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Tyner AC. BerryEasy: a GPU enabled python package for diagnosis of nth-order and spin-resolved topology in the presence of fields and effects. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:325902. [PMID: 38701825 DOI: 10.1088/1361-648x/ad475f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/05/2024] [Accepted: 05/03/2024] [Indexed: 05/05/2024]
Abstract
Multiple software packages currently exist for the computation of bulk topological invariants in both idealized tight-binding models and realistic Wannier tight-binding models derived from density functional theory. Currently, only one package is capable of computing nested Wilson loops and spin-resolved Wilson loops. These state-of-the-art techniques are vital for accurate analysis of band topology. In this paper we introduce BerryEasy, a python package harnessing the speed of graphical processing units to allow for efficient topological analysis of supercells in the presence of disorder and impurities. Moreover, the BerryEasy package has built-in functionality to accommodate use of realistic many-band tight-binding models derived from first-principles.
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Affiliation(s)
- Alexander C Tyner
- Nordita, KTH Royal Institute of Technology and Stockholm University, 106 91 Stockholm, Sweden
- Department of Physics, University of Connecticut, Storrs, CT 06269, United States of America
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2
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Vaidya S, Rechtsman MC, Benalcazar WA. Polarization and Weak Topology in Chern Insulators. PHYSICAL REVIEW LETTERS 2024; 132:116602. [PMID: 38563931 DOI: 10.1103/physrevlett.132.116602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2023] [Revised: 11/08/2023] [Accepted: 01/30/2024] [Indexed: 04/04/2024]
Abstract
Chern insulators, and more broadly, topological insulators, present an obstruction to the construction of exponentially localized electronic Wannier functions. This implies a fundamental difficulty in determining whether such insulators exhibit electric polarization. Here, we show that these insulators can indeed exhibit bound charges and adiabatic currents consistent with changes in bulk polarization over space and time, respectively. We also show that the change in polarization across crystalline domains within these strong topological insulators is quantized in the presence of crystalline symmetries.
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Affiliation(s)
- Sachin Vaidya
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Mikael C Rechtsman
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
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3
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Guan Y, Yazyev OV, Kruchkov A. Unconventional Flat Chern Bands and 2 e Charges in Skyrmionic Moiré Superlattices. NANO LETTERS 2023; 23:4209-4215. [PMID: 37133996 DOI: 10.1021/acs.nanolett.3c00121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
The interplay of topological characteristics in real space and reciprocal space can lead to the emergence of unconventional topological phases. In this Letter, we implement a novel mechanism for generating higher-Chern flat bands on the basis of twisted bilayer graphene (TBG) coupled to topological magnetic structures in the form of the skyrmion lattice. In particular, we discover a scenario for generating |C| = 2 dispersionless electronic bands when the skyrmion periodicity and the moiré periodicity match. Following the Wilczek argument, the statistics of the charge-carrying excitations in this case is bosonic, characterized by electronic charge Q = 2e, which is even in units of electron charge e. The skyrmion coupling strength triggering the topological phase transition is realistic, with its lower bound estimated as 4 meV. The Hofstadter butterfly spectrum results in an unexpected quantum Hall conductance sequence ±2e2h,±4e2h,... for TBG with the skyrmion order.
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Affiliation(s)
- Yifei Guan
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Oleg V Yazyev
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Alexander Kruchkov
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, United States
- Branco Weiss Society in Science, ETH Zürich, CH-8092 Zürich, Switzerland
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4
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Mao R, Xu X, Wang J, Xu C, Qian G, Cai H, Zhu SY, Wang DW. Measuring Zak phase in room-temperature atoms. LIGHT, SCIENCE & APPLICATIONS 2022; 11:291. [PMID: 36210366 PMCID: PMC9548506 DOI: 10.1038/s41377-022-00990-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/23/2022] [Revised: 09/20/2022] [Accepted: 09/21/2022] [Indexed: 06/16/2023]
Abstract
Cold atoms provide a flexible platform for synthesizing and characterizing topological matter, where geometric phases play a central role. However, cold atoms are intrinsically prone to thermal noise, which can overwhelm the topological response and hamper promised applications. On the other hand, geometric phases also determine the energy spectra of particles subjected to a static force, based on the polarization relation between Wannier-Stark ladders and geometric Zak phases. By exploiting this relation, we develop a method to extract geometric phases from energy spectra of room-temperature superradiance lattices, which are momentum-space lattices of timed Dicke states. In such momentum-space lattices the thermal motion of atoms, instead of being a source of noise, provides effective forces which lead to spectroscopic signatures of the Zak phases. We measure Zak phases directly from the anti-crossings between Wannier-Stark ladders in the Doppler-broadened absorption spectra of superradiance lattices. Our approach paves the way of measuring topological invariants and developing their applications in room-temperature atoms.
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Affiliation(s)
- Ruosong Mao
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, School of Physics, Zhejiang University, Hangzhou, 310027, China
| | - Xingqi Xu
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, School of Physics, Zhejiang University, Hangzhou, 310027, China
| | - Jiefei Wang
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, School of Physics, Zhejiang University, Hangzhou, 310027, China
| | - Chenran Xu
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, School of Physics, Zhejiang University, Hangzhou, 310027, China
| | - Gewei Qian
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, School of Physics, Zhejiang University, Hangzhou, 310027, China
| | - Han Cai
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, School of Physics, Zhejiang University, Hangzhou, 310027, China.
- College of Optical Science and Engineering, Zhejiang University, Hangzhou, 310027, China.
| | - Shi-Yao Zhu
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, School of Physics, Zhejiang University, Hangzhou, 310027, China
- Hefei National Laboratory, Hefei, 230088, China
| | - Da-Wei Wang
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, School of Physics, Zhejiang University, Hangzhou, 310027, China.
- Hefei National Laboratory, Hefei, 230088, China.
- CAS Center of Excellence in Topological Quantum Computation, 100190, Beijing, China.
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5
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Bandyopadhyay S, Bhattacharjee S, Sen D. Driven quantum many-body systems and out-of-equilibrium topology. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:393001. [PMID: 34225268 DOI: 10.1088/1361-648x/ac1151] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2021] [Accepted: 07/05/2021] [Indexed: 06/13/2023]
Abstract
In this review we present some of the work done in India in the area of driven and out-of-equilibrium systems with topological phases. After presenting some well-known examples of topological systems in one and two dimensions, we discuss the effects of periodic driving in some of them. We discuss the unitary as well as the non-unitary dynamical preparation of topologically non-trivial states in one and two dimensional systems. We then discuss the effects of Majorana end modes on transport through a Kitaev chain and a junction of three Kitaev chains. Following this, transport through the surface states of a three-dimensional topological insulator has also been reviewed. The effects of hybridization between the top and bottom surfaces in such systems and the application of electromagnetic radiation on a strip-like region on the top surface are described. Two unusual topological systems are mentioned briefly, namely, a spin system on a kagome lattice and a Josephson junction of three superconducting wires. We have also included a pedagogical discussion on topology and topological invariants in the appendices, where the connection between topological properties and the intrinsic geometry of many-body quantum states is also elucidated.
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Affiliation(s)
- Souvik Bandyopadhyay
- Department of Physics, Indian Institute of Technology Kanpur, Kanpur 208016, India
| | - Sourav Bhattacharjee
- Department of Physics, Indian Institute of Technology Kanpur, Kanpur 208016, India
| | - Diptiman Sen
- Center for High Energy Physics and Department of Physics, Indian Institute of Science, Bengaluru 560012, India
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6
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Kang B, Lee W, Cho GY. Many-Body Invariants for Chern and Chiral Hinge Insulators. PHYSICAL REVIEW LETTERS 2021; 126:016402. [PMID: 33480785 DOI: 10.1103/physrevlett.126.016402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2020] [Accepted: 12/03/2020] [Indexed: 06/12/2023]
Abstract
We construct new many-body invariants for 2D Chern and 3D chiral hinge insulators characterizing quantized pumping of bulk dipole and quadrupole moments. The many-body invariants are written entirely in terms of many-body ground state wave functions on a torus geometry with twisted boundary conditions and a set of unitary operators. We present a number of supporting arguments for the invariants via topological field theory interpretation, adiabatic pumping argument, and direct mapping to free-fermion band indices. Therefore, the invariants explicitly encircle several different pillars of theoretical descriptions of topological phases. Furthermore, our many-body invariants are written in forms which can be directly employed in various numerics including the exact diagonalization and the density-matrix renormalization group simulations. We finally confirm our invariants by numerical computations including an infinite density-matrix renormalization group on quasi-one-dimensional systems.
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Affiliation(s)
- Byungmin Kang
- School of Physics, Korea Institute for Advanced Study, Seoul 02455, Republic of Korea
| | - Wonjun Lee
- Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang 37673, Republic of Korea
| | - Gil Young Cho
- Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang 37673, Republic of Korea
- Asia Pacific Center for Theoretical Physics, Pohang 37673, Republic of Korea
- Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science (IBS), Pohang 37673, Republic of Korea
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7
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Piezoelectricity and topological quantum phase transitions in two-dimensional spin-orbit coupled crystals with time-reversal symmetry. Nat Commun 2020; 11:2290. [PMID: 32385246 PMCID: PMC7210280 DOI: 10.1038/s41467-020-16058-2] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2019] [Accepted: 04/09/2020] [Indexed: 11/08/2022] Open
Abstract
Finding new physical responses that signal topological quantum phase transitions is of both theoretical and experimental importance. Here, we demonstrate that the piezoelectric response can change discontinuously across a topological quantum phase transition in two-dimensional time-reversal invariant systems with spin-orbit coupling, thus serving as a direct probe of the transition. We study all gap closing cases for all 7 plane groups that allow non-vanishing piezoelectricity, and find that any gap closing with 1 fine-tuning parameter between two gapped states changes either the Z2 invariant or the locally stable valley Chern number. The jump of the piezoelectric response is found to exist for all these transitions, and we propose the HgTe/CdTe quantum well and BaMnSb2 as two potential experimental platforms. Our work provides a general theoretical framework to classify topological quantum phase transitions, and reveals their ubiquitous relation to the piezoelectric response. The linear response and topological electronic properties of a material both depend on the underlying crystal symmetry. Here the authors study how topological phase transitions in two-dimensional materials manifest themselves in the piezoelectric response.
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8
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Prentice JCA, Aarons J, Womack JC, Allen AEA, Andrinopoulos L, Anton L, Bell RA, Bhandari A, Bramley GA, Charlton RJ, Clements RJ, Cole DJ, Constantinescu G, Corsetti F, Dubois SMM, Duff KKB, Escartín JM, Greco A, Hill Q, Lee LP, Linscott E, O'Regan DD, Phipps MJS, Ratcliff LE, Serrano ÁR, Tait EW, Teobaldi G, Vitale V, Yeung N, Zuehlsdorff TJ, Dziedzic J, Haynes PD, Hine NDM, Mostofi AA, Payne MC, Skylaris CK. The ONETEP linear-scaling density functional theory program. J Chem Phys 2020; 152:174111. [PMID: 32384832 DOI: 10.1063/5.0004445] [Citation(s) in RCA: 51] [Impact Index Per Article: 12.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Abstract
We present an overview of the onetep program for linear-scaling density functional theory (DFT) calculations with large basis set (plane-wave) accuracy on parallel computers. The DFT energy is computed from the density matrix, which is constructed from spatially localized orbitals we call Non-orthogonal Generalized Wannier Functions (NGWFs), expressed in terms of periodic sinc (psinc) functions. During the calculation, both the density matrix and the NGWFs are optimized with localization constraints. By taking advantage of localization, onetep is able to perform calculations including thousands of atoms with computational effort, which scales linearly with the number or atoms. The code has a large and diverse range of capabilities, explored in this paper, including different boundary conditions, various exchange-correlation functionals (with and without exact exchange), finite electronic temperature methods for metallic systems, methods for strongly correlated systems, molecular dynamics, vibrational calculations, time-dependent DFT, electronic transport, core loss spectroscopy, implicit solvation, quantum mechanical (QM)/molecular mechanical and QM-in-QM embedding, density of states calculations, distributed multipole analysis, and methods for partitioning charges and interactions between fragments. Calculations with onetep provide unique insights into large and complex systems that require an accurate atomic-level description, ranging from biomolecular to chemical, to materials, and to physical problems, as we show with a small selection of illustrative examples. onetep has always aimed to be at the cutting edge of method and software developments, and it serves as a platform for developing new methods of electronic structure simulation. We therefore conclude by describing some of the challenges and directions for its future developments and applications.
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Affiliation(s)
- Joseph C A Prentice
- Department of Materials, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom
| | - Jolyon Aarons
- Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
| | - James C Womack
- School of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom
| | - Alice E A Allen
- TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Lampros Andrinopoulos
- Department of Physics, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom
| | - Lucian Anton
- UKAEA, Culham Science Centre, Abingdon OX14 3DB, United Kingdom
| | - Robert A Bell
- TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Arihant Bhandari
- School of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom
| | - Gabriel A Bramley
- School of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom
| | - Robert J Charlton
- Department of Materials, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom
| | - Rebecca J Clements
- School of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom
| | - Daniel J Cole
- School of Natural and Environmental Sciences, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom
| | - Gabriel Constantinescu
- TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Fabiano Corsetti
- Department of Materials, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom
| | - Simon M-M Dubois
- Institute of Condensed Matter and Nanosciences, Université Catholique de Louvain, Louvain-la-Neuve, Belgium
| | - Kevin K B Duff
- TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - José María Escartín
- TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Andrea Greco
- Department of Physics, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom
| | - Quintin Hill
- School of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom
| | - Louis P Lee
- TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Edward Linscott
- TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - David D O'Regan
- School of Physics, AMBER, and CRANN Institute, Trinity College Dublin, The University of Dublin, Dublin 2, Ireland
| | - Maximillian J S Phipps
- School of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom
| | - Laura E Ratcliff
- Department of Materials, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom
| | - Álvaro Ruiz Serrano
- School of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom
| | - Edward W Tait
- TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Gilberto Teobaldi
- School of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom
| | - Valerio Vitale
- Department of Materials, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom
| | - Nelson Yeung
- Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
| | - Tim J Zuehlsdorff
- Chemistry and Chemical Biology, University of California Merced, Merced, California 95343, USA
| | - Jacek Dziedzic
- School of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom
| | - Peter D Haynes
- Department of Materials, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom
| | - Nicholas D M Hine
- Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
| | - Arash A Mostofi
- Department of Materials, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom
| | - Mike C Payne
- TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Chris-Kriton Skylaris
- School of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom
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9
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Benalcazar WA, Bernevig BA, Hughes TL. Quantized electric multipole insulators. Science 2017; 357:61-66. [DOI: 10.1126/science.aah6442] [Citation(s) in RCA: 912] [Impact Index Per Article: 130.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2016] [Accepted: 06/02/2017] [Indexed: 11/02/2022]
Abstract
The Berry phase provides a modern formulation of electric polarization in crystals. We extend this concept to higher electric multipole moments and determine the necessary conditions and minimal models for which the quadrupole and octupole moments are topologically quantized electromagnetic observables. Such systems exhibit gapped boundaries that are themselves lower-dimensional topological phases. Furthermore, they host topologically protected corner states carrying fractional charge, exhibiting fractionalization at the boundary of the boundary. To characterize these insulating phases of matter, we introduce a paradigm in which “nested” Wilson loops give rise to topological invariants that have been overlooked. We propose three realistic experimental implementations of this topological behavior that can be immediately tested. Our work opens a venue for the expansion of the classification of topological phases of matter.
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10
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Zeng TS, Wang C, Zhai H. Charge Pumping of Interacting Fermion Atoms in the Synthetic Dimension. PHYSICAL REVIEW LETTERS 2015; 115:095302. [PMID: 26371662 DOI: 10.1103/physrevlett.115.095302] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2015] [Indexed: 06/05/2023]
Abstract
Recently it has been theoretically proposed and experimentally demonstrated that a spin-orbit coupled multicomponent gas in a 1D lattice can be viewed as a spinless gas in a synthetic 2D lattice with a magnetic flux. In this Letter we consider interaction effects in such a Fermi gas, and propose these effects can be easily detected in a charge pumping experiment. Using 1/3 filling of the lowest 2D band as an example, in the strongly interacting regime, we show that the charge pumping value gradually approaches a universal fractional value for large spin components and low filling of the 1D lattice, indicating a fractional quantum Hall-type behavior, while the charge pumping value is zero if the 1D lattice filling is commensurate, indicating a Mott insulator behavior. The charge-density-wave order is also discussed.
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Affiliation(s)
| | - Ce Wang
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Hui Zhai
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
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11
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Wang L, Soluyanov AA, Troyer M. Proposal for direct measurement of topological invariants in optical lattices. PHYSICAL REVIEW LETTERS 2013; 110:166802. [PMID: 23679630 DOI: 10.1103/physrevlett.110.166802] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2013] [Indexed: 06/02/2023]
Abstract
We propose an experimental technique for classifying the topology of band structures realized in optical lattices, based on a generalization of topological charge pumping in quantum Hall systems to cold atoms in optical lattices. Time-of-flight measurement along one spatial direction combined with in situ detection along the transverse direction provides a direct measure of the system's Chern number, as we illustrate by calculations for the Hofstadter lattice. Based on an analogy with Wannier function techniques of topological band theory, the method is very general and also allows the measurement of other topological invariants, such as the Z(2) topological invariant of time-reversal symmetric insulators.
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Affiliation(s)
- Lei Wang
- Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland
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12
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Garrity KF, Vanderbilt D. Chern insulators from heavy atoms on magnetic substrates. PHYSICAL REVIEW LETTERS 2013; 110:116802. [PMID: 25166562 DOI: 10.1103/physrevlett.110.116802] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2012] [Indexed: 06/03/2023]
Abstract
We propose searching for Chern insulators by depositing atomic layers of elements with large spin-orbit coupling (e.g., Bi) on the surface of a magnetic insulator. We argue that such systems will typically have isolated surface bands with nonzero Chern numbers. If these overlap in energy, a metallic surface with large anomalous Hall conductivity will result; if not, a Chern-insulator state will typically occur. Thus, our search strategy reduces to looking for examples having the Fermi level in a global gap extending across the entire Brillouin zone. We verify this search strategy and identify several candidate systems by using first-principles calculations to compute the Chern number and anomalous Hall conductivity of a large number of such systems on MnTe, MnSe, and EuS surfaces. Our search reveals several promising Chern insulators with gaps of up to 140 meV.
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Affiliation(s)
- Kevin F Garrity
- Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
| | - David Vanderbilt
- Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
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13
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Bianco R, Resta R. Orbital magnetization as a local property. PHYSICAL REVIEW LETTERS 2013; 110:087202. [PMID: 23473193 DOI: 10.1103/physrevlett.110.087202] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2012] [Indexed: 06/01/2023]
Abstract
The modern expressions for polarization P and orbital magnetization M are k-space integrals. But a genuine bulk property should also be expressible in r space, as an unambiguous function of the ground-state density matrix, "nearsighted" in insulators, independently of the boundary conditions--either periodic or open. While P--owing to its "quantum" indeterminacy--is not a bulk property in this sense, M is. We provide its r-space expression for any insulator, even with a nonzero Chern invariant. Simulations on a model Hamiltonian validate our theory.
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Affiliation(s)
- Raffaello Bianco
- Dipartimento di Fisica, Università di Trieste, 34127 Trieste, Italy
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14
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Qi XL. Generic wave-function description of fractional quantum anomalous Hall states and fractional topological insulators. PHYSICAL REVIEW LETTERS 2011; 107:126803. [PMID: 22026785 DOI: 10.1103/physrevlett.107.126803] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2011] [Indexed: 05/31/2023]
Abstract
We propose a systematical approach to construct generic fractional quantum anomalous Hall states, which are generalizations of the fractional quantum Hall states to lattice models with zero net magnetic field and full lattice translation symmetry. Local and translationally invariant Hamiltonians can also be constructed, for which the proposed states are unique ground states. Our result demonstrates that generic chiral topologically ordered states can be realized in lattice models, without requiring magnetic translation symmetry and Landau level structure. We further generalize our approach to fractional topological insulators, and provide the first explicit wave-function description of fractional topological insulators in the absence of spin conservation.
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Affiliation(s)
- Xiao-Liang Qi
- Department of Physics, Stanford University, Stanford, California 94305, USA
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