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Zeng C, Stanescu TD, Zhang C, Scarola VW, Tewari S. Majorana Corner Modes with Solitons in an Attractive Hubbard-Hofstadter Model of Cold Atom Optical Lattices. PHYSICAL REVIEW LETTERS 2019; 123:060402. [PMID: 31491186 DOI: 10.1103/physrevlett.123.060402] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2019] [Indexed: 06/10/2023]
Abstract
Higher-order topological superconductors hosting Majorana-Kramers pairs (MKPs) as corner modes have recently been proposed in a two-dimensional quantum spin Hall insulator proximity-coupled to unconventional cuprate or iron-based superconductors. Here, we show that such MKPs can be realized using a conventional s-wave superfluid with a soliton in cold atom systems governed by the Hubbard-Hofstadter model. The MKPs emerge in the presence of interaction at the "corners" defined by the intersections of line solitons and the one-dimensional edges of the system. Our scheme is based on the recently realized cold atom Hubbard-Hofstadter lattice and will pave the way for observing possible higher-order topological superfluidity with conventional s-wave superfluids or superconductors.
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Affiliation(s)
- Chuanchang Zeng
- Department of Physics and Astronomy, Clemson University, Clemson, South Carolina 29634, USA
| | - T D Stanescu
- Department of Physics and Astronomy, West Virginia University, Morgantown, West Virginia 26506, USA
| | - Chuanwei Zhang
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080, USA
| | - V W Scarola
- Department of Physics, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Sumanta Tewari
- Department of Physics and Astronomy, Clemson University, Clemson, South Carolina 29634, USA
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2
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Irsigler B, Zheng JH, Hofstetter W. Interacting Hofstadter Interface. PHYSICAL REVIEW LETTERS 2019; 122:010406. [PMID: 31012663 DOI: 10.1103/physrevlett.122.010406] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2018] [Revised: 08/02/2018] [Indexed: 06/09/2023]
Abstract
Two-dimensional topological insulators possess conducting edge states at their boundary while being insulating in the bulk. We investigate the edge state emergent at a smooth topological phase boundary of interacting fermions within a full real-space analysis of the time-reversal invariant Hofstadter-Hubbard model. We characterize the localization of the edge state and the topological phase boundary by means of the local compressibility, the spectral density, a generalized local spin Chern marker as well as the Hall response and find good agreement between all these quantities. Computing the edge state spectra at the interface we observe robustness of the edge state against fermionic two-body interactions and conclude that interactions only shift its position. Hence the bulk-boundary correspondence for the interacting system is confirmed. Since experimental probing of edge states remains a challenge in ultracold atom setups, we propose the detection of the local compressibility by measuring correlations with a quantum gas microscope.
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Affiliation(s)
- Bernhard Irsigler
- Institut für Theoretische Physik, Goethe-Universität, 60438 Frankfurt am Main, Germany
| | - Jun-Hui Zheng
- Institut für Theoretische Physik, Goethe-Universität, 60438 Frankfurt am Main, Germany
| | - Walter Hofstetter
- Institut für Theoretische Physik, Goethe-Universität, 60438 Frankfurt am Main, Germany
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Rachel S. Interacting topological insulators: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:116501. [PMID: 30057370 DOI: 10.1088/1361-6633/aad6a6] [Citation(s) in RCA: 53] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/02/2023]
Abstract
The discovery of the quantum spin Hall effect and topological insulators more than a decade ago has revolutionized modern condensed matter physics. Today, the field of topological states of matter is one of the most active and fruitful research areas for both experimentalists and theorists. The physics of topological insulators is typically well described by band theory and systems of non-interacting fermions. In contrast, several of the most fascinating effects in condensed matter physics merely exist due to electron-electron interactions, examples include unconventional superconductivity, the Kondo effect, and the Mott-Hubbard transition. The aim of this review article is to give an overview of the manifold directions which emerge when topological bandstructures and correlation physics interfere and compete. These include the study of the stability of topological bandstructures and correlated topological insulators. Interaction-induced topological phases such as the topological Kondo insulator provide another exciting topic. More exotic states of matter such as topological Mott insulator and fractional Chern insulators only exist due to the interplay of topology and strong interactions and do not have any bandstructure analogue. Eventually the relation between topological bandstructures and frustrated quantum magnetism in certain transition metal oxides is emphasized.
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Affiliation(s)
- Stephan Rachel
- School of Physics, University of Melbourne, Parkville, VIC 3010, Australia
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Umucalılar RO, Iskin M. BCS Theory of Time-Reversal-Symmetric Hofstadter-Hubbard Model. PHYSICAL REVIEW LETTERS 2017; 119:085301. [PMID: 28952771 DOI: 10.1103/physrevlett.119.085301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2017] [Indexed: 06/07/2023]
Abstract
The competition between the length scales associated with the periodicity of a lattice potential and the cyclotron radius of a uniform magnetic field is known to have dramatic effects on the single-particle properties of a quantum particle, e.g., the fractal spectrum is known as the Hofstadter butterfly. Having this intricate competition in mind, we consider a two-component Fermi gas on a square optical lattice with opposite synthetic magnetic fields for the components, and study its effects on the many-body BCS-pairing phenomenon. By a careful addressing of the distinct superfluid transitions from the semimetal, quantum spin-Hall insulator, or normal phases, we explore the low-temperature phase diagrams of the model, displaying lobe structures that are reminiscent of the well-known Mott-insulator transitions of the Bose-Hubbard model.
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Affiliation(s)
- R O Umucalılar
- Department of Physics, Koç University, Rumelifeneri Yolu, 34450 Sarıyer, Istanbul, Turkey
- Department of Physics, Mimar Sinan Fine Arts University, 34380 Şişli, Istanbul, Turkey
| | - M Iskin
- Department of Physics, Koç University, Rumelifeneri Yolu, 34450 Sarıyer, Istanbul, Turkey
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Rachel S. Quantum phase transitions of topological insulators without gap closing. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:405502. [PMID: 27530509 DOI: 10.1088/0953-8984/28/40/405502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We consider two-dimensional Chern insulators and time-reversal invariant topological insulators and discuss the effect of perturbations breaking either particle-number conservation or time-reversal symmetry. The appearance of trivial mass terms is expected to cause quantum phase transitions into trivial phases when such a perturbation overweighs the topological term. These phase transitions are usually associated with a bulk-gap closing. In contrast, the chiral Chern insulator is unaffected by particle-number breaking perturbations. Moreover, the [Formula: see text] topological insulator undergoes phase transitions into topologically trivial phases without bulk-gap closing in the presence of any of such perturbations. In certain cases, these phase transitions can be circumvented and the protection restored by another U(1) symmetry, e.g. due to spin conservation. These findings are discussed in the context of interacting topological insulators.
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Affiliation(s)
- Stephan Rachel
- Institute for Theoretical Physics, TU Dresden, 01062 Dresden, Germany
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Ren Y, Qiao Z, Niu Q. Topological phases in two-dimensional materials: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2016; 79:066501. [PMID: 27176924 DOI: 10.1088/0034-4885/79/6/066501] [Citation(s) in RCA: 104] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Topological phases with insulating bulk and gapless surface or edge modes have attracted intensive attention because of their fundamental physics implications and potential applications in dissipationless electronics and spintronics. In this review, we mainly focus on recent progress in the engineering of topologically nontrivial phases (such as [Formula: see text] topological insulators, quantum anomalous Hall effects, quantum valley Hall effects etc) in two-dimensional systems, including quantum wells, atomic crystal layers of elements from group III to group VII, and the transition metal compounds.
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Affiliation(s)
- Yafei Ren
- ICQD, Hefei National Laboratory for Physical Sciences at Microscale, and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China. CAS Key Laboratory of Strongly-Coupled Quantum Matter Physics and Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
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Manchon A, Koo HC, Nitta J, Frolov SM, Duine RA. New perspectives for Rashba spin-orbit coupling. NATURE MATERIALS 2015; 14:871-882. [PMID: 26288976 DOI: 10.1038/nmat4360] [Citation(s) in RCA: 444] [Impact Index Per Article: 49.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2015] [Accepted: 06/22/2015] [Indexed: 06/04/2023]
Abstract
In 1984, Bychkov and Rashba introduced a simple form of spin-orbit coupling to explain the peculiarities of electron spin resonance in two-dimensional semiconductors. Over the past 30 years, Rashba spin-orbit coupling has inspired a vast number of predictions, discoveries and innovative concepts far beyond semiconductors. The past decade has been particularly creative, with the realizations of manipulating spin orientation by moving electrons in space, controlling electron trajectories using spin as a steering wheel, and the discovery of new topological classes of materials. This progress has reinvigorated the interest of physicists and materials scientists in the development of inversion asymmetric structures, ranging from layered graphene-like materials to cold atoms. This Review discusses relevant recent and ongoing realizations of Rashba physics in condensed matter.
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Affiliation(s)
- A Manchon
- King Abdullah University of Science and Technology (KAUST), Physical Science and Engineering Division, Thuwal 23955-6900, Saudi Arabia
| | - H C Koo
- Center for Spintronics, Korea Institute of Science and Technology (KIST), 39-1 Hawolgok-dong, Seongbukgu, Seoul 136-791, Korea
- KU-KIST Graduate School of Converging Science and Technology, Korea University, Seoul 136-701, Korea
| | - J Nitta
- Department of Materials Science, Tohoku University, 980-8579 Sendai, Miyagi, Japan
| | - S M Frolov
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - R A Duine
- Institute for Theoretical Physics and Center for Extreme Matter and Emergent Phenomena, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands
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Albert VV, Glazman LI, Jiang L. Topological properties of linear circuit lattices. PHYSICAL REVIEW LETTERS 2015; 114:173902. [PMID: 25978235 DOI: 10.1103/physrevlett.114.173902] [Citation(s) in RCA: 50] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2014] [Indexed: 06/04/2023]
Abstract
Motivated by the topologically insulating circuit of capacitors and inductors proposed and tested by Jia et al. [arXiv:1309.0878], we present a related circuit with fewer elements per site. The normal mode frequency matrix of our circuit is unitarily equivalent to the hopping matrix of a quantum spin Hall insulator, and we identify perturbations that do not backscatter the circuit's edge modes. The idea behind these models is generalized, providing a platform to simulate tunable and locally accessible lattices with arbitrary complex spin-dependent hopping of any range. A simulation of a non-Abelian Aharonov-Bohm effect using such linear circuit designs is discussed.
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Affiliation(s)
- Victor V Albert
- Departments of Applied Physics and Physics, Yale University, New Haven, Connecticut, USA
| | - Leonid I Glazman
- Departments of Applied Physics and Physics, Yale University, New Haven, Connecticut, USA
| | - Liang Jiang
- Departments of Applied Physics and Physics, Yale University, New Haven, Connecticut, USA
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9
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Scheurer MS, Rachel S, Orth PP. Dimensional crossover and cold-atom realization of topological Mott insulators. Sci Rep 2015; 5:8386. [PMID: 25669431 PMCID: PMC4323638 DOI: 10.1038/srep08386] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2014] [Accepted: 01/19/2015] [Indexed: 11/25/2022] Open
Abstract
Interacting cold-atomic gases in optical lattices offer an experimental approach to outstanding problems of many body physics. One important example is the interplay of interaction and topology which promises to generate a variety of exotic phases such as the fractionalized Chern insulator or the topological Mott insulator. Both theoretically understanding these states of matter and finding suitable systems that host them have proven to be challenging problems. Here we propose a cold-atom setup where Hubbard on-site interactions give rise to spin liquid-like phases: weak and strong topological Mott insulators. They represent the celebrated paradigm of an interacting and topological quantum state with fractionalized spinon excitations that inherit the topology of the non-interacting system. Our proposal shall help to pave the way for a controlled experimental investigation of this exotic state of matter in optical lattices. Furthermore, it allows for the investigation of a dimensional crossover from a two-dimensional quantum spin Hall insulating phase to a three-dimensional strong topological insulator by tuning the hopping between the layers.
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Affiliation(s)
- Mathias S Scheurer
- Institute for Theory of Condensed Matter, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
| | - Stephan Rachel
- Institute for Theoretical Physics, TU Dresden, 01062 Dresden, Germany
| | - Peter P Orth
- Institute for Theory of Condensed Matter, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
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10
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Zhai H. Degenerate quantum gases with spin-orbit coupling: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2015; 78:026001. [PMID: 25640665 DOI: 10.1088/0034-4885/78/2/026001] [Citation(s) in RCA: 73] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
This review focuses on recent developments in synthetic spin-orbit (SO) coupling in ultracold atomic gases. Two types of SO coupling are discussed. One is Raman process induced coupling between spin and motion along one of the spatial directions and the other is Rashba SO coupling. We emphasize their common features in both single-particle and two-body physics and the consequences of both in many-body physics. For instance, single particle ground state degeneracy leads to novel features of superfluidity and a richer phase diagram; increased low-energy density-of-state enhances interaction effects; the absence of Galilean invariance and spin-momentum locking gives rise to intriguing behaviours of superfluid critical velocity and novel quantum dynamics; and the mixing of two-body singlet and triplet states yields a novel fermion pairing structure and topological superfluids. With these examples, we show that investigating SO coupling in cold atom systems can, enrich our understanding of basic phenomena such as superfluidity, provide a good platform for simulating condensed matter states such as topological superfluids and more importantly, result in novel quantum systems such as SO coupled unitary Fermi gas and high spin quantum gases. Finally we also point out major challenges and some possible future directions.
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Affiliation(s)
- Hui Zhai
- Institute for Advanced Study, Tsinghua University, Beijing 100084, People's Republic of China
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Goldman N, Juzeliūnas G, Öhberg P, Spielman IB. Light-induced gauge fields for ultracold atoms. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2014; 77:126401. [PMID: 25422950 DOI: 10.1088/0034-4885/77/12/126401] [Citation(s) in RCA: 181] [Impact Index Per Article: 18.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Gauge fields are central in our modern understanding of physics at all scales. At the highest energy scales known, the microscopic universe is governed by particles interacting with each other through the exchange of gauge bosons. At the largest length scales, our Universe is ruled by gravity, whose gauge structure suggests the existence of a particle-the graviton-that mediates the gravitational force. At the mesoscopic scale, solid-state systems are subjected to gauge fields of different nature: materials can be immersed in external electromagnetic fields, but they can also feature emerging gauge fields in their low-energy description. In this review, we focus on another kind of gauge field: those engineered in systems of ultracold neutral atoms. In these setups, atoms are suitably coupled to laser fields that generate effective gauge potentials in their description. Neutral atoms 'feeling' laser-induced gauge potentials can potentially mimic the behavior of an electron gas subjected to a magnetic field, but also, the interaction of elementary particles with non-Abelian gauge fields. Here, we review different realized and proposed techniques for creating gauge potentials-both Abelian and non-Abelian-in atomic systems and discuss their implication in the context of quantum simulation. While most of these setups concern the realization of background and classical gauge potentials, we conclude with more exotic proposals where these synthetic fields might be made dynamical, in view of simulating interacting gauge theories with cold atoms.
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Affiliation(s)
- N Goldman
- College de France, 11 place Marcelin Berthelot & Laboratoire Kastler Brossel, CNRS, UPMC, ENS, 24 rue Lhomond, 75005 Paris, France
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12
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Wang D, Liu Z, Cao J, Fan H. Tunable band topology reflected by fractional quantum Hall States in two-dimensional lattices. PHYSICAL REVIEW LETTERS 2013; 111:186804. [PMID: 24237549 DOI: 10.1103/physrevlett.111.186804] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2013] [Indexed: 06/02/2023]
Abstract
Two-dimensional lattice models subjected to an external effective magnetic field can form nontrivial band topologies characterized by nonzero integer band Chern numbers. In this Letter, we investigate such a lattice model originating from the Hofstadter model and demonstrate that the band topology transitions can be realized by simply introducing tunable longer-range hopping. The rich phase diagram of band Chern numbers is obtained for the simple rational flux density and a classification of phases is presented. In the presence of interactions, the existence of fractional quantum Hall states in both |C| = 1 and |C| > 1 bands is confirmed, which can reflect the band topologies in different phases. In contrast, when our model reduces to a one-dimensional lattice, the ground states are crucially different from fractional quantum Hall states. Our results may provide insights into the study of new fractional quantum Hall states and experimental realizations of various topological phases in optical lattices.
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Affiliation(s)
- Dong Wang
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
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Dauphin A, Goldman N. Extracting the Chern number from the dynamics of a Fermi gas: implementing a quantum Hall bar for cold atoms. PHYSICAL REVIEW LETTERS 2013; 111:135302. [PMID: 24116789 DOI: 10.1103/physrevlett.111.135302] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2013] [Revised: 08/03/2013] [Indexed: 06/02/2023]
Abstract
We propose a scheme to measure the quantized Hall conductivity of an ultracold Fermi gas initially prepared in a topological Chern insulating phase and driven by a constant force. We show that the time evolution of the center of mass, after releasing the cloud, provides a direct and clear signature of the topologically invariant Chern number. We discuss the validity of this scheme, highlighting the importance of driving the system with a sufficiently strong force to displace the cloud over measurable distances while avoiding band-mixing effects. The unusual shapes of the driven atomic cloud are qualitatively discussed in terms of a semiclassical approach.
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Affiliation(s)
- Alexandre Dauphin
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium and Departamento de Física Teórica I, Universidad Complutense, 28040 Madrid, Spain
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Hohenadler M, Assaad FF. Correlation effects in two-dimensional topological insulators. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:143201. [PMID: 23470861 DOI: 10.1088/0953-8984/25/14/143201] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Topological insulators have become one of the most active research areas in condensed matter physics. This article reviews progress on the topic of electronic correlation effects in the two-dimensional case, with a focus on systems with intrinsic spin-orbit coupling and numerical results. Topics addressed include an introduction to the noninteracting case, an overview of theoretical models, correlated topological band insulators, interaction-driven phase transitions, topological Mott insulators and fractional topological states, correlation effects on helical edge states, and topological invariants of interacting systems.
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Affiliation(s)
- M Hohenadler
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany.
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