2023]
Abstract
In order to identify the spin contribution to superconducting pairing compatible with the so-called "hidden order", ^{29}Si nuclear magnetic resonance measurements have been performed using a high-quality single crystal of URu_{2}Si_{2}. A clear reduction of the ^{29}Si Knight shift in the superconducting state has been observed under a magnetic field applied along the crystalline c axis, corresponding to the magnetic easy axis. These results provide direct evidence for the formation of spin-singlet Cooper pairs. Consequently, results indicating a very tiny change of the in-plane Knight shift reported previously demonstrate extreme uniaxial anisotropy for the spin susceptibility in the hidden order state.
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Affiliation(s)
- T Hattori
- Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan
| | - H Sakai
- Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan
| | - Y Tokunaga
- Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan
| | - S Kambe
- Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan
| | - T D Matsuda
- Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan
| | - Y Haga
- Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan
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Abstract
Owing to a strong Coulomb repulsion, heavy electron superconductors mostly have anisotropic gap functions which have nodes for certain directions in the momentum space. Since the nodal structure is closely related to the pairing mechanism, its experimental determination is of primary importance. This article discusses the experimental methods of the gap determination by bulk heat capacity measurements in a rotating magnetic field. The basic idea is based on the fact that the quasiparticle density of states in the vortex state of nodal superconductors is field and direction dependent. We present our recent experimental results of the field-orientation dependence of the heat capacity in heavy fermion superconductors CeTIn5 (T = Co, Ir), UPt3, CeCu2Si2, and UBe13 and discuss their gap structures.
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Affiliation(s)
- Toshiro Sakakibara
- Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
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Abstract
Chiral superconductivity is a striking quantum phenomenon in which an unconventional superconductor spontaneously develops an angular momentum and lowers its free energy by eliminating nodes in the gap. It is a topologically non-trivial state and, as such, exhibits distinctive topological modes at surfaces and defects. In this paper we discuss the current theory and experimental results on chiral superconductors, focusing on two of the best-studied systems, Sr2RuO4, which is thought to be a chiral triplet p-wave superconductor, and UPt3, which has two low-temperature superconducting phases (in zero magnetic field), the lower of which is believed to be chiral triplet f-wave. Other systems that may exhibit chiral superconductivity are also discussed. Key signatures of chiral superconductivity are surface currents and chiral Majorana modes, Majorana states in vortex cores, and the possibility of half-flux quantum vortices in the case of triplet pairing. Experimental evidence for chiral superconductivity from μSR, NMR, strain, polar Kerr effect and Josephson tunneling experiments are discussed.
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Abstract
Topological superconductors have become a subject of intense research due to their potential use for technical applications in device fabrication and quantum information. Besides fully gapped superconductors, unconventional superconductors with point or line nodes in their order parameter can also exhibit nontrivial topological characteristics. This article reviews recent progress in the theoretical understanding of nodal topological superconductors, with a focus on Weyl and noncentrosymmetric superconductors and their protected surface states. Using selected examples, we review the bulk topological properties of these systems, study different types of topological surface states, and examine their unusual properties. Furthermore, we survey some candidate materials for topological superconductivity and discuss different experimental signatures of topological surface states.
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Affiliation(s)
- Andreas P Schnyder
- Max-Planck-Institut für Festkörperforschung, Heißenbergstrasse 1, D-70569 Stuttgart, Germany
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Aoki D, Bourdarot F, Hassinger E, Knebel G, Miyake A, Raymond S, Taufour V, Flouquet J. Field re-entrant hidden-order phase under pressure in URu2Si2. J Phys Condens Matter 2010; 22:164205. [PMID: 21386411 DOI: 10.1088/0953-8984/22/16/164205] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We succeeded in growing high quality single crystals of URu(2)Si(2) and performed thermal expansion measurements under pressure. Applying a magnetic field along the [001] direction in the tetragonal structure, the so-called hidden-order phase reappears after the suppression of the antiferromagnetic phase above the critical pressure P(x). We determined the pressure-temperature-field phase diagram for the paramagnetic, hidden-order and antiferromagnetic states for the [Formula: see text] direction. We also present the temperature dependence of the upper critical field H(c2) for [Formula: see text] and [100] determined by the AC specific heat measurements, corresponding to the bulk superconductivity in a high quality single crystal.
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Affiliation(s)
- D Aoki
- INAC/SPSMS, CEA-Grenoble, 17 rue des Martyrs, F-38054 Grenoble, France.
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An K, Sakakibara T, Settai R, Onuki Y, Hiragi M, Ichioka M, Machida K. Sign reversal of field-angle resolved heat capacity oscillations in a heavy Fermion superconductor CeCoIn5 and d{x{2}-y{2}} pairing symmetry. Phys Rev Lett 2010; 104:037002. [PMID: 20366675 DOI: 10.1103/physrevlett.104.037002] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2009] [Indexed: 05/29/2023]
Abstract
To identify the superconducting gap symmetry in CeCoIn5 (T{c}=2.3 K), we measured the angle-resolved specific heat (C{phi}) in a field rotated around the c axis down to a very low temperature, 0.05T{c}, and made detailed theoretical calculations. In a field of 1 T, a sign reversal of the fourfold angular oscillation in C{phi} was observed at T approximately 0.1T{c} upon entering a quasiclassical regime where the maximum of C{phi} corresponds to the antinodal direction, coinciding with the angle-resolved density of states (ADOS) calculation. The C{phi} behavior, which exhibits minima along the [110] directions, unambiguously allows us to conclude d{x{2}-y{2}} symmetry of this system. The ADOS-quasiclassical region is confined to a narrow T and H domain within T/T{c} approximately 0.1 and 1.5 T (0.13H{c2}).
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Affiliation(s)
- K An
- Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan
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Shishido H, Hashimoto K, Shibauchi T, Sasaki T, Oizumi H, Kobayashi N, Takamasu T, Takehana K, Imanaka Y, Matsuda TD, Haga Y, Onuki Y, Matsuda Y. Possible phase transition deep inside the hidden order phase of ultraclean URu2Si2. Phys Rev Lett 2009; 102:156403. [PMID: 19518659 DOI: 10.1103/physrevlett.102.156403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/24/2008] [Indexed: 05/27/2023]
Abstract
To elucidate the underlying nature of the hidden order (HO) state in heavy-fermion compound URu(2)Si(2), we measure electrical transport properties of ultraclean crystals in a high field, low temperature regime. Unlike previous studies, the present system with much less impurity scattering resolves a distinct anomaly of the Hall resistivity at H;{*} = 22.5 T, well below the destruction field of the HO phase = or approximately 36 T. In addition, a novel quantum oscillation appears above a magnetic field slightly below H;{*}. These results indicate an abrupt reconstruction of the Fermi surface, which implies a possible phase transition well within the HO phase caused by a band-dependent destruction of the HO parameter.
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Affiliation(s)
- H Shishido
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
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Elgazzar S, Rusz J, Amft M, Oppeneer PM, Mydosh JA. Hidden order in URu2Si2 originates from Fermi surface gapping induced by dynamic symmetry breaking. Nat Mater 2009; 8:337-341. [PMID: 19234447 DOI: 10.1038/nmat2395] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2008] [Accepted: 01/20/2009] [Indexed: 05/27/2023]
Abstract
Spontaneous, collective ordering of electronic degrees of freedom leads to second-order phase transitions that are characterized by an order parameter driving the transition. The notion of a 'hidden order' has recently been used for a variety of materials where a clear phase transition occurs without a known order parameter. The prototype example is the heavy-fermion compound URu(2)Si(2), where a mysterious hidden-order transition occurs at 17.5 K. For more than twenty years this system has been studied theoretically and experimentally without a firm grasp of the underlying physics. Here, we provide a microscopic explanation of the hidden order using density-functional theory calculations. We identify the Fermi surface 'hot spots' where degeneracy induces a Fermi surface instability and quantify how symmetry breaking lifts the degeneracy, causing a surprisingly large Fermi surface gapping. As the mechanism for the hidden order, we deduce spontaneous symmetry breaking through a dynamic mode of antiferromagnetic moment excitations.
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Affiliation(s)
- S Elgazzar
- Department of Physics and Materials Science, Uppsala University, Box 530, S-751 21 Uppsala, Sweden
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