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Ghuneim M, Weda Bomantara R. Topological phases of tight-binding trimer lattice in the BDI symmetry class. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:495402. [PMID: 39191288 DOI: 10.1088/1361-648x/ad744c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2024] [Accepted: 08/27/2024] [Indexed: 08/29/2024]
Abstract
In this work, we theoretically study a modified Su-Schrieffer-Heeger (SSH) model in which each unit cell consists of three sites. Unlike existing extensions of the SSH model which are made by enlarging the periodicity of the (nearest-neighbor) hopping amplitudes, our modification is obtained by replacing the Pauli matrices in the system's Hamiltonian by their higher dimensional counterparts. This, in turn, leads to the presence of next-nearest neighbor hopping terms and the emergence of different symmetries than those of other extended SSH models. Moreover, the system supports a number of edge states that are protected by a combination of particle-hole, time-reversal, and chiral symmetry. Finally, our system could be potentially realized in various experimental platforms including superconducting circuits as well as acoustic/optical waveguide arrays.
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Affiliation(s)
- Mohammad Ghuneim
- Department of Physics, King Fahd University of Petroleum and Minerals, 31261 Dhahran, Saudi Arabia
| | - Raditya Weda Bomantara
- Department of Physics, Interdisciplinary Research Center for Intelligent Secure Systems, King Fahd University of Petroleum and Minerals, 31261 Dhahran, Saudi Arabia
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2
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Shen PX, Lu Z, Lado JL, Trif M. Non-Hermitian Fermi-Dirac Distribution in Persistent Current Transport. PHYSICAL REVIEW LETTERS 2024; 133:086301. [PMID: 39241705 DOI: 10.1103/physrevlett.133.086301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2024] [Revised: 06/06/2024] [Accepted: 07/19/2024] [Indexed: 09/09/2024]
Abstract
Persistent currents circulate continuously without requiring external power sources. Here, we extend their theory to include dissipation within the framework of non-Hermitian quantum Hamiltonians. Using Green's function formalism, we introduce a non-Hermitian Fermi-Dirac distribution and derive an analytical expression for the persistent current that relies solely on the complex spectrum. We apply our formula to two dissipative models supporting persistent currents: (i) a phase-biased superconducting-normal-superconducting junction; (ii) a normal ring threaded by a magnetic flux. We show that the persistent currents in both systems exhibit no anomalies at any emergent exceptional points, whose signatures are only discernible in the current susceptibility. We validate our findings by exact diagonalization and extend them to account for finite temperatures and interaction effects. Our formalism offers a general framework for computing quantum many-body observables of non-Hermitian systems in equilibrium, with potential extensions to nonequilibrium scenarios.
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3
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Yoshida T, Zhang SB, Neupert T, Kawakami N. Non-Hermitian Mott Skin Effect. PHYSICAL REVIEW LETTERS 2024; 133:076502. [PMID: 39213584 DOI: 10.1103/physrevlett.133.076502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2023] [Revised: 04/17/2024] [Accepted: 06/24/2024] [Indexed: 09/04/2024]
Abstract
We propose a novel type of skin effects in non-Hermitian quantum many-body systems that we dub a "non-Hermitian Mott skin effect." This phenomenon is induced by the interplay between strong correlations and the non-Hermitian point-gap topology. The Mott skin effect induces extreme sensitivity to the boundary conditions only in the spin degree of freedom (i.e., the charge distribution is not sensitive to boundary conditions), which is in sharp contrast to the ordinary non-Hermitian skin effect in noninteracting systems. Concretely, we elucidate that a bosonic non-Hermitian chain exhibits the Mott skin effect in the strongly correlated regime by closely examining an effective Hamiltonian. The emergence of the Mott skin effect is also supported by numerical diagonalization of the bosonic chain. The difference between the ordinary non-Hermitian skin effect and the Mott skin effect is also reflected in the time evolution of physical quantities; under the time evolution spin accumulation is observed while the charge distribution remains spatially uniform.
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Affiliation(s)
| | | | | | - Norio Kawakami
- Department of Materials Engineering Science, Osaka University, Toyonaka 560-8531, Japan
- Department of Physics, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan
- Fundamental Quantum Science Program, TRIP Headquarters, RIKEN, Wako 351-0198, Japan
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4
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Nakamura D, Bessho T, Sato M. Bulk-Boundary Correspondence in Point-Gap Topological Phases. PHYSICAL REVIEW LETTERS 2024; 132:136401. [PMID: 38613277 DOI: 10.1103/physrevlett.132.136401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2022] [Revised: 01/18/2024] [Accepted: 02/27/2024] [Indexed: 04/14/2024]
Abstract
A striking feature of non-Hermitian systems is the presence of two different types of topology. One generalizes Hermitian topological phases, and the other is intrinsic to non-Hermitian systems, which are called line-gap topology and point-gap topology, respectively. Whereas the bulk-boundary correspondence is a fundamental principle in the former topology, its role in the latter has not been clear yet. This Letter establishes the bulk-boundary correspondence in the point-gap topology in non-Hermitian systems. After revealing the requirement for point-gap topology in the open boundary conditions, we clarify that the bulk point-gap topology in open boundary conditions can be different from that in periodic boundary conditions. On the basis of real space topological invariants and the K theory, we give a complete classification of the open boundary point-gap topology with symmetry and show that the nontrivial open boundary topology results in robust and exotic surface states.
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Affiliation(s)
- Daichi Nakamura
- Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
| | - Takumi Bessho
- Corporate Research and Development Center, Toshiba Corporation, Kawasaki, Japan
| | - Masatoshi Sato
- Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
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5
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Zhang X, Wu C, Yan M, Liu N, Wang Z, Chen G. Observation of continuum Landau modes in non-Hermitian electric circuits. Nat Commun 2024; 15:1798. [PMID: 38413597 PMCID: PMC10899205 DOI: 10.1038/s41467-024-46122-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2023] [Accepted: 02/08/2024] [Indexed: 02/29/2024] Open
Abstract
Continuum Landau modes - predicted recently in a non-Hermitian Dirac Hamiltonian under a uniform magnetic field - are continuous bound states with no counterparts in Hermitian systems. However, they have still not been confirmed in experiments. Here, we report an experimental observation of continuum Landau modes in non-Hermitian electric circuits, in which the non-Hermitian Dirac Hamiltonian is simulated by non-reciprocal hoppings and the pseudomagnetic field is introduced by inhomogeneous complex on-site potentials. Through measuring the admittance spectrum and the eigenstates, we successfully verify key features of continuum Landau modes. Particularly, we observe the exotic voltage response acting as a rainbow trap or wave funnel through full-field excitation. This response originates from the linear relationship between the modes' center position and complex eigenvalues. Our work builds a bridge between non-Hermiticity and magnetic fields, and thus opens an avenue to explore exotic non-Hermitian physics.
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Affiliation(s)
- Xuewei Zhang
- School of Physics and Microelectronics, Key Laboratory of Materials Physics of Ministry of Education, Zhengzhou University, Zhengzhou, 450001, China
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser spectroscopy, Shanxi University, Taiyuan, 030006, China
| | - Chaohua Wu
- School of Physics and Microelectronics, Key Laboratory of Materials Physics of Ministry of Education, Zhengzhou University, Zhengzhou, 450001, China
| | - Mou Yan
- School of Physics and Microelectronics, Key Laboratory of Materials Physics of Ministry of Education, Zhengzhou University, Zhengzhou, 450001, China
- Institute of Quantum Materials and Physics, Henan Academy of Sciences, Zhengzhou, 450046, China
| | - Ni Liu
- Institute of Theoretical Physics, Shanxi University, Taiyuan, 030006, China
| | - Ziyu Wang
- The Institute of Technological Sciences, Wuhan University, Wuhan, 430072, China.
| | - Gang Chen
- School of Physics and Microelectronics, Key Laboratory of Materials Physics of Ministry of Education, Zhengzhou University, Zhengzhou, 450001, China.
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser spectroscopy, Shanxi University, Taiyuan, 030006, China.
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Nakamura D, Inaka K, Okuma N, Sato M. Universal Platform of Point-Gap Topological Phases from Topological Materials. PHYSICAL REVIEW LETTERS 2023; 131:256602. [PMID: 38181366 DOI: 10.1103/physrevlett.131.256602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2023] [Revised: 08/10/2023] [Accepted: 09/29/2023] [Indexed: 01/07/2024]
Abstract
Whereas point-gap topological phases are responsible for exceptional phenomena intrinsic to non-Hermitian systems, their realization in quantum materials is still elusive. Here, we propose a simple and universal platform of point-gap topological phases constructed from Hermitian topological insulators and superconductors. We show that (d-1)-dimensional point-gap topological phases are realized by making a boundary in d-dimensional topological insulators and superconductors dissipative. A crucial observation of the proposal is that adding a decay constant to boundary modes in d-dimensional topological insulators and superconductors is topologically equivalent to attaching a (d-1)-dimensional point-gap topological phase to the boundary. We furthermore establish the proposal from the extended version of the Nielsen-Ninomiya theorem, relating dissipative gapless modes to point-gap topological numbers. From the bulk-boundary correspondence of the point-gap topological phases, the resultant point-gap topological phases exhibit exceptional boundary states or in-gap higher-order non-Hermitian skin effects.
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Affiliation(s)
- Daichi Nakamura
- Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
| | - Kazuya Inaka
- Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
| | - Nobuyuki Okuma
- Graduate School of Engineering, Kyushu Institute of Technology, Kitakyushu 804-8550, Japan
| | - Masatoshi Sato
- Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
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Li CA, Trauzettel B, Neupert T, Zhang SB. Enhancement of Second-Order Non-Hermitian Skin Effect by Magnetic Fields. PHYSICAL REVIEW LETTERS 2023; 131:116601. [PMID: 37774272 DOI: 10.1103/physrevlett.131.116601] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/30/2022] [Revised: 07/03/2023] [Accepted: 08/16/2023] [Indexed: 10/01/2023]
Abstract
The non-Hermitian skin effect is a unique phenomenon in which an extensive number of eigenstates are localized at the boundaries of a non-Hermitian system. Recent studies show that the non-Hermitian skin effect is significantly suppressed by magnetic fields. In contrast, we demonstrate that the second-order skin effect (SOSE) is robust and can even be enhanced by magnetic fields. Remarkably, SOSE can also be induced by magnetic fields from a trivial non-Hermitian system that does not experience any skin effect at zero field. These properties are intimately related to to the persistence and emergence of topological line gaps in the complex energy spectrum in the presence of magnetic fields. Moreover, we show that a magnetic field can drive a non-Hermitian system from a hybrid skin effect, where the first-order skin effect and SOSE coexist, to pure SOSE. Our results describe a qualitatively new magnetic field behavior of the non-Hermitian skin effect.
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Affiliation(s)
- Chang-An Li
- Institute for Theoretical Physics and Astrophysics, University of Würzburg, 97074 Würzburg, Germany
| | - Björn Trauzettel
- Institute for Theoretical Physics and Astrophysics, University of Würzburg, 97074 Würzburg, Germany
| | - Titus Neupert
- Department of Physics, University of Zürich, Winterthurerstrasse 190, 8057, Zürich, Switzerland
| | - Song-Bo Zhang
- Department of Physics, University of Zürich, Winterthurerstrasse 190, 8057, Zürich, Switzerland
- International Center for Quantum Design of Functional Materials (ICQD), Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
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8
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Zhang K, Fang C, Yang Z. Dynamical Degeneracy Splitting and Directional Invisibility in Non-Hermitian Systems. PHYSICAL REVIEW LETTERS 2023; 131:036402. [PMID: 37540867 DOI: 10.1103/physrevlett.131.036402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2022] [Revised: 02/28/2023] [Accepted: 06/21/2023] [Indexed: 08/06/2023]
Abstract
In this Letter, we introduce the concept of dynamical degeneracy splitting to describe the anisotropic decay behaviors in non-Hermitian systems. We demonstrate that systems with dynamical degeneracy splitting exhibit two distinctive features: (i) the system shows frequency-resolved non-Hermitian skin effect; (ii) Green's function exhibits anomalous behavior at given frequency, leading to uneven broadening in spectral function and anomalous scattering. As an application, we propose directional invisibility based on wave packet dynamics to investigate the geometry-dependent skin effect in higher dimensions. Our work elucidates a faithful correspondence between non-Hermitian skin effect and Green's function, offering a guiding principle for exploration of novel physical phenomena emerging from this effect.
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Affiliation(s)
- Kai Zhang
- Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Chen Fang
- Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
- Kavli Institute for Theoretical Sciences, Chinese Academy of Sciences, Beijing 100190, China
| | - Zhesen Yang
- Kavli Institute for Theoretical Sciences, Chinese Academy of Sciences, Beijing 100190, China
- Department of Physics, Xiamen University, Xiamen 361005, Fujian Province, China
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Gao Z, Qiao X, Pan M, Wu S, Yim J, Chen K, Midya B, Ge L, Feng L. Two-Dimensional Reconfigurable Non-Hermitian Gauged Laser Array. PHYSICAL REVIEW LETTERS 2023; 130:263801. [PMID: 37450823 DOI: 10.1103/physrevlett.130.263801] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/27/2022] [Accepted: 05/11/2023] [Indexed: 07/18/2023]
Abstract
Topological effects in photonic non-Hermitian systems have recently led to extraordinary discoveries including nonreciprocal lasing, topological insulator lasers, and topological metamaterials, to mention a few. These effects, although realized in non-Hermitian systems, are all stemming from their Hermitian components. Here we experimentally demonstrate the topological skin effect and boundary sensitivity, induced by the imaginary gauge field in a two-dimensional laser array, which are fundamentally different from any Hermitian topological effects and intrinsic to open systems. By selectively and asymmetrically injecting gain into the system, we have synthesized an imaginary gauge field on chip, which can be flexibly reconfigured on demand. We show not only that the non-Hermitian topological features remain intact in a nonlinear nonequilibrium system, but also that they can be harnessed to enable persistent phase locking with intensity morphing. Our work lays the foundation for a dynamically reconfigurable on-chip coherent system with robust scalability, attractive for building high-brightness sources with arbitrary intensity profiles.
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Affiliation(s)
- Zihe Gao
- Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Xingdu Qiao
- Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Mingsen Pan
- Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Shuang Wu
- Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Jieun Yim
- Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Kaiyuan Chen
- Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Bikashkali Midya
- Department of Physical Sciences, Indian Institute of Science Education and Research, Berhampur, Odisha 760003, India
| | - Li Ge
- Department of Physics and Astronomy, College of Staten Island, CUNY, Staten Island, New York 10314, USA
- The Graduate Center, CUNY, New York, New York 10016, USA
| | - Liang Feng
- Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
- Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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Wang Q, Qian J, Jiang L. Non-Hermitian kagome photonic crystal with a totally topological spatial mode selection. OPTICS EXPRESS 2023; 31:5363-5377. [PMID: 36823818 DOI: 10.1364/oe.482836] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2022] [Accepted: 01/11/2023] [Indexed: 06/18/2023]
Abstract
Recently, the study of non-Hermitian topological edge and corner states in sonic crystals (SCs) and photonic crystals (PCs) has drawn much attention. In this paper, we propose a Wannier-type higher-order topological insulator (HOTI) model based on the kagome PC containing dimer units and study its non-Hermitian topological corner states. When balanced gain and loss are introduced into the dimer units with a proper parity-time symmetric setting, the system will show asymmetric Wannier bands and can support two Hermitian corner states and two pairs of complex-conjugate or pseudo complex-conjugate non-Hermitian corner states. These topological corner states are solely confined at three corners of the triangular supercell constructed by the trivial and non-trivial kagome PCs, corresponding to a topological spatial mode selection effect. As compared to the non-Hermitian quadrupole-type HOTIs, the non-Hermitian Wannier-type HOTIs can realize totally topological spatial mode selection by using much lower coefficients of gain and loss. Our results pave the way for the development of novel non-Hermitian photonic topological devices based on Wannier-type HOTIs.
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Rui WB, Zheng Z, Wang C, Wang ZD. Non-Hermitian Spatial Symmetries and Their Stabilized Normal and Exceptional Topological Semimetals. PHYSICAL REVIEW LETTERS 2022; 128:226401. [PMID: 35714264 DOI: 10.1103/physrevlett.128.226401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/25/2021] [Revised: 03/18/2022] [Accepted: 05/04/2022] [Indexed: 06/15/2023]
Abstract
We study non-Hermitian spatial symmetries-a class of symmetries that have no counterparts in Hermitian systems-and study how normal and exceptional semimetals can be stabilized by these symmetries. Different from internal ones, spatial symmetries act nonlocally in momentum space and enforce global constraints on both band degeneracies and topological quantities at different locations. In deriving general constraints on band degeneracies and topological invariants, we demonstrate that non-Hermitian spatial symmetries are on an equal footing with, but are essentially different from Hermitian ones. First, we discover the nonlocal Hermitian conjugate pair of exceptional or normal band degeneracies that are enforced by non-Hermitian spatial symmetries. Remarkably, we find that these pairs lead to the symmetry-enforced violation of the Fermion doubling theorem in the long-time limit. Second, with the topological constraints, we unravel that a certain exceptional manifold is only compatible with and stabilized by non-Hermitian spatial symmetries but is intrinsically incompatible with Hermitian spatial symmetries. We illustrate these findings using two three-dimensional models of a non-Hermitian Weyl semimetal and an exceptional unconventional Weyl semimetal. Experimental cold-atom realizations of both models are also proposed.
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Affiliation(s)
- W B Rui
- Department of Physics and HKU-UCAS Joint Institute for Theoretical and Computational Physics at Hong Kong, The University of Hong Kong, Pokfulam Road, Hong Kong, China
| | - Zhen Zheng
- Department of Physics and HKU-UCAS Joint Institute for Theoretical and Computational Physics at Hong Kong, The University of Hong Kong, Pokfulam Road, Hong Kong, China
| | - Chenjie Wang
- Department of Physics and HKU-UCAS Joint Institute for Theoretical and Computational Physics at Hong Kong, The University of Hong Kong, Pokfulam Road, Hong Kong, China
| | - Z D Wang
- Department of Physics and HKU-UCAS Joint Institute for Theoretical and Computational Physics at Hong Kong, The University of Hong Kong, Pokfulam Road, Hong Kong, China
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