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Pirie H, Mascot E, Matt CE, Liu Y, Chen P, Hamidian MH, Saha S, Wang X, Paglione J, Luke G, Goldhaber-Gordon D, Hirjibehedin CF, Davis JCS, Morr DK, Hoffman JE. Visualizing the atomic-scale origin of metallic behavior in Kondo insulators. Science 2023; 379:1214-1218. [PMID: 36952423 DOI: 10.1126/science.abq5375] [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] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/25/2023]
Abstract
A Kondo lattice is often electrically insulating at low temperatures. However, several recent experiments have detected signatures of bulk metallicity within this Kondo insulating phase. In this study, we visualized the real-space charge landscape within a Kondo lattice with atomic resolution using a scanning tunneling microscope. We discovered nanometer-scale puddles of metallic conduction electrons centered around uranium-site substitutions in the heavy-fermion compound uranium ruthenium silicide (URu2Si2) and around samarium-site defects in the topological Kondo insulator samarium hexaboride (SmB6). These defects disturbed the Kondo screening cloud, leaving behind a fingerprint of the metallic parent state. Our results suggest that the three-dimensional quantum oscillations measured in SmB6 arise from Kondo-lattice defects, although we cannot exclude other explanations. Our imaging technique could enable the development of atomic-scale charge sensors using heavy-fermion probes.
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Affiliation(s)
- Harris Pirie
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
- Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, UK
| | - Eric Mascot
- Department of Physics, University of Illinois at Chicago, Chicago, IL 60607, USA
| | - Christian E Matt
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Yu Liu
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Pengcheng Chen
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - M H Hamidian
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Shanta Saha
- Maryland Quantum Materials Center, Department of Physics, University of Maryland, College Park, MD 20742, USA
| | - Xiangfeng Wang
- Maryland Quantum Materials Center, Department of Physics, University of Maryland, College Park, MD 20742, USA
| | - Johnpierre Paglione
- Maryland Quantum Materials Center, Department of Physics, University of Maryland, College Park, MD 20742, USA
| | - Graeme Luke
- Department of Physics and Astronomy, McMaster University, Hamilton, ON L8S 4M1, Canada
| | - David Goldhaber-Gordon
- Department of Physics, Stanford University, Stanford, CA 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
| | - Cyrus F Hirjibehedin
- London Centre for Nanotechnology, University College London (UCL), London WC1H 0AH, UK
- Department of Physics and Astronomy, UCL, London WC1E 6BT, UK
- Department of Chemistry, UCL, London WC1H 0AJ, UK
| | - J C Séamus Davis
- Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, UK
- Department of Physics, University College Cork, Cork T12 R5C, Ireland
- Laboratory of Atomic and Solid State Physics, Department of Physics, Cornell University, Ithaca, NY 14850, USA
- Max Planck Institute for Chemical Physics of Solids, D-01187 Dresden, Germany
| | - Dirk K Morr
- Department of Physics, University of Illinois at Chicago, Chicago, IL 60607, USA
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Edkins SD, Kostin A, Fujita K, Mackenzie AP, Eisaki H, Uchida S, Sachdev S, Lawler MJ, Kim EA, Séamus Davis JC, Hamidian MH. Magnetic field-induced pair density wave state in the cuprate vortex halo. Science 2019; 364:976-980. [PMID: 31171694 DOI: 10.1126/science.aat1773] [Citation(s) in RCA: 33] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2018] [Accepted: 05/15/2019] [Indexed: 11/02/2022]
Abstract
High magnetic fields suppress cuprate superconductivity to reveal an unusual density wave (DW) state coexisting with unexplained quantum oscillations. Although routinely labeled a charge density wave (CDW), this DW state could actually be an electron-pair density wave (PDW). To search for evidence of a field-induced PDW, we visualized modulations in the density of electronic states N(r) within the halo surrounding Bi2Sr2CaCu2O8 vortex cores. We detected numerous phenomena predicted for a field-induced PDW, including two sets of particle-hole symmetric N(r) modulations with wave vectors QP and 2Q P , with the latter decaying twice as rapidly from the core as the former. These data imply that the primary field-induced state in underdoped superconducting cuprates is a PDW, with approximately eight CuO2 unit-cell periodicity and coexisting with its secondary CDWs.
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Affiliation(s)
- S D Edkins
- Laboratory of Atomic and Solid State Physics, Department of Physics, Cornell University, Ithaca, NY 14853, USA.,Department of Applied Physics, Stanford University, Stanford, CA 94305, USA.,School of Physics and Astronomy, University of St. Andrews, Fife KY16 9SS, Scotland
| | - A Kostin
- Laboratory of Atomic and Solid State Physics, Department of Physics, Cornell University, Ithaca, NY 14853, USA
| | - K Fujita
- Laboratory of Atomic and Solid State Physics, Department of Physics, Cornell University, Ithaca, NY 14853, USA.,Condensed Matter Physics Department, Brookhaven National Laboratory, Upton, NY, USA
| | - A P Mackenzie
- School of Physics and Astronomy, University of St. Andrews, Fife KY16 9SS, Scotland.,Max-Planck Institute for Chemical Physics of Solids, D-01187 Dresden, Germany
| | - H Eisaki
- Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568, Japan
| | - S Uchida
- Department of Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Subir Sachdev
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Michael J Lawler
- Laboratory of Atomic and Solid State Physics, Department of Physics, Cornell University, Ithaca, NY 14853, USA.,Department of Physics and Astronomy, Binghamton University, Binghamton, NY 13902, USA
| | - E-A Kim
- Laboratory of Atomic and Solid State Physics, Department of Physics, Cornell University, Ithaca, NY 14853, USA
| | - J C Séamus Davis
- Laboratory of Atomic and Solid State Physics, Department of Physics, Cornell University, Ithaca, NY 14853, USA. .,Condensed Matter Physics Department, Brookhaven National Laboratory, Upton, NY, USA.,Department of Physics, University College Cork, Cork T12R5C, Ireland.,Clarendon Laboratory, Oxford University, Oxford, OX1 3PU, UK
| | - M H Hamidian
- Laboratory of Atomic and Solid State Physics, Department of Physics, Cornell University, Ithaca, NY 14853, USA. .,Department of Physics, Harvard University, Cambridge, MA 02138, USA
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3
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Zhang Y, Mesaros A, Fujita K, Edkins SD, Hamidian MH, Ch'ng K, Eisaki H, Uchida S, Davis JCS, Khatami E, Kim EA. Machine learning in electronic-quantum-matter imaging experiments. Nature 2019; 570:484-490. [PMID: 31217587 DOI: 10.1038/s41586-019-1319-8] [Citation(s) in RCA: 43] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2018] [Accepted: 04/08/2019] [Indexed: 11/09/2022]
Abstract
For centuries, the scientific discovery process has been based on systematic human observation and analysis of natural phenomena1. Today, however, automated instrumentation and large-scale data acquisition are generating datasets of such large volume and complexity as to defy conventional scientific methodology. Radically different scientific approaches are needed, and machine learning (ML) shows great promise for research fields such as materials science2-5. Given the success of ML in the analysis of synthetic data representing electronic quantum matter (EQM)6-16, the next challenge is to apply this approach to experimental data-for example, to the arrays of complex electronic-structure images17 obtained from atomic-scale visualization of EQM. Here we report the development and training of a suite of artificial neural networks (ANNs) designed to recognize different types of order hidden in such EQM image arrays. These ANNs are used to analyse an archive of experimentally derived EQM image arrays from carrier-doped copper oxide Mott insulators. In these noisy and complex data, the ANNs discover the existence of a lattice-commensurate, four-unit-cell periodic, translational-symmetry-breaking EQM state. Further, the ANNs determine that this state is unidirectional, revealing a coincident nematic EQM state. Strong-coupling theories of electronic liquid crystals18,19 are consistent with these observations.
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Affiliation(s)
- Yi Zhang
- Department of Physics, Cornell University, Ithaca, NY, USA
| | - A Mesaros
- Department of Physics, Cornell University, Ithaca, NY, USA.,Laboratoire de Physique des Solides, Université Paris-Sud, CNRS, Orsay, France
| | - K Fujita
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY, USA
| | - S D Edkins
- Department of Physics, Cornell University, Ithaca, NY, USA.,Department of Applied Physics, Stanford University, Stanford, CA, USA
| | - M H Hamidian
- Department of Physics, Cornell University, Ithaca, NY, USA.,Department of Physics, Harvard University, Cambridge, MA, USA
| | - K Ch'ng
- Department of Physics and Astronomy, San Jose State University, San Jose, CA, USA
| | - H Eisaki
- National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan
| | - S Uchida
- National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan.,Department of Physics, University of Tokyo, Tokyo, Japan
| | - J C Séamus Davis
- Department of Physics, Cornell University, Ithaca, NY, USA.,Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY, USA.,Department of Physics, University College Cork, Cork, Ireland.,Clarendon Laboratory, University of Oxford, Oxford, UK
| | - Ehsan Khatami
- Department of Physics and Astronomy, San Jose State University, San Jose, CA, USA
| | - Eun-Ah Kim
- Department of Physics, Cornell University, Ithaca, NY, USA.
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4
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Hamidian MH, Edkins SD, Joo SH, Kostin A, Eisaki H, Uchida S, Lawler MJ, Kim EA, Mackenzie AP, Fujita K, Lee J, Davis JCS. Detection of a Cooper-pair density wave in Bi2Sr2CaCu2O8+x. Nature 2016; 532:343-7. [PMID: 27074504 DOI: 10.1038/nature17411] [Citation(s) in RCA: 169] [Impact Index Per Article: 21.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2015] [Accepted: 02/08/2016] [Indexed: 11/09/2022]
Abstract
The quantum condensate of Cooper pairs forming a superconductor was originally conceived as being translationally invariant. In theory, however, pairs can exist with finite momentum Q, thus generating a state with a spatially modulated Cooper-pair density. Such a state has been created in ultracold (6)Li gas but never observed directly in any superconductor. It is now widely hypothesized that the pseudogap phase of the copper oxide superconductors contains such a 'pair density wave' state. Here we report the use of nanometre-resolution scanned Josephson tunnelling microscopy to image Cooper pair tunnelling from a d-wave superconducting microscope tip to the condensate of the superconductor Bi2Sr2CaCu2O8+x. We demonstrate condensate visualization capabilities directly by using the Cooper-pair density variations surrounding zinc impurity atoms and at the Bi2Sr2CaCu2O8+x crystal supermodulation. Then, by using Fourier analysis of scanned Josephson tunnelling images, we discover the direct signature of a Cooper-pair density modulation at wavevectors QP ≈ (0.25, 0)2π/a0 and (0, 0.25)2π/a0 in Bi2Sr2CaCu2O8+x. The amplitude of these modulations is about five per cent of the background condensate density and their form factor exhibits primarily s or s' symmetry. This phenomenology is consistent with Ginzburg-Landau theory when a charge density wave with d-symmetry form factor and wavevector QC = QP coexists with a d-symmetry superconductor; it is also predicted by several contemporary microscopic theories for the pseudogap phase.
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Affiliation(s)
- M H Hamidian
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - S D Edkins
- Laboratory of Atomic and Solid State Physics, Department of Physics, Cornell University, Ithaca, New York 14853, USA.,School of Physics and Astronomy, University of St Andrews, Fife KY16 9SS, UK
| | - Sang Hyun Joo
- Institute of Applied Physics, Department of Physics and Astronomy, Seoul National University, Seoul 151-747, South Korea.,Center for Correlated Electron Systems, Institute of Basic Science, Seoul 151-742, South Korea
| | - A Kostin
- Laboratory of Atomic and Solid State Physics, Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - H Eisaki
- Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568, Japan
| | - S Uchida
- Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568, Japan.,Department of Physics, University of Tokyo, Bunkyo, Tokyo 113-0011, Japan
| | - M J Lawler
- Laboratory of Atomic and Solid State Physics, Department of Physics, Cornell University, Ithaca, New York 14853, USA.,Department of Physics, Binghamton University, Binghamton, New York 13902-6000, USA
| | - E-A Kim
- Laboratory of Atomic and Solid State Physics, Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - A P Mackenzie
- School of Physics and Astronomy, University of St Andrews, Fife KY16 9SS, UK.,Max Planck Institute for Chemical Physics of Solids, D-01187 Dresden, Germany
| | - K Fujita
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - Jinho Lee
- Institute of Applied Physics, Department of Physics and Astronomy, Seoul National University, Seoul 151-747, South Korea.,Center for Correlated Electron Systems, Institute of Basic Science, Seoul 151-742, South Korea
| | - J C Séamus Davis
- Laboratory of Atomic and Solid State Physics, Department of Physics, Cornell University, Ithaca, New York 14853, USA.,School of Physics and Astronomy, University of St Andrews, Fife KY16 9SS, UK.,Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA.,Kavli Institute at Cornell for Nanoscale Science, Cornell University, Ithaca, New York 14853, USA
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5
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Fujita K, Kim CK, Lee I, Lee J, Hamidian MH, Firmo IA, Mukhopadhyay S, Eisaki H, Uchida S, Lawler MJ, Kim EA, Davis JC. Simultaneous transitions in cuprate momentum-space topology and electronic symmetry breaking. Science 2014; 344:612-6. [PMID: 24812397 DOI: 10.1126/science.1248783] [Citation(s) in RCA: 185] [Impact Index Per Article: 18.5] [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
The existence of electronic symmetry breaking in the underdoped cuprates and its disappearance with increased hole density p are now widely reported. However, the relation between this transition and the momentum-space (k-space) electronic structure underpinning the superconductivity has not yet been established. Here, we visualize the Q = 0 (intra-unit-cell) and Q ≠ 0 (density-wave) broken-symmetry states, simultaneously with the coherent k-space topology, for Bi₂Sr₂CaCu₂O(8+δ) samples spanning the phase diagram 0.06 ≤ p ≤ 0.23. We show that the electronic symmetry-breaking tendencies weaken with increasing p and disappear close to a critical doping p(c) = 0.19. Concomitantly, the coherent k-space topology undergoes an abrupt transition, from arcs to closed contours, at the same p(c). These data reveal that the k-space topology transformation in cuprates is linked intimately with the disappearance of the electronic symmetry breaking at a concealed critical point.
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Affiliation(s)
- K Fujita
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY 11973, USA
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