1
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Yang YB, Wang JH, Li K, Xu Y. Higher-order topological phases in crystalline and non-crystalline systems: a review. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:283002. [PMID: 38574683 DOI: 10.1088/1361-648x/ad3abd] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2023] [Accepted: 04/04/2024] [Indexed: 04/06/2024]
Abstract
In recent years, higher-order topological phases have attracted great interest in various fields of physics. These phases have protected boundary states at lower-dimensional boundaries than the conventional first-order topological phases due to the higher-order bulk-boundary correspondence. In this review, we summarize current research progress on higher-order topological phases in both crystalline and non-crystalline systems. We firstly introduce prototypical models of higher-order topological phases in crystals and their topological characterizations. We then discuss effects of quenched disorder on higher-order topology and demonstrate disorder-induced higher-order topological insulators. We also review the theoretical studies on higher-order topological insulators in amorphous systems without any crystalline symmetry and higher-order topological phases in non-periodic lattices including quasicrystals, hyperbolic lattices, and fractals, which have no crystalline counterparts. We conclude the review by a summary of experimental realizations of higher-order topological phases and discussions on potential directions for future study.
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Affiliation(s)
- Yan-Bin Yang
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong Special Administrative Region of China, People's Republic of China
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
| | - Jiong-Hao Wang
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
| | - Kai Li
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
| | - Yong Xu
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
- Hefei National Laboratory, Hefei 230088, People's Republic of China
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2
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Wang FJ, Xiao ZY, Queiroz R, Bernevig BA, Stern A, Song ZD. Anderson critical metal phase in trivial states protected by average magnetic crystalline symmetry. Nat Commun 2024; 15:3069. [PMID: 38594296 PMCID: PMC11003978 DOI: 10.1038/s41467-024-47467-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2023] [Accepted: 03/28/2024] [Indexed: 04/11/2024] Open
Abstract
Transitions between distinct obstructed atomic insulators (OAIs) protected by crystalline symmetries, where electrons form molecular orbitals centering away from the atom positions, must go through an intermediate metallic phase. In this work, we find that the intermediate metals will become a scale-invariant critical metal phase (CMP) under certain types of quenched disorder that respect the magnetic crystalline symmetries on average. We explicitly construct models respecting average C2zT, m, and C4zT and show their scale-invariance under chemical potential disorder by the finite-size scaling method. Conventional theories, such as weak anti-localization and topological phase transition, cannot explain the underlying mechanism. A quantitative mapping between lattice and network models shows that the CMP can be understood through a semi-classical percolation problem. Ultimately, we systematically classify all the OAI transitions protected by (magnetic) groups P m , P 2 ' , P 4 ' , and P 6 ' with and without spin-orbit coupling, most of which can support CMP.
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Affiliation(s)
- Fa-Jie Wang
- International Center for Quantum Materials, School of Physics, Peking University, 100871, Beijing, China
| | - Zhen-Yu Xiao
- International Center for Quantum Materials, School of Physics, Peking University, 100871, Beijing, China
| | - Raquel Queiroz
- Department of Physics, Columbia University, New York, NY, USA
| | - B Andrei Bernevig
- Department of Physics, Princeton University, Princeton, NJ, 08544, USA
| | - Ady Stern
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 7610001, Israel
| | - Zhi-Da Song
- International Center for Quantum Materials, School of Physics, Peking University, 100871, Beijing, China.
- Hefei National Laboratory, Hefei, 230088, China.
- Collaborative Innovation Center of Quantum Matter, Beijing, 100871, China.
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3
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Xiao Z, Kawabata K, Luo X, Ohtsuki T, Shindou R. Anisotropic Topological Anderson Transitions in Chiral Symmetry Classes. PHYSICAL REVIEW LETTERS 2023; 131:056301. [PMID: 37595207 DOI: 10.1103/physrevlett.131.056301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2022] [Revised: 02/23/2023] [Accepted: 06/23/2023] [Indexed: 08/20/2023]
Abstract
We study quantum phase transitions of three-dimensional disordered systems in the chiral classes (AIII and BDI) with and without weak topological indices. We show that the systems with a nontrivial weak topological index universally exhibit an emergent thermodynamic phase where wave functions are delocalized along one spatial direction but exponentially localized in the other two spatial directions, which we call the quasilocalized phase. Our extensive numerical study clarifies that the critical exponent of the Anderson transition between the metallic and quasilocalized phases, as well as that between the quasilocalized and localized phases, are different from that with no weak topological index, signaling the new universality classes induced by topology. The quasilocalized phase and concomitant topological Anderson transition manifest themselves in the anisotropic transport phenomena of disordered weak topological insulators and nodal-line semimetals, which exhibit the metallic behavior in one direction but the insulating behavior in the other directions.
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Affiliation(s)
- Zhenyu Xiao
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Kohei Kawabata
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
- Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
| | - Xunlong Luo
- Science and Technology on Surface Physics and Chemistry Laboratory, Mianyang 621907, China
| | - Tomi Ohtsuki
- Physics Division, Sophia University, Chiyoda-ku, Tokyo 102-8554, Japan
| | - Ryuichi Shindou
- International Center for Quantum Materials, Peking University, Beijing 100871, China
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4
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Karaki MJ, Yang X, Williams AJ, Nawwar M, Doan-Nguyen V, Goldberger JE, Lu YM. An efficient material search for room-temperature topological magnons. SCIENCE ADVANCES 2023; 9:eade7731. [PMID: 36800420 PMCID: PMC9937570 DOI: 10.1126/sciadv.ade7731] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/14/2022] [Accepted: 01/18/2023] [Indexed: 06/18/2023]
Abstract
Topologically protected magnon surface states are highly desirable as an ideal platform to engineer low-dissipation spintronics devices. However, theoretical prediction of topological magnons in strongly correlated materials proves to be challenging because the ab initio density functional theory calculations fail to reliably predict magnetic interactions in correlated materials. Here, we present a symmetry-based approach, which predicts topological magnons in magnetically ordered crystals, upon applying external perturbations such as magnetic/electric fields and/or mechanical strains. We apply this approach to carry out an efficient search for magnetic materials in the Bilbao Crystallographic Server, where, among 198 compounds with an over 300-K transition temperature, we identify 12 magnetic insulators that support room-temperature topological magnons. They feature Weyl magnons with surface magnon arcs and magnon axion insulators with either chiral surface or hinge magnon modes, offering a route to realize energy-efficient devices based on protected surface magnons.
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Affiliation(s)
- Mohammed J. Karaki
- Department of Physics, The Ohio State University, Columbus, OH 43210, USA
| | - Xu Yang
- Department of Physics, The Ohio State University, Columbus, OH 43210, USA
| | - Archibald J. Williams
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, OH 43210, USA
| | - Mohamed Nawwar
- Department of Material Science and Engineering, The Ohio State University, Columbus, OH 43210, USA
| | - Vicky Doan-Nguyen
- Department of Material Science and Engineering, The Ohio State University, Columbus, OH 43210, USA
| | - Joshua E. Goldberger
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, OH 43210, USA
| | - Yuan-Ming Lu
- Department of Physics, The Ohio State University, Columbus, OH 43210, USA
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5
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Song ZD, Lian B, Queiroz R, Ilan R, Bernevig BA, Stern A. Delocalization Transition of a Disordered Axion Insulator. PHYSICAL REVIEW LETTERS 2021; 127:016602. [PMID: 34270311 DOI: 10.1103/physrevlett.127.016602] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2020] [Accepted: 05/30/2021] [Indexed: 06/13/2023]
Abstract
The axion insulator is a higher-order topological insulator protected by inversion symmetry. We show that, under quenched disorder respecting inversion symmetry on average, the topology of the axion insulator stays robust, and an intermediate metallic phase in which states are delocalized is unavoidable at the transition from an axion insulator to a trivial insulator. We derive this conclusion from general arguments, from classical percolation theory, and from the numerical study of a 3D quantum network model simulating a disordered axion insulator through a layer construction. We find the localization length critical exponent near the delocalization transition to be ν=1.42±0.12. We further show that this delocalization transition is stable even to weak breaking of the average inversion symmetry, up to a critical strength. We also quantitatively map our quantum network model to an effective Hamiltonian and we find its low-energy k·p expansion.
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Affiliation(s)
- Zhi-Da Song
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Biao Lian
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Raquel Queiroz
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Roni Ilan
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel
| | - B Andrei Bernevig
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
- Physics Department, Freie Universitat Berlin, Arnimallee 14, 14195 Berlin, Germany
- Max Planck Institute of Microstructure Physics, 06120 Halle, Germany
| | - Ady Stern
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
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6
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Wang JH, Yang YB, Dai N, Xu Y. Structural-Disorder-Induced Second-Order Topological Insulators in Three Dimensions. PHYSICAL REVIEW LETTERS 2021; 126:206404. [PMID: 34110216 DOI: 10.1103/physrevlett.126.206404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2021] [Accepted: 04/22/2021] [Indexed: 06/12/2023]
Abstract
Higher-order topological insulators are established as topological crystalline insulators protected by crystalline symmetries. One celebrated example is the second-order topological insulator in three dimensions that hosts chiral hinge modes protected by crystalline symmetries. Since amorphous solids are ubiquitous, it is important to ask whether such a second-order topological insulator can exist in an amorphous system without any spatial order. Here, we predict the existence of a second-order topological insulating phase in an amorphous system without any crystalline symmetry. Such a topological phase manifests in the winding number of the quadrupole moment, the quantized longitudinal conductance, and the hinge states. Furthermore, in stark contrast to the viewpoint that structural disorder should be detrimental to the higher-order topological phase, we remarkably find that structural disorder can induce a second-order topological insulator from a topologically trivial phase in a regular geometry. We finally demonstrate the existence of a second-order topological phase in amorphous systems with time-reversal symmetry.
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Affiliation(s)
- Jiong-Hao Wang
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
| | - Yan-Bin Yang
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
| | - Ning Dai
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
| | - Yong Xu
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
- Shanghai Qi Zhi Institute, Shanghai 200030, People's Republic of China
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7
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Ma C, Wang Q, Mills S, Chen X, Deng B, Yuan S, Li C, Watanabe K, Taniguchi T, Du X, Zhang F, Xia F. Moiré Band Topology in Twisted Bilayer Graphene. NANO LETTERS 2020; 20:6076-6083. [PMID: 32692566 DOI: 10.1021/acs.nanolett.0c02131] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Recently twisted bilayer graphene (t-BLG) has emerged as a strongly correlated physical platform. Besides the apparent significance of band flatness, band topology may be another critical element in t-BLG and yet receives much less attention. Here we report the compelling evidence for nontrivial noninteracting Moiré band topology in t-BLG through a systematic nonlocal transport study and a K-theory examination. The nontrivial topology manifests itself as two pronounced nonlocal responses in the electron and hole superlattice gaps. We show that the nonlocal responses are robust to the twist angle and edge termination, exhibiting a universal scaling law. We elucidate that, although Berry curvature is symmetry-trivialized, two nontrivial Z2 invariants characterize the Moiré Dirac bands, validating the topological origin of the observed nonlocal responses. Our findings not only provide a new perspective for understanding the strongly correlated t-BLG but also suggest a potential strategy to achieve topological metamaterials from trivial vdW materials.
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Affiliation(s)
- Chao Ma
- Department of Electrical Engineering, Yale University, New Haven, Connecticut 06511, United States
| | - Qiyue Wang
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 7508, United States
| | - Scott Mills
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, United States
| | - Xiaolong Chen
- Department of Electrical Engineering, Yale University, New Haven, Connecticut 06511, United States
| | - Bingchen Deng
- Department of Electrical Engineering, Yale University, New Haven, Connecticut 06511, United States
| | - Shaofan Yuan
- Department of Electrical Engineering, Yale University, New Haven, Connecticut 06511, United States
| | - Cheng Li
- Department of Electrical Engineering, Yale University, New Haven, Connecticut 06511, United States
| | - Kenji Watanabe
- National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Takashi Taniguchi
- National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Xu Du
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, United States
| | - Fan Zhang
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 7508, United States
| | - Fengnian Xia
- Department of Electrical Engineering, Yale University, New Haven, Connecticut 06511, United States
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8
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Daido A, Yoshida T, Yanase Y. Z_{4} Topological Superconductivity in UCoGe. PHYSICAL REVIEW LETTERS 2019; 122:227001. [PMID: 31283273 DOI: 10.1103/physrevlett.122.227001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2019] [Indexed: 06/09/2023]
Abstract
Topological nonsymmorphic crystalline superconductivity (TNCS) is an intriguing phase of matter, offering a platform to study the interplay between topology, superconductivity, and nonsymmorphic crystalline symmetries. Interestingly, some of TNCSs are classified into Z_{4} topological phases, which have unique surface states referred to as a Möbius strip or an hourglass, and they have not been achieved in symmorphic superconductors. However, material realization of Z_{4} TNCS has never been known, to the best of our knowledge. Here, we propose that the paramagnetic superconducting phase of UCoGe under pressure is a promising candidate of Z_{4}-nontrivial TNCS enriched by glide symmetry. We evaluate Z_{4} invariants of UCoGe by deriving the formulas relating Z_{4} invariants to the topology of Fermi surfaces. Applying the formulas and previous ab initio calculations, we clarify that three odd-parity representations out of four are Z_{4}-nontrivial TNCS, whereas the other is also Z_{2}-nontrivial TNCS. We also discuss possible Z_{4} TNCS in CrAs and related materials.
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Affiliation(s)
- Akito Daido
- Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Tsuneya Yoshida
- Department of Physics, University of Tsukuba, Ibaraki 305-8571, Japan
| | - Youichi Yanase
- Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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9
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Yarmohammadi M, Mirabbaszadeh K. A methodical study of quantum phase engineering in topological crystalline insulator SnTe and related alloys. Phys Chem Chem Phys 2019; 21:21633-21650. [DOI: 10.1039/c9cp03655e] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A detailed analysis of the perturbation effects on the quantum phase of SnTe(001) surface states.
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Affiliation(s)
- Mohsen Yarmohammadi
- Department of Energy Engineering and Physics
- Amirkabir University of Technology
- Tehran
- Iran
| | - Kavoos Mirabbaszadeh
- Department of Energy Engineering and Physics
- Amirkabir University of Technology
- Tehran
- Iran
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10
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On Anderson Localization and Chiral Anomaly in Disordered Time-Reversal Invariant Weyl Semimetals: Nonperturbative and Berry Phase Effects. Sci Rep 2018; 8:6719. [PMID: 29712919 PMCID: PMC5928164 DOI: 10.1038/s41598-018-22466-8] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2017] [Accepted: 05/31/2017] [Indexed: 11/08/2022] Open
Abstract
Weyl semimetal, a three-dimensional electronic system with relativistic linear energy dispersion around gapless points carrying nontrivial Berry charge, is predicted to exhibit a wealth of unique response and transport properties. A crucial question is whether those properties are robust against disorder and whether Anderson localization occurs. In this work, the effects of nonperturbative topological (vortex loop) excitations and Berry phase in disordered time-reversal invariant 3d Weyl semimetal are studied. It is shown that the chiral symmetry is restored in the nonlinear sigma model describing the diffusons upon disorder average as any net topological term and its delocalization result do not take effect at sufficiently short length scales. Anderson localization occurs at sufficiently strong disorder and we predict that chirality and related phenomena disappear at such transition. Nevertheless, we uncover a mechanism that originates from Berry phase that impedes such localization effect. We show the occurrence of destructive interference between the vortex loops and between scattering paths due to the the vortex loops' Berry phase which resists the Anderson localization. We emphasize the applicability of our theory to the candidate Weyl materials where we point out the consistency of our theory with a recent experimental finding of the absent chiral anomaly in a noncentrosymmetric Weyl semimetal.
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11
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Enhanced electron dephasing in three-dimensional topological insulators. Nat Commun 2017; 8:16071. [PMID: 28695894 PMCID: PMC5508222 DOI: 10.1038/ncomms16071] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2017] [Accepted: 05/25/2017] [Indexed: 11/08/2022] Open
Abstract
Study of the dephasing in electronic systems is not only important for probing the nature of their ground states, but also crucial to harnessing the quantum coherence for information processing. In contrast to well-studied conventional metals and semiconductors, it remains unclear which mechanism is mainly responsible for electron dephasing in three-dimensional topological insulators (TIs). Here, we report on using weak antilocalization effect to measure the dephasing rates in highly tunable (Bi,Sb)2Te3 thin films. As the transport is varied from a bulk-conducting regime to surface-dominant transport, the dephasing rate is observed to evolve from a linear temperature dependence to a sublinear power-law dependence. Although the former is consistent with the Nyquist electron-electron interactions commonly seen in ordinary 2D systems, the latter leads to enhanced electron dephasing at low temperatures and is attributed to the coupling between the surface states and the localized charge puddles in the bulk of 3D TIs.
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12
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Sato M, Ando Y. Topological superconductors: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2017; 80:076501. [PMID: 28367833 DOI: 10.1088/1361-6633/aa6ac7] [Citation(s) in RCA: 247] [Impact Index Per Article: 35.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
This review elaborates pedagogically on the fundamental concept, basic theory, expected properties, and materials realizations of topological superconductors. The relation between topological superconductivity and Majorana fermions are explained, and the difference between dispersive Majorana fermions and a localized Majorana zero mode is emphasized. A variety of routes to topological superconductivity are explained with an emphasis on the roles of spin-orbit coupling. Present experimental situations and possible signatures of topological superconductivity are summarized with an emphasis on intrinsic topological superconductors.
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Affiliation(s)
- Masatoshi Sato
- Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
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13
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Xu Y, Chiu J, Miao L, He H, Alpichshev Z, Kapitulnik A, Biswas RR, Wray LA. Disorder enabled band structure engineering of a topological insulator surface. Nat Commun 2017; 8:14081. [PMID: 28155858 PMCID: PMC5296772 DOI: 10.1038/ncomms14081] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2016] [Accepted: 11/23/2016] [Indexed: 11/23/2022] Open
Abstract
Three-dimensional topological insulators are bulk insulators with Z2 topological electronic order that gives rise to conducting light-like surface states. These surface electrons are exceptionally resistant to localization by non-magnetic disorder, and have been adopted as the basis for a wide range of proposals to achieve new quasiparticle species and device functionality. Recent studies have yielded a surprise by showing that in spite of resisting localization, topological insulator surface electrons can be reshaped by defects into distinctive resonance states. Here we use numerical simulations and scanning tunnelling microscopy data to show that these resonance states have significance well beyond the localized regime usually associated with impurity bands. At native densities in the model Bi2X3 (X=Bi, Te) compounds, defect resonance states are predicted to generate a new quantum basis for an emergent electron gas that supports diffusive electrical transport. The surface electrons in a topological insulator are resistant to localization by nonmagnetic disorder, but are affected by lattice disorder. Here, the authors show that resonance states near lattice defects on the surface have significance beyond the localized regime usually associated with impurity bands.
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Affiliation(s)
- Yishuai Xu
- Department of Physics, New York University, New York, New York 10003, USA
| | - Janet Chiu
- Department of Physics, New York University, New York, New York 10003, USA
| | - Lin Miao
- Department of Physics, New York University, New York, New York 10003, USA.,Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Haowei He
- Department of Physics, New York University, New York, New York 10003, USA
| | - Zhanybek Alpichshev
- Massachusetts Institute of Technology, Department of Physics, Cambridge, Massachusetts 02139, USA.,Department of Physics, Stanford University, Stanford, California 94305, USA
| | - A Kapitulnik
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Rudro R Biswas
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
| | - L Andrew Wray
- Department of Physics, New York University, New York, New York 10003, USA.,NYU-ECNU Institute of Physics at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
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14
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Zhu L, Wang SS, Guan S, Liu Y, Zhang T, Chen G, Yang SA. Blue Phosphorene Oxide: Strain-Tunable Quantum Phase Transitions and Novel 2D Emergent Fermions. NANO LETTERS 2016; 16:6548-6554. [PMID: 27648670 DOI: 10.1021/acs.nanolett.6b03208] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Tunable quantum phase transitions and novel emergent fermions in solid-state materials are fascinating subjects of research. Here, we propose a new stable two-dimensional (2D) material, the blue phosphorene oxide (BPO), which exhibits both. On the basis of first-principles calculations, we show that its equilibrium state is a narrow-bandgap semiconductor with three bands at low energy. Remarkably, a moderate strain can drive a semiconductor-to-semimetal quantum phase transition in BPO. At the critical transition point, the three bands cross at a single point at Fermi level, around which the quasiparticles are a novel type of 2D pseudospin-1 fermions. Going beyond the transition, the system becomes a symmetry-protected semimetal, for which the conduction and valence bands touch quadratically at a single Fermi point that is protected by symmetry, and the low-energy quasiparticles become another novel type of 2D double Weyl fermions. We construct effective models characterizing the phase transition and these novel emergent fermions, and we point out several exotic effects, including super Klein tunneling, supercollimation, and universal optical absorbance. Our result reveals BPO as an intriguing platform for the exploration of fundamental properties of quantum phase transitions and novel emergent fermions and also suggests its great potential in nanoscale device applications.
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Affiliation(s)
- Liyan Zhu
- School of Physics and Electronic & Electrical Engineering, and Jiangsu Key Laboratory of Modern Measurement Technology and Intelligent Systems, Huaiyin Normal University , Huai'an, Jiangsu 223300, P. R. China
| | - Shan-Shan Wang
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design , Singapore, 487372, Singapore
| | - Shan Guan
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design , Singapore, 487372, Singapore
| | - Ying Liu
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design , Singapore, 487372, Singapore
| | - Tingting Zhang
- School of Physics and Electronic & Electrical Engineering, and Jiangsu Key Laboratory of Modern Measurement Technology and Intelligent Systems, Huaiyin Normal University , Huai'an, Jiangsu 223300, P. R. China
| | - Guibin Chen
- School of Physics and Electronic & Electrical Engineering, and Jiangsu Key Laboratory of Modern Measurement Technology and Intelligent Systems, Huaiyin Normal University , Huai'an, Jiangsu 223300, P. R. China
| | - Shengyuan A Yang
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design , Singapore, 487372, Singapore
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15
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Fulga IC, Pikulin DI, Loring TA. Aperiodic Weak Topological Superconductors. PHYSICAL REVIEW LETTERS 2016; 116:257002. [PMID: 27391744 DOI: 10.1103/physrevlett.116.257002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/22/2015] [Indexed: 06/06/2023]
Abstract
Weak topological phases are usually described in terms of protection by the lattice translation symmetry. Their characterization explicitly relies on periodicity since weak invariants are expressed in terms of the momentum-space torus. We prove the compatibility of weak topological superconductors with aperiodic systems, such as quasicrystals. We go beyond usual descriptions of weak topological phases and introduce a novel, real-space formulation of the weak invariant, based on the Clifford pseudospectrum. A nontrivial value of this index implies a nontrivial bulk phase, which is robust against disorder and hosts localized zero-energy modes at the edge. Our recipe for determining the weak invariant is directly applicable to any finite-sized system, including disordered lattice models. This direct method enables a quantitative analysis of the level of disorder the topological protection can withstand.
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Affiliation(s)
- I C Fulga
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - D I Pikulin
- Department of Physics and Astronomy and Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
| | - T A Loring
- Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131, USA
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16
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Pauly C, Rasche B, Koepernik K, Richter M, Borisenko S, Liebmann M, Ruck M, van den Brink J, Morgenstern M. Electronic Structure of the Dark Surface of the Weak Topological Insulator Bi14Rh3I9. ACS NANO 2016; 10:3995-4003. [PMID: 26967061 DOI: 10.1021/acsnano.6b00841] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Compound Bi14Rh3I9 consists of ionic stacks of intermetallic [(Bi4Rh)3I](2+) and insulating [Bi2I8](2-) layers and has been identified to be a weak topological insulator. Scanning tunneling microscopy revealed the robust edge states at all step edges of the cationic layer as a topological fingerprint. However, these edge states are found 0.25 eV below the Fermi level, which is an obstacle for transport experiments. Here, we address this obstacle by comparing results of density functional slab calculations with scanning tunneling spectroscopy and angle-resolved photoemission spectroscopy. We show that the n-type doping of the intermetallic layer is intrinsically caused by the polar surface and is well-screened toward the bulk. In contrast, the anionic "spacer" layer shows a gap at the Fermi level, both on the surface and in the bulk; that is, it is not surface-doped due to iodine desorption. The well-screened surface dipole implies that a buried edge state, probably already below a single spacer layer, is located at the Fermi level. Consequently, a multilayer step covered by a spacer layer could provide access to the transport properties of the topological edge states. In addition, we find a lateral electronic modulation of the topologically nontrivial surface layer, which is traced back to the coupling with the underlying zigzag chain structure of the spacer layer.
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Affiliation(s)
- Christian Pauly
- II. Institute of Physics B and JARA-FIT, RWTH Aachen University , D-52074 Aachen, Germany
| | - Bertold Rasche
- Department of Chemistry and Food Chemistry, TU Dresden , D-01062 Dresden, Germany
| | - Klaus Koepernik
- Leibniz Institute for Solid State and Materials Research, IFW Dresden e.V. , P.O. Box 270116, D-01171 Dresden, Germany
- Dresden Center for Computational Materials Science (DCMS), TU Dresden , D-01069 Dresden, Germany
| | - Manuel Richter
- Leibniz Institute for Solid State and Materials Research, IFW Dresden e.V. , P.O. Box 270116, D-01171 Dresden, Germany
- Dresden Center for Computational Materials Science (DCMS), TU Dresden , D-01069 Dresden, Germany
| | - Sergey Borisenko
- Leibniz Institute for Solid State and Materials Research, IFW Dresden e.V. , P.O. Box 270116, D-01171 Dresden, Germany
| | - Marcus Liebmann
- II. Institute of Physics B and JARA-FIT, RWTH Aachen University , D-52074 Aachen, Germany
| | - Michael Ruck
- Department of Chemistry and Food Chemistry, TU Dresden , D-01062 Dresden, Germany
- Max Planck Institute for Chemical Physics of Solids , D-01187 Dresden, Germany
| | - Jeroen van den Brink
- Leibniz Institute for Solid State and Materials Research, IFW Dresden e.V. , P.O. Box 270116, D-01171 Dresden, Germany
- Dresden Center for Computational Materials Science (DCMS), TU Dresden , D-01069 Dresden, Germany
| | - Markus Morgenstern
- II. Institute of Physics B and JARA-FIT, RWTH Aachen University , D-52074 Aachen, Germany
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17
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Pretti M. Polymer models with competing collapse interactions on Husimi and Bethe lattices. Phys Rev E 2016; 93:032110. [PMID: 27078295 DOI: 10.1103/physreve.93.032110] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2015] [Indexed: 11/07/2022]
Abstract
In the framework of Husimi and Bethe lattices, we investigate a generalized polymer model that incorporates as special cases different models previously studied in the literature, namely, the standard interacting self-avoiding walk, the interacting self-avoiding trail, and the vertex-interacting self-avoiding walk. These models are characterized by different microscopic interactions, giving rise, in the two-dimensional case, to collapse transitions of an apparently different nature. We expect that our results, even though of a mean-field type, could provide some useful information to elucidate the role of such different θ points in the polymer phase diagram. These issues are at the core of a long-standing unresolved debate.
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Affiliation(s)
- M Pretti
- Consiglio Nazionale delle Ricerche-Istituto dei Sistemi Complessi (CNR-ISC), Dipartimento di Scienze Applicate e Tecnologia (DISAT), Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy
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18
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Rasche B, Isaeva A, Ruck M, Koepernik K, Richter M, van den Brink J. Correlation between topological band character and chemical bonding in a Bi14Rh3I9-based family of insulators. Sci Rep 2016; 6:20645. [PMID: 26875525 PMCID: PMC4753431 DOI: 10.1038/srep20645] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2015] [Accepted: 12/16/2015] [Indexed: 11/12/2022] Open
Abstract
Recently the presence of topologically protected edge-states in Bi14Rh3I9 was confirmed by scanning tunnelling microscopy consolidating this compound as a weak 3D topological insulator (TI). Here, we present a density-functional-theory-based study on a family of TIs derived from the Bi14Rh3I9 parent structure via substitution of Ru, Pd, Os, Ir and Pt for Rh. Comparative analysis of the band-structures throughout the entire series is done by means of a unified minimalistic tight-binding model that evinces strong similarity between the quantum-spin-Hall (QSH) layer in Bi14Rh3I9 and graphene in terms of -molecular orbitals. Topologically non-trivial energy gaps are found for the Ir-, Rh-, Pt- and Pd-based systems, whereas the Os- and Ru-systems remain trivial. Furthermore, the energy position of the metal -band centre is identified as the parameter which governs the evolution of the topological character of the band structure through the whole family of TIs. The -band position is shown to correlate with the chemical bonding within the QSH layers, thus revealing how the chemical nature of the constituents affects the topological band character.
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Affiliation(s)
- Bertold Rasche
- Department of Chemistry and Food Chemistry, TU Dresden, D-01062 Dresden, Germany
| | - Anna Isaeva
- Department of Chemistry and Food Chemistry, TU Dresden, D-01062 Dresden, Germany
| | - Michael Ruck
- Department of Chemistry and Food Chemistry, TU Dresden, D-01062 Dresden, Germany.,Max Planck Institute for Chemical Physics of Solids, D-01187 Dresden, Germany
| | - Klaus Koepernik
- Leibniz Institute for Solid State and Materials Research, IFW Dresden, D-01069 Dresden, Germany.,Dresden Center for Computational Materials Science (DCMS), TU Dresden, D-01069 Dresden, Germany
| | - Manuel Richter
- Leibniz Institute for Solid State and Materials Research, IFW Dresden, D-01069 Dresden, Germany.,Dresden Center for Computational Materials Science (DCMS), TU Dresden, D-01069 Dresden, Germany
| | - Jeroen van den Brink
- Leibniz Institute for Solid State and Materials Research, IFW Dresden, D-01069 Dresden, Germany.,Dresden Center for Computational Materials Science (DCMS), TU Dresden, D-01069 Dresden, Germany.,Department of Physics, TU Dresden, D-01069 Dresden, Germany
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19
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Liu CC, Zhou JJ, Yao Y, Zhang F. Weak Topological Insulators and Composite Weyl Semimetals: β-Bi4X4 (X=Br, I). PHYSICAL REVIEW LETTERS 2016; 116:066801. [PMID: 26919004 DOI: 10.1103/physrevlett.116.066801] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2015] [Indexed: 06/05/2023]
Abstract
While strong topological insulators (STIs) were experimentally realized soon after they were theoretically predicted, a weak topological insulator (WTI) has yet to be unambiguously confirmed. A major obstacle is the lack of distinct natural cleavage surfaces to test the surface selective hallmark of a WTI. With a new scheme, we discover that β-Bi4X4 (X=Br, I), dynamically stable or synthesized before, can be a prototype WTI with two natural cleavage surfaces, where two anisotropic Dirac cones stabilize and annihilate, respectively. We further find four surface-state Lifshitz transitions under charge doping and two bulk topological phase transitions under uniaxial strain. Near the WTI-STI transition, there emerges a novel Weyl semimetal phase, in which the Fermi arcs generically appear at both cleavage surfaces whereas the Fermi circle only appears at one selected surface.
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Affiliation(s)
- Cheng-Cheng Liu
- Department of Physics, University of Texas at Dallas, Richardson, Texas 75080, USA
- School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Jin-Jian Zhou
- School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Yugui Yao
- School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Fan Zhang
- Department of Physics, University of Texas at Dallas, Richardson, Texas 75080, USA
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20
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Mross DF, Essin A, Alicea J, Stern A. Anomalous Quasiparticle Symmetries and Non-Abelian Defects on Symmetrically Gapped Surfaces of Weak Topological Insulators. PHYSICAL REVIEW LETTERS 2016; 116:036803. [PMID: 26849608 DOI: 10.1103/physrevlett.116.036803] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2015] [Indexed: 06/05/2023]
Abstract
We show that boundaries of 3D weak topological insulators can become gapped by strong interactions while preserving all symmetries, leading to Abelian surface topological order. The anomalous nature of weak topological insulator surfaces manifests itself in a nontrivial action of symmetries on the quasiparticles; most strikingly, translations change the anyon types in a manner impossible in strictly 2D systems with the same symmetry. As a further consequence, screw dislocations form non-Abelian defects that trap Z_{4} parafermion zero modes.
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Affiliation(s)
- David F Mross
- Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
| | - Andrew Essin
- Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
| | - Jason Alicea
- Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
- Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA
| | - Ady Stern
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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21
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Roychowdhury S, Shenoy US, Waghmare UV, Biswas K. Tailoring of Electronic Structure and Thermoelectric Properties of a Topological Crystalline Insulator by Chemical Doping. Angew Chem Int Ed Engl 2015; 54:15241-5. [PMID: 26509937 DOI: 10.1002/anie.201508492] [Citation(s) in RCA: 47] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2015] [Revised: 10/08/2015] [Indexed: 11/07/2022]
Affiliation(s)
- Subhajit Roychowdhury
- New Chemistry Unit, Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR), Jakkur P.O., Bangalore (India) http://www.jncasr.ac.in/kanishka/
| | - U Sandhya Shenoy
- Theoretical Science Unit, Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR), Jakkur P.O., Bangalore 560 064 (India)
| | - Umesh V Waghmare
- Theoretical Science Unit, Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR), Jakkur P.O., Bangalore 560 064 (India)
| | - Kanishka Biswas
- New Chemistry Unit, Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR), Jakkur P.O., Bangalore (India) http://www.jncasr.ac.in/kanishka/.
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22
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Roychowdhury S, Shenoy US, Waghmare UV, Biswas K. Tailoring of Electronic Structure and Thermoelectric Properties of a Topological Crystalline Insulator by Chemical Doping. Angew Chem Int Ed Engl 2015. [DOI: 10.1002/ange.201508492] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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23
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Young SM, Kane CL. Dirac Semimetals in Two Dimensions. PHYSICAL REVIEW LETTERS 2015; 115:126803. [PMID: 26431004 DOI: 10.1103/physrevlett.115.126803] [Citation(s) in RCA: 135] [Impact Index Per Article: 15.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2015] [Indexed: 06/05/2023]
Abstract
Graphene is famous for being a host of 2D Dirac fermions. However, spin-orbit coupling introduces a small gap, so that graphene is formally a quantum spin Hall insulator. Here we present symmetry-protected 2D Dirac semimetals, which feature Dirac cones at high-symmetry points that are not gapped by spin-orbit interactions and exhibit behavior distinct from both graphene and 3D Dirac semimetals. Using a two-site tight-binding model, we construct representatives of three possible distinct Dirac semimetal phases and show that single symmetry-protected Dirac points are impossible in two dimensions. An essential role is played by the presence of nonsymmorphic space group symmetries. We argue that these symmetries tune the system to the boundary between a 2D topological and trivial insulator. By breaking the symmetries we are able to access trivial and topological insulators as well as Weyl semimetal phases.
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Affiliation(s)
- Steve M Young
- Center for Computational Materials Science, U.S. Naval Research Laboratory, Washington, D.C. 20375, USA
| | - Charles L Kane
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323, USA
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24
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Di Sante D, Barone P, Plekhanov E, Ciuchi S, Picozzi S. Robustness of Rashba and Dirac Fermions against Strong Disorder. Sci Rep 2015; 5:11285. [PMID: 26067146 PMCID: PMC4650895 DOI: 10.1038/srep11285] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2014] [Accepted: 04/30/2015] [Indexed: 11/13/2022] Open
Abstract
By addressing the interplay between substitutional disorder and spin-orbit-coupling in chalcogenide alloys, we predict a strong robustness of spectral features at the Fermi energy. Indeed, supplementing our state of the art first-principles calculations with modeling analysis, we show that the disorder self-energy is vanishingly small close to the band gap, thus i) allowing for bulk Rashba-like spin splitting to be observed in ferroelectric alloys by means of Angle Resolved PhotoEmission Spectroscopy, and ii) protecting the band-character inversion related to the topological transition in recently discovered Topological Crystalline Insulators. Such a protection against strong disorder, which we demonstrate to be general for three dimensional Dirac systems, has potential and valuable implications for novel technologies, as spintronics and/or spinorbitronics.
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Affiliation(s)
- Domenico Di Sante
- 1] Consiglio Nazionale delle Ricerche (CNR-SPIN), Via Vetoio, L'Aquila, Italy [2] Department of Physical and Chemical Sciences, University of L'Aquila, Via Vetoio 10, I-67010 L'Aquila, Italy
| | - Paolo Barone
- Consiglio Nazionale delle Ricerche (CNR-SPIN), Via Vetoio, L'Aquila, Italy
| | - Evgeny Plekhanov
- Consiglio Nazionale delle Ricerche (CNR-SPIN), Via Vetoio, L'Aquila, Italy
| | - Sergio Ciuchi
- 1] Department of Physical and Chemical Sciences, University of L'Aquila, Via Vetoio 10, I-67010 L'Aquila, Italy [2] Consiglio Nazionale delle Ricerche (CNR-ISC), Via dei Taurini, Rome, Italy
| | - Silvia Picozzi
- Consiglio Nazionale delle Ricerche (CNR-SPIN), Via Vetoio, L'Aquila, Italy
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25
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Liao J, Ou Y, Feng X, Yang S, Lin C, Yang W, Wu K, He K, Ma X, Xue QK, Li Y. Observation of Anderson localization in ultrathin films of three-dimensional topological insulators. PHYSICAL REVIEW LETTERS 2015; 114:216601. [PMID: 26066450 DOI: 10.1103/physrevlett.114.216601] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2015] [Indexed: 06/04/2023]
Abstract
Anderson localization, the absence of diffusive transport in disordered systems, has been manifested as hopping transport in numerous electronic systems, whereas in recently discovered topological insulators it has not been directly observed. Here, we report experimental demonstration of a crossover from diffusive transport in the weak antilocalization regime to variable range hopping transport in the Anderson localization regime with ultrathin (Bi_{1-x}Sb_{x})_{2}Te_{3} films. As disorder becomes stronger, negative magnetoconductivity due to the weak antilocalization is gradually suppressed, and eventually, positive magnetoconductivity emerges when the electron system becomes strongly localized. This work reveals the critical role of disorder in the quantum transport properties of ultrathin topological insulator films, in which theories have predicted rich physics related to topological phase transitions.
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Affiliation(s)
- Jian Liao
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Yunbo Ou
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Xiao Feng
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Shuo Yang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Chaojing Lin
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Wenmin Yang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Kehui Wu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Ke He
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Xucun Ma
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Qi-Kun Xue
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Yongqing Li
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
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26
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Wang C, Su Y, Avishai Y, Meir Y, Wang XR. Band of critical States in anderson localization in a strong magnetic field with random spin-orbit scattering. PHYSICAL REVIEW LETTERS 2015; 114:096803. [PMID: 25793840 DOI: 10.1103/physrevlett.114.096803] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2014] [Indexed: 06/04/2023]
Abstract
The Anderson localization problem for a noninteracting two-dimensional electron gas subject to a strong magnetic field, disordered potential, and spin-orbit coupling is studied numerically on a square lattice. The nature of the corresponding localization-delocalization transition and the properties of the pertinent extended states depend on whether the spin-orbit coupling is uniform or fully random. For uniform spin-orbit coupling (such as Rashba coupling due to a uniform electric field), there is a band of metallic extended states in the center of a Landau band as in a "standard" Anderson metal-insulator transition. However, for fully random spin-orbit coupling, the familiar pattern of Landau bands disappears. Instead, there is a central band of critical states with definite fractal structure separated at two critical energies from two side bands of localized states. Moreover, finite size scaling analysis suggests that for this novel transition, on the localized side of a critical energy E_{c}, the localization length diverges as ξ(E)∝exp(α/sqrt[|E-E_{c}|]), a behavior which, together with the emergence of a band of critical states, is reminiscent of a Berezinskii-Kosterlitz-Thouless transition.
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Affiliation(s)
- C Wang
- Physics Department, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
- HKUST Shenzhen Research Institute, Shenzhen 518057, China
| | - Ying Su
- Physics Department, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
- HKUST Shenzhen Research Institute, Shenzhen 518057, China
| | - Y Avishai
- Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva, Israel
| | - Yigal Meir
- Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva, Israel
| | - X R Wang
- Physics Department, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
- HKUST Shenzhen Research Institute, Shenzhen 518057, China
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27
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Liu H, Jiang H, Sun QF, Xie XC. Dephasing effect on backscattering of helical surface states in 3D topological insulators. PHYSICAL REVIEW LETTERS 2014; 113:046805. [PMID: 25105645 DOI: 10.1103/physrevlett.113.046805] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2013] [Indexed: 06/03/2023]
Abstract
We analyze the dephasing effect on the backscattering behavior of the helical surface states in 3D topological insulators. We show that the combination of dephasing and impurity scattering can cause backscattering in the helical states. Especially for the charge impurity case, the backscattering cross section becomes extremely large around the Dirac point. This large backscattering behavior can lead to the anomalous "gaplike" features found in recent experiments [T. Sato et al., Nat. Phys. 7, 840 (2011)].
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Affiliation(s)
- Haiwen Liu
- International Center for Quantum Materials and School of Physics, Peking University, Beijing 100871, China and Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Hua Jiang
- College of Physics, Optoelectronics and Energy, Soochow University, Suzhou 215006, China
| | - Qing-Feng Sun
- International Center for Quantum Materials and School of Physics, Peking University, Beijing 100871, China and Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - X C Xie
- International Center for Quantum Materials and School of Physics, Peking University, Beijing 100871, China and Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
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28
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Amanatidis E, Kleftogiannis I, Katsanos DE, Evangelou SN. Critical level statistics for weakly disordered graphene. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:155601. [PMID: 24675743 DOI: 10.1088/0953-8984/26/15/155601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
In two dimensions chaotic level statistics with the Wigner spacing distribution P(S) is expected for massless fermions in the Dirac region. The obtained P(S) for weakly disordered finite graphene samples with zigzag edges turns out, however, to be neither chaotic (Wigner) nor localized (Poisson). It is similar to the intermediate statistics at the critical point of the Anderson metal-insulator transition. The quantum transport of finite graphene for weak disorder, with critical level statistics can occur via edge states as in topological insulators, and for strong disorder, graphene behaves as an ordinary Anderson insulator with Poisson statistics.
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Affiliation(s)
- E Amanatidis
- Department of Physics, University of Ioannina, Ioannina 45110, Greece
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29
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Fang C, Gilbert MJ, Bernevig BA. New class of topological superconductors protected by magnetic group symmetries. PHYSICAL REVIEW LETTERS 2014; 112:106401. [PMID: 24679310 DOI: 10.1103/physrevlett.112.106401] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2013] [Indexed: 06/03/2023]
Abstract
We study a new type of three-dimensional topological superconductor that exhibits Majorana zero modes (MZM) protected by a magnetic group symmetry, a combined antiunitary symmetry composed of a mirror reflection and time reversal. This new symmetry enhances the noninteracting topological classification of a superconducting vortex from Z2 to Z, indicating that multiple MZMs can coexist at the end of one magnetic vortex of unit flux. Especially, we show that a vortex binding two MZMs can be realized on the (001) surface of a topological crystalline insulator SnTe with proximity induced BCS Cooper pairing, or in bulk superconductor InxSn1-xTe.
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Affiliation(s)
- Chen Fang
- Department of Physics, University of Illinois, Urbana, Illinois 61801-3080, USA and Micro and Nanotechnology Laboratory, University of Illinois, Urbana, Illinois 61801, USA and Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Matthew J Gilbert
- Department of Electrical and Computer Engineering, University of Illinois, Urbana, Illinois 61801, USA and Micro and Nanotechnology Laboratory, University of Illinois, Urbana, Illinois 61801, USA
| | - B Andrei Bernevig
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
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30
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Ueno Y, Yamakage A, Tanaka Y, Sato M. Symmetry-protected Majorana fermions in topological crystalline superconductors: theory and application to Sr2RuO4. PHYSICAL REVIEW LETTERS 2013; 111:087002. [PMID: 24010466 DOI: 10.1103/physrevlett.111.087002] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2013] [Indexed: 06/02/2023]
Abstract
Crystal point group symmetry is shown to protect Majorana fermions (MFs) in spinfull superconductors (SCs). We elucidate the condition necessary to obtain MFs protected by the point group symmetry. We argue that superconductivity in Sr2RuO4 hosts a topological phase transition to a topological crystalline SC, which accompanies a d-vector rotation under a magnetic field along the c axis. Taking all three bands and spin-orbit interactions into account, symmetry-protected MFs in the topological crystalline SC are identified. Detection of such MFs provides evidence of the d-vector rotation in Sr2RuO4 expected from Knight shift measurements but not yet verified.
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Affiliation(s)
- Yuji Ueno
- Department of Applied Physics, Nagoya University, Nagoya 464-8603, Japan
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31
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Zhang F, Kane CL, Mele EJ. Topological mirror superconductivity. PHYSICAL REVIEW LETTERS 2013; 111:056403. [PMID: 23952424 DOI: 10.1103/physrevlett.111.056403] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2013] [Indexed: 06/02/2023]
Abstract
We demonstrate the existence of topological superconductors (SCs) protected by mirror and time-reversal symmetries. D-dimensional (D=1, 2, 3) crystalline SCs are characterized by 2(D-1) independent integer topological invariants, which take the form of mirror Berry phases. These invariants determine the distribution of Majorana modes on a mirror symmetric boundary. The parity of total mirror Berry phase is the Z(2) index of a class DIII SC, implying that a DIII topological SC with a mirror line must also be a topological mirror SC but not vice versa and that a DIII SC with a mirror plane is always time-reversal trivial but can be mirror topological. We introduce representative models and suggest experimental signatures in feasible systems. Advances in quantum computing, the case for nodal SCs, the case for class D, and topological SCs protected by rotational symmetries are pointed out.
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Affiliation(s)
- Fan Zhang
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
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32
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Väyrynen JI, Goldstein M, Glazman LI. Helical edge resistance introduced by charge puddles. PHYSICAL REVIEW LETTERS 2013; 110:216402. [PMID: 23745899 DOI: 10.1103/physrevlett.110.216402] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2013] [Indexed: 06/02/2023]
Abstract
We study the influence of electron puddles created by doping of a 2D topological insulator on its helical edge conductance. A single puddle is modeled by a quantum dot tunnel coupled to the helical edge. It may lead to significant inelastic backscattering within the edge because of the long electron dwelling time in the dot. We find the resulting correction to the perfect edge conductance. Generalizing to multiple puddles, we assess the dependence of the helical edge resistance on the temperature and doping level and compare it with recent experimental data.
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Affiliation(s)
- Jukka I Väyrynen
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
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Bardarson JH, Moore JE. Quantum interference and Aharonov-Bohm oscillations in topological insulators. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2013; 76:056501. [PMID: 23552181 DOI: 10.1088/0034-4885/76/5/056501] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Topological insulators (TIs) have an insulating bulk but a metallic surface. In the simplest case, the surface electronic structure of a three-dimensional (3D) TI is described by a single two-dimensional (2D) Dirac cone. A single 2D Dirac fermion cannot be realized in an isolated 2D system with time-reversal symmetry, but rather owes its existence to the topological properties of the 3D bulk wavefunctions. The transport properties of such a surface state are of considerable current interest; they have some similarities with graphene, which also realizes Dirac fermions, but have several unique features in their response to magnetic fields. In this review we give an overview of some of the main quantum transport properties of TI surfaces. We focus on the efforts to use quantum interference phenomena, such as weak anti-localization and the Aharonov-Bohm effect, to verify in a transport experiment the Dirac nature of the surface state and its defining properties. In addition to explaining the basic ideas and predictions of the theory, we provide a survey of recent experimental work.
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Affiliation(s)
- Jens H Bardarson
- Department of Physics, University of California, Berkeley, CA 94720, USA
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Verbin M, Zilberberg O, Kraus YE, Lahini Y, Silberberg Y. Observation of topological phase transitions in photonic quasicrystals. PHYSICAL REVIEW LETTERS 2013; 110:076403. [PMID: 25166388 DOI: 10.1103/physrevlett.110.076403] [Citation(s) in RCA: 57] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2012] [Indexed: 06/03/2023]
Abstract
Topological insulators and topological superconductors are distinguished by their bulk phase transitions and gapless states at a sharp boundary with the vacuum. Quasicrystals have recently been found to be topologically nontrivial. In quasicrystals, the bulk phase transitions occur in the same manner as standard topological materials, but their boundary phenomena are more subtle. In this Letter we directly observe bulk phase transitions, using photonic quasicrystals, by constructing a smooth boundary between topologically distinct one-dimensional quasicrystals. Moreover, we use the same method to experimentally confirm the topological equivalence between the Harper and Fibonacci quasicrystals.
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Affiliation(s)
- Mor Verbin
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Oded Zilberberg
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Yaacov E Kraus
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Yoav Lahini
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Yaron Silberberg
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
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