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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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Gassner S, Weber CS, Claassen M. Light-induced switching between singlet and triplet superconducting states. Nat Commun 2024; 15:1776. [PMID: 38413590 PMCID: PMC10899631 DOI: 10.1038/s41467-024-45949-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2023] [Accepted: 02/08/2024] [Indexed: 02/29/2024] Open
Abstract
While the search for topological triplet-pairing superconductivity has remained a challenge, recent developments in optically stabilizing metastable superconducting states suggest a new route to realizing this elusive phase. Here, we devise a testable theory of competing superconducting orders that permits ultrafast switching to an opposite-parity superconducting phase in centrosymmetric crystals with strong spin-orbit coupling. Using both microscopic and phenomenological models, we show that dynamical inversion symmetry breaking with a tailored light pulse can induce odd-parity (spin triplet) order parameter oscillations in a conventional even-parity (spin singlet) superconductor, which when driven strongly can send the system to a competing minimum in its free energy landscape. Our results provide new guiding principles for engineering unconventional electronic phases using light, suggesting a fundamentally non-equilibrium route toward realizing topological superconductivity.
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Affiliation(s)
- Steven Gassner
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA, 19104, USA.
| | - Clara S Weber
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA, 19104, USA
- Institut für Theorie der Statistischen Physik, RWTH Aachen and JARA - Fundamentals of Future Information Technology, D-52056, Aachen, Germany
| | - Martin Claassen
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA, 19104, USA.
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3
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Liu A, Zhang X, Liu Z, Li Y, Peng X, Li X, Qin Y, Hu C, Qiu Y, Jiang H, Wang Y, Li Y, Tang J, Liu J, Guo H, Deng T, Peng S, Tian H, Ren TL. The Roadmap of 2D Materials and Devices Toward Chips. NANO-MICRO LETTERS 2024; 16:119. [PMID: 38363512 PMCID: PMC10873265 DOI: 10.1007/s40820-023-01273-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2023] [Accepted: 10/30/2023] [Indexed: 02/17/2024]
Abstract
Due to the constraints imposed by physical effects and performance degradation, silicon-based chip technology is facing certain limitations in sustaining the advancement of Moore's law. Two-dimensional (2D) materials have emerged as highly promising candidates for the post-Moore era, offering significant potential in domains such as integrated circuits and next-generation computing. Here, in this review, the progress of 2D semiconductors in process engineering and various electronic applications are summarized. A careful introduction of material synthesis, transistor engineering focused on device configuration, dielectric engineering, contact engineering, and material integration are given first. Then 2D transistors for certain electronic applications including digital and analog circuits, heterogeneous integration chips, and sensing circuits are discussed. Moreover, several promising applications (artificial intelligence chips and quantum chips) based on specific mechanism devices are introduced. Finally, the challenges for 2D materials encountered in achieving circuit-level or system-level applications are analyzed, and potential development pathways or roadmaps are further speculated and outlooked.
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Affiliation(s)
- Anhan Liu
- School of Integrated Circuits and Beijing National Research Center for Information Science and Technology (BNRist), Tsinghua University, Beijing, 100049, People's Republic of China
| | - Xiaowei Zhang
- School of Integrated Circuits and Beijing National Research Center for Information Science and Technology (BNRist), Tsinghua University, Beijing, 100049, People's Republic of China
| | - Ziyu Liu
- School of Microelectronics, Fudan University, Shanghai, 200433, People's Republic of China
| | - Yuning Li
- School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing, 100044, People's Republic of China
| | - Xueyang Peng
- High-Frequency High-Voltage Device and Integrated Circuits R&D Center, Institute of Microelectronics, Chinese Academy of Sciences, Beijing, 100029, People's Republic of China
- School of Integrated Circuits, University of Chinese Academy of Sciences, Beijing, 100049, People's Republic of China
| | - Xin Li
- State Key Laboratory of Dynamic Measurement Technology, Shanxi Province Key Laboratory of Quantum Sensing and Precision Measurement, North University of China, Taiyuan, 030051, People's Republic of China
| | - Yue Qin
- State Key Laboratory of Dynamic Measurement Technology, Shanxi Province Key Laboratory of Quantum Sensing and Precision Measurement, North University of China, Taiyuan, 030051, People's Republic of China
| | - Chen Hu
- High-Frequency High-Voltage Device and Integrated Circuits R&D Center, Institute of Microelectronics, Chinese Academy of Sciences, Beijing, 100029, People's Republic of China
- School of Integrated Circuits, University of Chinese Academy of Sciences, Beijing, 100049, People's Republic of China
| | - Yanqing Qiu
- High-Frequency High-Voltage Device and Integrated Circuits R&D Center, Institute of Microelectronics, Chinese Academy of Sciences, Beijing, 100029, People's Republic of China
- School of Integrated Circuits, University of Chinese Academy of Sciences, Beijing, 100049, People's Republic of China
| | - Han Jiang
- School of Microelectronics, Fudan University, Shanghai, 200433, People's Republic of China
| | - Yang Wang
- School of Microelectronics, Fudan University, Shanghai, 200433, People's Republic of China
| | - Yifan Li
- School of Integrated Circuits and Beijing National Research Center for Information Science and Technology (BNRist), Tsinghua University, Beijing, 100049, People's Republic of China
| | - Jun Tang
- State Key Laboratory of Dynamic Measurement Technology, Shanxi Province Key Laboratory of Quantum Sensing and Precision Measurement, North University of China, Taiyuan, 030051, People's Republic of China
| | - Jun Liu
- State Key Laboratory of Dynamic Measurement Technology, Shanxi Province Key Laboratory of Quantum Sensing and Precision Measurement, North University of China, Taiyuan, 030051, People's Republic of China
| | - Hao Guo
- State Key Laboratory of Dynamic Measurement Technology, Shanxi Province Key Laboratory of Quantum Sensing and Precision Measurement, North University of China, Taiyuan, 030051, People's Republic of China.
| | - Tao Deng
- School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing, 100044, People's Republic of China.
| | - Songang Peng
- High-Frequency High-Voltage Device and Integrated Circuits R&D Center, Institute of Microelectronics, Chinese Academy of Sciences, Beijing, 100029, People's Republic of China.
- IMECAS-HKUST-Joint Laboratory of Microelectronics, Beijing, 100029, People's Republic of China.
| | - He Tian
- School of Integrated Circuits and Beijing National Research Center for Information Science and Technology (BNRist), Tsinghua University, Beijing, 100049, People's Republic of China.
| | - Tian-Ling Ren
- School of Integrated Circuits and Beijing National Research Center for Information Science and Technology (BNRist), Tsinghua University, Beijing, 100049, People's Republic of China.
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Mandal M, Drucker NC, Siriviboon P, Nguyen T, Boonkird A, Lamichhane TN, Okabe R, Chotrattanapituk A, Li M. Topological Superconductors from a Materials Perspective. CHEMISTRY OF MATERIALS : A PUBLICATION OF THE AMERICAN CHEMICAL SOCIETY 2023; 35:6184-6200. [PMID: 37637011 PMCID: PMC10448998 DOI: 10.1021/acs.chemmater.3c00713] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2023] [Revised: 07/12/2023] [Indexed: 08/29/2023]
Abstract
Topological superconductors (TSCs) have garnered significant research and industry attention in the past two decades. By hosting Majorana bound states which can be used as qubits that are robust against local perturbations, TSCs offer a promising platform toward (nonuniversal) topological quantum computation. However, there has been a scarcity of TSC candidates, and the experimental signatures that identify a TSC are often elusive. In this Perspective, after a short review of the TSC basics and theories, we provide an overview of the TSC materials candidates, including natural compounds and synthetic material systems. We further introduce various experimental techniques to probe TSCs, focusing on how a system is identified as a TSC candidate and why a conclusive answer is often challenging to draw. We conclude by calling for new experimental signatures and stronger computational support to accelerate the search for new TSC candidates.
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Affiliation(s)
- Manasi Mandal
- Quantum
Measurement Group, MIT, Cambridge, Massachusetts 02139, United States
- Department
of Nuclear Science and Engineering, MIT, Cambridge, Massachusetts 02139, United States
| | - Nathan C. Drucker
- Quantum
Measurement Group, MIT, Cambridge, Massachusetts 02139, United States
- School
of Engineering and Applied Sciences, Harvard
University, Cambridge, Massachusetts 02138, United States
| | - Phum Siriviboon
- Department
of Physics, MIT, Cambridge, Massachusetts 02139, United States
| | - Thanh Nguyen
- Quantum
Measurement Group, MIT, Cambridge, Massachusetts 02139, United States
- Department
of Nuclear Science and Engineering, MIT, Cambridge, Massachusetts 02139, United States
| | - Artittaya Boonkird
- Quantum
Measurement Group, MIT, Cambridge, Massachusetts 02139, United States
- Department
of Nuclear Science and Engineering, MIT, Cambridge, Massachusetts 02139, United States
| | - Tej Nath Lamichhane
- Quantum
Measurement Group, MIT, Cambridge, Massachusetts 02139, United States
- Department
of Nuclear Science and Engineering, MIT, Cambridge, Massachusetts 02139, United States
| | - Ryotaro Okabe
- Quantum
Measurement Group, MIT, Cambridge, Massachusetts 02139, United States
- Department
of Chemistry, MIT, Cambridge, Massachusetts 02139, United States
| | - Abhijatmedhi Chotrattanapituk
- Quantum
Measurement Group, MIT, Cambridge, Massachusetts 02139, United States
- Department
of Electrical Engineering and Computer Science, MIT, Cambridge, Massachusetts 02139, United States
| | - Mingda Li
- Quantum
Measurement Group, MIT, Cambridge, Massachusetts 02139, United States
- Department
of Nuclear Science and Engineering, MIT, Cambridge, Massachusetts 02139, United States
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5
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Wu YJ, Tu W, Li N. Majorana corner states in an attractive quantum spin Hall insulator with opposite in-plane Zeeman energy at two sublattice sites. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:375601. [PMID: 35793693 DOI: 10.1088/1361-648x/ac7f19] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2022] [Accepted: 07/06/2022] [Indexed: 06/15/2023]
Abstract
Higher-order topological superconductors and superfluids (SFs) host lower-dimensional Majorana corner and hinge states since novel topology exhibitions on boundaries. While such topological nontrivial phases have been explored extensively, more possible schemes are necessary for engineering Majorana states. In this paper we propose Majorana corner states could be realized in a two-dimensional attractive quantum spin-Hall insulator with opposite in-plane Zeeman energy at two sublattice sites. The appropriate Zeeman field leads to the opposite Dirac mass for adjacent edges of a square sample, and naturally induce Majorana corner states. This topological phase can be characterized by Majorana edge polarizations, and it is robust against perturbations on random potentials and random phase fluctuations as long as the edge gap remains open. Our work provides a new possibility to realize a second-order topological SF in two dimensions and engineer Majorana corner states.
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Affiliation(s)
- Ya-Jie Wu
- School of Sciences, Xi'an Technological University, Xi'an 710032, People's Republic of China
| | - Wei Tu
- School of Sciences, Xi'an Technological University, Xi'an 710032, People's Republic of China
| | - Ning Li
- School of Sciences, Xi'an Technological University, Xi'an 710032, People's Republic of China
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6
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Abstract
We present a mechanism for unconventional superconductivity in doped band insulators, where short-ranged pairing interaction arises from Coulomb repulsion due to virtual interband or excitonic processes. Remarkably, electron pairing is found upon infinitesimal doping, giving rise to Bose–Einstein condensate (BEC)–Bardeen–Cooper–Schrieffer (BCS) crossover at low density. Our theory explains puzzling behaviors of superconductivity and predicts spin-triplet pairing in electron-doped ZrNCl and WTe2. Despite being of fundamental importance and potential interest for topological quantum computing, spin-triplet superconductors remain rare in solid state materials after decades of research. In this work, we present a three-particle mechanism for spin-triplet superconductivity in multiband systems, where an effective attraction between doped electrons is produced from the Coulomb repulsion via a virtual interband transition involving a third electron [V. Crépel, L. Fu, Sci. Adv. 7, eabh2233 (2021)]. Our theory is analytically controlled by an interband hybridization parameter and explicitly demonstrated in doped band insulators with the example of an extended Hubbard model. Our theory of exciton-mediated pairing reveals how, as a matter of principle, a two-particle bound state can arise from the strong electron repulsion upon doping, opening a viable path to Bose–Einstein condensate (BEC)–Bardeen–Cooper–Schrieffer (BCS) physics in solid state systems. In light of this theory, we propose that recently discovered dilute superconductors such as ZrNCl, WTe2, and moiré materials can be spin-triplet and compare the expected consequences of our theory with experimental data.
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7
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Tsuppayakorn-aek P, Pluengphon P, Phansuke P, Inceesungvorn B, Busayaporn W, Kaewtubtim P, Bovornratanaraks T. Effect of substitution on the superconducting phase of transition metal dichalcogenide Nb(Se[Formula: see text]S[Formula: see text])[Formula: see text] van der Waals layered structure. Sci Rep 2021; 11:15215. [PMID: 34312409 PMCID: PMC8313716 DOI: 10.1038/s41598-021-94000-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2020] [Accepted: 06/30/2021] [Indexed: 11/08/2022] Open
Abstract
By means of first-principles cluster expansion, anisotropic superconductivity in the transition metal dichalcogenide Nb(Se[Formula: see text]S[Formula: see text])[Formula: see text] forming a van der Waals (vdW) layered structure is observed theoretically. We show that the Nb(Se[Formula: see text]S[Formula: see text])[Formula: see text] vdW-layered structure exhibits minimum ground-state energy. The Pnnm structure is more thermodynamically stable when compared to the 2H-NbSe[Formula: see text] and 2H-NbS[Formula: see text] structures. The characteristics of its phonon dispersions confirm its dynamical stability. According to electronic properties, i.e., electronic band structure, density of states, and Fermi surface indicate metallicity of Nb(Se[Formula: see text]S[Formula: see text])[Formula: see text]. The corresponding superconductivity is then investigated through the Eliashberg spectral function, which gives rise to a superconducting transition temperature of 14.5 K. This proposes a remarkable improvement of superconductivity in this transition metal dichalcogenide.
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Affiliation(s)
- Prutthipong Tsuppayakorn-aek
- Extreme Conditions Physics Research Laboratory (ECPRL) and Physics of Energy Materials Research Unit, Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok, 10330 Thailand
- Thailand Centre of Excellence in Physics, Ministry of Higher Education, Science, Research and Innovation, 328 Si Ayutthaya Road, Bangkok, 10400 Thailand
| | - Prayoonsak Pluengphon
- Division of Physical Science, Faculty of Science and Technology, Huachiew Chalermprakiet University, Samutprakarn, 10540 Thailand
| | - Piya Phansuke
- Department of Science, Faculty of Science and Technology, Prince of Songkla University, Pattani Campus, Pattani, 94000 Thailand
| | - Burapat Inceesungvorn
- Department of Chemistry, Center of Excellence in Materials Science and Technology and Materials Science Research Centre, Faculty of Science, Chiang Mai University, Chiang Mai, 50200 Thailand
| | - Wutthikrai Busayaporn
- Synchrotron Light Research Institute (Public Organization), Nakhon Ratchasima, 30000 Thailand
| | - Pungtip Kaewtubtim
- Department of Science, Faculty of Science and Technology, Prince of Songkla University, Pattani Campus, Pattani, 94000 Thailand
| | - Thiti Bovornratanaraks
- Extreme Conditions Physics Research Laboratory (ECPRL) and Physics of Energy Materials Research Unit, Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok, 10330 Thailand
- Thailand Centre of Excellence in Physics, Ministry of Higher Education, Science, Research and Innovation, 328 Si Ayutthaya Road, Bangkok, 10400 Thailand
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8
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Niu J, Yan T, Zhou Y, Tao Z, Li X, Liu W, Zhang L, Jia H, Liu S, Yan Z, Chen Y, Yu D. Simulation of higher-order topological phases and related topological phase transitions in a superconducting qubit. Sci Bull (Beijing) 2021; 66:1168-1175. [PMID: 36654354 DOI: 10.1016/j.scib.2021.02.035] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2020] [Revised: 01/08/2021] [Accepted: 02/23/2021] [Indexed: 01/20/2023]
Abstract
Higher-order topological phases give rise to new bulk and boundary physics, as well as new classes of topological phase transitions. While the realization of higher-order topological phases has been confirmed in many platforms by detecting the existence of gapless boundary modes, a direct determination of the higher-order topology and related topological phase transitions through the bulk in experiments has still been lacking. To bridge the gap, in this work we carry out the simulation of a two-dimensional second-order topological phase in a superconducting qubit. Owing to the great flexibility and controllability of the quantum simulator, we observe the realization of higher-order topology directly through the measurement of the pseudo-spin texture in momentum space of the bulk for the first time, in sharp contrast to previous experiments based on the detection of gapless boundary modes in real space. Also through the measurement of the evolution of pseudo-spin texture with parameters, we further observe novel topological phase transitions from the second-order topological phase to the trivial phase, as well as to the first-order topological phase with nonzero Chern number. Our work sheds new light on the study of higher-order topological phases and topological phase transitions.
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Affiliation(s)
- Jingjing Niu
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China; Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Tongxing Yan
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China; Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China; Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Yuxuan Zhou
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China; Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Ziyu Tao
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China; Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Xiaole Li
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China; Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Weiyang Liu
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China; Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Libo Zhang
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China; Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Hao Jia
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China; Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Song Liu
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China; Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China.
| | - Zhongbo Yan
- School of Physics, Sun Yat-sen University, Guangzhou 510275, China.
| | - Yuanzhen Chen
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China; Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China.
| | - Dapeng Yu
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China; Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
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9
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Ono S, Po HC, Watanabe H. Refined symmetry indicators for topological superconductors in all space groups. SCIENCE ADVANCES 2020; 6:eaaz8367. [PMID: 32426480 PMCID: PMC7195178 DOI: 10.1126/sciadv.aaz8367] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/12/2019] [Accepted: 02/05/2020] [Indexed: 06/11/2023]
Abstract
Topological superconductors are exotic phases of matter featuring robust surface states that could be leveraged for topological quantum computation. A useful guiding principle for the search of topological superconductors is to relate the topological invariants with the behavior of the pairing order parameter on the normal-state Fermi surfaces. The existing formulas, however, become inadequate for the prediction of the recently proposed classes of topological crystalline superconductors. In this work, we advance the theory of symmetry indicators for topological (crystalline) superconductors to cover all space groups. Our main result is the exhaustive computation of the indicator groups for superconductors under a variety of symmetry settings. We further illustrate the power of this approach by analyzing fourfold symmetric superconductors with or without inversion symmetry and show that the indicators can diagnose topological superconductors with surface states of different dimensionalities or dictate gaplessness in the bulk excitation spectrum.
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Affiliation(s)
- Seishiro Ono
- Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan
| | - Hoi Chun Po
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Haruki Watanabe
- Department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan
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