1
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Le T, Zhang R, Li C, Jiang R, Sheng H, Tu L, Cao X, Lyu Z, Shen J, Liu G, Liu F, Wang Z, Lu L, Qu F. Magnetic field filtering of the boundary supercurrent in unconventional metal NiTe 2-based Josephson junctions. Nat Commun 2024; 15:2785. [PMID: 38555347 PMCID: PMC10981750 DOI: 10.1038/s41467-024-47103-z] [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: 03/31/2023] [Accepted: 03/15/2024] [Indexed: 04/02/2024] Open
Abstract
Topological materials with boundary (surface/edge/hinge) states have attracted tremendous research interest. Additionally, unconventional (obstructed atomic) materials have recently drawn lots of attention owing to their obstructed boundary states. Experimentally, Josephson junctions (JJs) constructed on materials with boundary states produce the peculiar boundary supercurrent, which was utilized as a powerful diagnostic approach. Here, we report the observations of boundary supercurrent in NiTe2-based JJs. Particularly, applying an in-plane magnetic field along the Josephson current can rapidly suppress the bulk supercurrent and retain the nearly pure boundary supercurrent, namely the magnetic field filtering of supercurrent. Further systematic comparative analysis and theoretical calculations demonstrate the existence of unconventional nature and obstructed hinge states in NiTe2, which could produce hinge supercurrent that accounts for the observation. Our results reveal the probable hinge states in unconventional metal NiTe2, and demonstrate in-plane magnetic field as an efficient method to filter out the bulk contributions and thereby to highlight the hinge states hidden in topological/unconventional materials.
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Affiliation(s)
- Tian Le
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China
| | - Ruihan Zhang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China
| | - Changcun Li
- School of Optoelectronic Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China
| | - Ruiyang Jiang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China
| | - Haohao Sheng
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China
| | - Linfeng Tu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China
- School of Physics, Nankai University, Tianjin, China
| | - Xuewei Cao
- School of Physics, Nankai University, Tianjin, China
| | - Zhaozheng Lyu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China
- Hefei National Laboratory, Hefei, China
| | - Jie Shen
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong, China
| | - Guangtong Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China
- Hefei National Laboratory, Hefei, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong, China
| | - Fucai Liu
- School of Optoelectronic Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China.
- Yangtze Delta Region Institute (Huzhou), University of Electronic Science and Technology of China, Huzhou, China.
| | - Zhijun Wang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China.
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China.
| | - Li Lu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China.
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China.
- Hefei National Laboratory, Hefei, China.
- Songshan Lake Materials Laboratory, Dongguan, Guangdong, China.
| | - Fanming Qu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China.
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China.
- Hefei National Laboratory, Hefei, China.
- Songshan Lake Materials Laboratory, Dongguan, Guangdong, China.
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2
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Li X, Zhang S, Zhang X, Vardeny ZV, Liu F. Topological Nodal-Point Superconductivity in Two-Dimensional Ferroelectric Hybrid Perovskites. NANO LETTERS 2024; 24:2705-2711. [PMID: 38240732 DOI: 10.1021/acs.nanolett.3c04085] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/07/2024]
Abstract
Two-dimensional (2D) hybrid organic-inorganic perovskites (HOIPs) with enhanced stability, high tunability, and strong spin-orbit coupling have shown great potential in vast applications. Here, we extend the already rich functionality of 2D HOIPs to a new territory, realizing topological superconductivity and Majorana modes for fault-tolerant quantum computation. Especially, we predict that room-temperature ferroelectric BA2PbCl4 (BA for benzylammonium) exhibits topological nodal-point superconductivity (NSC) and gapless Majorana modes on selected edges and ferroelectric domain walls when proximity-coupled to an s-wave superconductor and an in-plane Zeeman field, attractive for experimental verification and application. Since NSC is protected by spatial symmetry of 2D HOIPs, we envision more exotic topological superconducting states to be found in this class of materials due to their diverse noncentrosymmetric space groups, which may open a new avenue in the fields of HOIPs and topological superconductivity.
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Affiliation(s)
- Xiaoyin Li
- Department of Materials Science and Engineering, University of Utah, Salt Lake City, Utah 84112, United States
| | - Shunhong Zhang
- International Center for Quantum Design of Functional Materials (ICQD), University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Xiaoming Zhang
- College of Physics and Optoelectronic Engineering, Ocean University of China, Qingdao, Shandong 266100, People's Republic of China
| | - Zeev Valy Vardeny
- Department of Physics & Astronomy, University of Utah, Salt Lake City, Utah 84112, United States
| | - Feng Liu
- Department of Materials Science and Engineering, University of Utah, Salt Lake City, Utah 84112, United States
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3
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Pan XH, Chen L, Liu DE, Zhang FC, Liu X. Majorana Zero Modes Induced by the Meissner Effect at Small Magnetic Field. PHYSICAL REVIEW LETTERS 2024; 132:036602. [PMID: 38307040 DOI: 10.1103/physrevlett.132.036602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2023] [Accepted: 11/28/2023] [Indexed: 02/04/2024]
Abstract
One key difficulty in realizing Majorana zero modes (MZMs) is the required high magnetic field, which causes serious issues, e.g., shrinks the superconducting gap, reduces topological region, and weakens their robustness against disorders. In this Letter, we propose that the Meissner effect can bring the topological superconducting phase to a superconductor/topological-insulator/superconductor (SC/TI/SC) hybrid system. Remarkably, the required magnetic field strength (<10 mT) to support MZMs has been reduced by several orders of magnitude compared to that (>0.5 T) in the previous schemes. Tuning the phase difference between the top and bottom superconductors can control the number and position of the MZMs. In addition, we account for the electrostatic potential in the superconductor/topological-insulator (SC/TI) interface through the self-consistent Schrödinger-Poisson calculation, which shows the experimental accessibility of our proposal. Our proposal only needs a small magnetic field of less than 10 mT and is robust against the chemical potential fluctuation, which makes the SC/TI/SC hybrid an ideal Majorana platform.
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Affiliation(s)
- Xiao-Hong Pan
- School of Physics and Institute for Quantum Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
- Hubei Key Laboratory of Gravitation and Quantum Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
- Wuhan Institute of Quantum Technology, Wuhan, Hubei 430074, China
| | - Li Chen
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing, 100084, China
| | - Dong E Liu
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing, 100084, China
| | - Fu-Chun Zhang
- Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Xin Liu
- School of Physics and Institute for Quantum Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
- Hubei Key Laboratory of Gravitation and Quantum Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
- Wuhan Institute of Quantum Technology, Wuhan, Hubei 430074, China
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4
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Hu J, Yu F, Luo A, Pan XH, Zou J, Liu X, Xu G. Chiral Topological Superconductivity in Superconductor-Obstructed Atomic Insulator-Ferromagnetic Insulator Heterostructures. PHYSICAL REVIEW LETTERS 2024; 132:036601. [PMID: 38307042 DOI: 10.1103/physrevlett.132.036601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2023] [Accepted: 12/08/2023] [Indexed: 02/04/2024]
Abstract
Implementing topological superconductivity (TSC) and Majorana states (MSs) is one of the most significant and challenging tasks in both fundamental physics and topological quantum computations. In this work, taking the obstructed atomic insulator (OAI) Nb_{3}Br_{8}, s-wave superconductor (SC) NbSe_{2}, and ferromagnetic insulator (FMI) CrI_{3} as an example, we propose a new setup to realize the 2D chiral TSC and MSs in the SC/OAI/FMI heterostructure, which could avoid the subband problem effectively and has the advantage of huge Rashba spin-orbit coupling. As a result, the TSC phase can be stabilized in a wide region of chemical potential and Zeeman splitting, and four distinct TSC phases with superconducting Chern number N=-1,-2,-3, 3 can be achieved. Moreover, a 2D Bogoliubov-de Gennes Hamiltonian based on the triangular lattice of obstructed Wannier charge centers, combined with the s-wave superconductivity paring and Zeeman splitting, is constructed to understand the whole topological phase diagram analytically. These results expand the application of OAIs and pave a new way to realize the TSC and MSs with unique advantages.
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Affiliation(s)
- Jingnan Hu
- Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Fei Yu
- Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Aiyun Luo
- Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Xiao-Hong Pan
- Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Jinyu Zou
- Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Xin Liu
- Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
- Institute for Quantum Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
- Wuhan Institute of Quantum Technology, Wuhan 430206, China
| | - Gang Xu
- Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
- Institute for Quantum Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
- Wuhan Institute of Quantum Technology, Wuhan 430206, China
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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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Lei Y, Luo XW, Zhang S. Second-order topological insulator in periodically driven optical lattices. OPTICS EXPRESS 2022; 30:24048-24061. [PMID: 36225074 DOI: 10.1364/oe.457757] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2022] [Accepted: 06/06/2022] [Indexed: 06/16/2023]
Abstract
The higher-order topological insulator (HOTI) is a new type of topological system which has special bulk-edge correspondence compared with conventional topological insulators. In this work, we propose a scheme to realize Floquet HOTI with ultracold atoms in optical lattices. With the combination of periodically spin-dependent driving of the superlattices and a long-range coupling term, a Floquet second-order topological insulator with four zero-energy corner states emerges, whose Wannier bands are gapless and exhibit interesting bulk topology. Furthermore, the nearest-neighbor anisotropic coupling term also induced other intriguing topological phenomena, e.g. non-topologically protected corner states and topological semimetal for two different types of lattice structures respectively. Our scheme may give insight into the construction of different types of higher-order topological insulators in synthetic systems. It also provides an experimentally feasible platform to research the relations between different types of topological states and may have a wide range of applications in future.
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7
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Lu B, Zhang Y. Tunable Majorana corner modes by orbital-dependent exchange interaction in a two-dimensional topological superconductor. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:305302. [PMID: 35580592 DOI: 10.1088/1361-648x/ac709e] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2022] [Accepted: 05/17/2022] [Indexed: 06/15/2023]
Abstract
We theoretically study the effect of orbital-dependent exchange field in the formation of second order topological superconductors. We demonstrate that changing the orbital difference can induce topological transition and the Majorana corner modes therein can be manipulated. We further propose to detect the corner modes via a normal probe terminal. The conductance quantization is found to be robust to changes of the relevant system parameters.
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Affiliation(s)
- Bo Lu
- Center for Joint Quantum Studies and Department of Physics, Tianjin University, Tianjin 300072, People's Republic of China
| | - Yiying Zhang
- Center for Joint Quantum Studies and Department of Physics, Tianjin University, Tianjin 300072, People's Republic of China
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8
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Li C, Luo XJ, Chen L, Liu DE, Zhang FC, Liu X. Controllable majorana vortex states in iron-based superconducting nanowires. Natl Sci Rev 2022; 9:nwac095. [PMID: 36196249 PMCID: PMC9521342 DOI: 10.1093/nsr/nwac095] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2021] [Revised: 04/15/2022] [Accepted: 04/15/2022] [Indexed: 11/14/2022] Open
Abstract
To reveal the non-Abelian braiding statistics of Majorana zero modes (MZMs), it is crucial to design a Majorana platform, in which MZMs can be easily manipulated in a broad topological nontrivial parameter space. This is also an essential step to confirm their existence. In this study, we propose an iron-based superconducting nanowire system with Majorana vortex states to satisfy desirable conditions. This system has a radius-induced topological phase transition, giving a lower bound for the nanowire radius. In the topological phase, the iron-based superconducting nanowires have only one pair of MZMs over a wide range of radii, chemical potential and external magnetic fields. The wave function of MZMs has a sizable distribution at the side edge of the nanowires. This property enables the control of the interaction of MZMs in neighboring vortex nanowires and paves the way for Majorana fusion and braiding.
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Affiliation(s)
- Chuang Li
- School of Physics and Institute for Quantum Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China
- Wuhan National High Magnetic Field Center and Hubei Key Laboratory of Gravitation and Quantum Physics, Wuhan, 430074, China
| | - Xun-Jiang Luo
- School of Physics and Institute for Quantum Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China
- Wuhan National High Magnetic Field Center and Hubei Key Laboratory of Gravitation and Quantum Physics, Wuhan, 430074, China
| | - Li Chen
- School of Physics and Institute for Quantum Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China
- Wuhan National High Magnetic Field Center and Hubei Key Laboratory of Gravitation and Quantum Physics, Wuhan, 430074, China
| | - Dong E Liu
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing, 100084, China
| | - Fu-Chun Zhang
- Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Xin Liu
- School of Physics and Institute for Quantum Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China
- Wuhan National High Magnetic Field Center and Hubei Key Laboratory of Gravitation and Quantum Physics, Wuhan, 430074, China
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9
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Wu X, Liu X, Thomale R, Liu CX. High- T c superconductor Fe(Se,Te) monolayer: an intrinsic, scalable and electrically tunable Majorana platform. Natl Sci Rev 2022; 9:nwab087. [PMID: 35308561 PMCID: PMC8924703 DOI: 10.1093/nsr/nwab087] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2020] [Revised: 04/25/2021] [Accepted: 04/25/2021] [Indexed: 11/30/2022] Open
Abstract
Iron-based superconductors have been identified as a novel platform for realizing Majorana zero modes (MZMs) without heterostructures, due to their intrinsic topological properties and high-T c superconductivity. In the two-dimensional limit, the FeTe1-x Se x monolayer, a topological band inversion has recently been experimentally observed. Here, we propose to create MZMs by applying an in-plane magnetic field to the FeTe1-x Se x monolayer and tuning the local chemical potential via electric gating. Owing to the anisotropic magnetic couplings on edges, an in-plane magnetic field drives the system into an intrinsic high-order topological superconductor phase with Majorana corner modes. Furthermore, MZMs can occur at the domain wall of chemical potentials at either one edge or certain type of tri-junction in the two-dimensional bulk. Our study not only reveals the FeTe1-x Se x monolayer as a promising Majorana platform with scalability and electrical tunability and within reach of contemporary experimental capability, but also provides a general principle to search for realistic realization of high-order topological superconductivity.
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Affiliation(s)
- Xianxin Wu
- Institut für Theoretische Physik und Astrophysik, Julius-Maximilians-Universität Würzburg, 97074 Würzburg, Germany
| | - Xin Liu
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
- Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Ronny Thomale
- Institut für Theoretische Physik und Astrophysik, Julius-Maximilians-Universität Würzburg, 97074 Würzburg, Germany
| | - Chao-Xing Liu
- Department of Physics, the Pennsylvania State University, University Park, PA 16802, USA
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10
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Liu T, He JJ, Yang Z, Nori F. Higher-Order Weyl-Exceptional-Ring Semimetals. PHYSICAL REVIEW LETTERS 2021; 127:196801. [PMID: 34797150 DOI: 10.1103/physrevlett.127.196801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2021] [Accepted: 09/30/2021] [Indexed: 06/13/2023]
Abstract
For first-order topological semimetals, non-Hermitian perturbations can drive the Weyl nodes into Weyl exceptional rings having multiple topological structures and no Hermitian counterparts. Recently, it was discovered that higher-order Weyl semimetals, as a novel class of higher-order topological phases, can uniquely exhibit coexisting surface and hinge Fermi arcs. However, non-Hermitian higher-order topological semimetals have not yet been explored. Here, we identify a new type of topological semimetal, i.e., a higher-order topological semimetal with Weyl exceptional rings. In such a semimetal, these rings are characterized by both a spectral winding number and a Chern number. Moreover, the higher-order Weyl-exceptional-ring semimetal supports both surface and hinge Fermi-arc states, which are bounded by the projection of the Weyl exceptional rings onto the surface and hinge, respectively. Noticeably, the dissipative terms can cause the coupling of two exceptional rings with opposite topological charges, so as to induce topological phase transitions. Our studies open new avenues for exploring novel higher-order topological semimetals in non-Hermitian systems.
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Affiliation(s)
- Tao Liu
- School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China
| | - James Jun He
- RIKEN Center for Emergent Matter Science, Wako, Saitama 351-0198, Japan
| | - Zhongmin Yang
- School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China
- South China Normal University, Guangzhou 510006, China
- State Key Laboratory of Luminescent Materials and Devices and Institute of Optical Communication Materials, South China University of Technology, Guangzhou 510640, China
| | - Franco Nori
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
- RIKEN Center for Quantum Computing (RQC), Wako-shi, Saitama 351-0198, Japan
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA
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11
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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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Zhou L. Floquet Second-Order Topological Phases in Momentum Space. NANOMATERIALS (BASEL, SWITZERLAND) 2021; 11:1170. [PMID: 33947026 PMCID: PMC8146154 DOI: 10.3390/nano11051170] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/09/2021] [Revised: 04/04/2021] [Accepted: 04/26/2021] [Indexed: 11/30/2022]
Abstract
Higher-order topological phases (HOTPs) are characterized by symmetry-protected bound states at the corners or hinges of the system. In this work, we reveal a momentum-space counterpart of HOTPs in time-periodic driven systems, which are demonstrated in a two-dimensional extension of the quantum double-kicked rotor. The found Floquet HOTPs are protected by chiral symmetry and characterized by a pair of topological invariants, which could take arbitrarily large integer values with the increase of kicking strengths. These topological numbers are shown to be measurable from the chiral dynamics of wave packets. Under open boundary conditions, multiple quartets Floquet corner modes with zero and π quasienergies emerge in the system and coexist with delocalized bulk states at the same quasienergies, forming second-order Floquet topological bound states in the continuum. The number of these corner modes is further counted by the bulk topological invariants according to the relation of bulk-corner correspondence. Our findings thus extend the study of HOTPs to momentum-space lattices and further uncover the richness of HOTPs and corner-localized bound states in continuum in Floquet systems.
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Affiliation(s)
- Longwen Zhou
- Department of Physics, College of Information Science and Engineering, Ocean University of China, Qingdao 266100, China
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Kheirkhah M, Yan Z, Nagai Y, Marsiglio F. First- and Second-Order Topological Superconductivity and Temperature-Driven Topological Phase Transitions in the Extended Hubbard Model with Spin-Orbit Coupling. PHYSICAL REVIEW LETTERS 2020; 125:017001. [PMID: 32678655 DOI: 10.1103/physrevlett.125.017001] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2020] [Accepted: 06/02/2020] [Indexed: 06/11/2023]
Abstract
The combination of spin-orbit coupling with interactions results in many exotic phases of matter. In this Letter, we investigate the superconducting pairing instability of the two-dimensional extended Hubbard model with both Rashba and Dresselhaus spin-orbit coupling within the mean-field level at both zero and finite temperature. We find that both first- and second-order time-reversal symmetry breaking topological gapped phases can be achieved under appropriate parameters and temperature regimes due to the presence of a favored even-parity s+id-wave pairing even in the absence of an external magnetic field or intrinsic magnetism. This results in two branches of chiral Majorana edge states on each edge or a single zero-energy Majorana corner state at each corner of the sample. Interestingly, we also find that not only does tuning the doping level lead to a direct topological phase transition between these two distinct topological gapped phases, but also using the temperature as a highly controllable and reversible tuning knob leads to different direct temperature-driven topological phase transitions between gapped and gapless topological superconducting phases. Our findings suggest new possibilities in interacting spin-orbit coupled systems by unifying both first- and higher-order topological superconductors in a simple but realistic microscopic model.
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Affiliation(s)
- Majid Kheirkhah
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
| | - Zhongbo Yan
- School of Physics, Sun Yat-Sen University, Guangzhou 510275, China
| | - Yuki Nagai
- CCSE, Japan Atomic Energy Agency, 178-4-4, Wakashiba, Kashiwa, Chiba 277-0871, Japan
- Mathematical Science Team, RIKEN Center for Advanced Intelligence Project (AIP), 1-4-1 Nihonbashi, Chuo-ku, Tokyo 103-0027, Japan
| | - Frank Marsiglio
- Department of Physics, University of Alberta, Edmonton, Alberta T6G 2E1, Canada
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Wu YJ, Hou J, Li YM, Luo XW, Shi X, Zhang C. In-Plane Zeeman-Field-Induced Majorana Corner and Hinge Modes in an s-Wave Superconductor Heterostructure. PHYSICAL REVIEW LETTERS 2020; 124:227001. [PMID: 32567912 DOI: 10.1103/physrevlett.124.227001] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2019] [Accepted: 05/18/2020] [Indexed: 06/11/2023]
Abstract
Second-order topological superconductors host Majorana corner and hinge modes in contrast to conventional edge and surface modes in two and three dimensions. However, the realization of such second-order corner modes usually demands unconventional superconducting pairing or complicated junctions or layered structures. Here we show that Majorana corner modes could be realized using a 2D quantum spin Hall insulator in proximity contact with an s-wave superconductor and subject to an in-plane Zeeman field. Beyond a critical value, the in-plane Zeeman field induces opposite effective Dirac masses between adjacent boundaries, leading to one Majorana mode at each corner. A similar paradigm also applies to 3D topological insulators with the emergence of Majorana hinge states. Avoiding complex superconductor pairing and material structure, our scheme provides an experimentally realistic platform for implementing Majorana corner and hinge states.
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Affiliation(s)
- Ya-Jie Wu
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080-3021, USA
- School of Science, Xi'an Technological University, Xi'an 710032, China
| | - Junpeng Hou
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080-3021, USA
| | - Yun-Mei Li
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080-3021, USA
| | - Xi-Wang Luo
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080-3021, USA
| | - Xiaoyan Shi
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080-3021, USA
| | - Chuanwei Zhang
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080-3021, USA
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