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Li J, Zhang A, Liu Y, Liu Q. Group Theory on Quasisymmetry and Protected Near Degeneracy. PHYSICAL REVIEW LETTERS 2024; 133:026402. [PMID: 39073939 DOI: 10.1103/physrevlett.133.026402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2023] [Accepted: 05/23/2024] [Indexed: 07/31/2024]
Abstract
In solid state systems, group representation theory is powerful in characterizing the behavior of quasiparticles, notably the energy degeneracy. While conventional group theory is effective in answering yes-or-no questions related to symmetry breaking, its application to determining the magnitude of energy splitting resulting from symmetry lowering is limited. Here, we propose a theory on quasisymmetry and near degeneracy, thereby expanding the applicability of group theory to address questions regarding large-or-small energy splitting. Defined within the degenerate subspace of an unperturbed Hamiltonian, quasisymmetries form an enlarged symmetry group eliminating the first-order splitting. This framework ensures that the magnitude of splitting arises as a second-order effect of symmetry-lowering perturbations, such as external fields and spin-orbit coupling. We systematically tabulate the quasisymmetry groups within 32 crystallographic point groups and find all the possible unitary quasisymmetry group structures regarding double degeneracy. Applying our theory to the realistic material AgLa, we predict a "quasi-Dirac semimetal" phase characterized by two tiny-gap band anticrossings.
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Wang H, Huang YX, Liu H, Feng X, Zhu J, Wu W, Xiao C, Yang SA. Orbital Origin of the Intrinsic Planar Hall Effect. PHYSICAL REVIEW LETTERS 2024; 132:056301. [PMID: 38364160 DOI: 10.1103/physrevlett.132.056301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2022] [Revised: 10/12/2023] [Accepted: 12/20/2023] [Indexed: 02/18/2024]
Abstract
Recent experiments reported an antisymmetric planar Hall effect, where the Hall current is odd in the in plane magnetic field and scales linearly with both electric and magnetic fields applied. Existing theories rely exclusively on a spin origin, which requires spin-orbit coupling to take effect. Here, we develop a general theory for the intrinsic planar Hall effect (IPHE), highlighting a previously unknown orbital mechanism and connecting it to a band geometric quantity-the anomalous orbital polarizability (AOP). Importantly, the orbital mechanism does not request spin-orbit coupling, so sizable IPHE can occur and is dominated by an orbital contribution in systems with weak spin-orbit coupling. Combined with first-principles calculations, we demonstrate our theory with quantitative evaluation for bulk materials TaSb_{2}, NbAs_{2}, and SrAs_{3}. We further show that AOP and its associated orbital IPHE can be greatly enhanced at topological band crossings, offering a new way to probe topological materials.
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Affiliation(s)
- Hui Wang
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Yue-Xin Huang
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
- School of Sciences, Great Bay University, Dongguan 523000, China
- Great Bay Institute for Advanced Study, Dongguan 523000, China
| | - Huiying Liu
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
- School of Physics, Beihang University, Beijing 100191, China
| | - Xiaolong Feng
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
- Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Strasse 40, D-01187 Dresden, Germany
| | - Jiaojiao Zhu
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
| | - Weikang Wu
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
- Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials, Ministry of Education, Shandong University, Jinan 250061, China
| | - Cong Xiao
- Institute of Applied Physics and Materials Engineering, University of Macau, Macau, China
- Department of Physics, The University of Hong Kong, Hong Kong, China
- HKU-UCAS Joint Institute of Theoretical and Computational Physics at Hong Kong, Hong Kong, China
| | - Shengyuan A Yang
- Institute of Applied Physics and Materials Engineering, University of Macau, Macau, China
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Niu C, Qiu G, Wang Y, Tan P, Wang M, Jian J, Wang H, Wu W, Ye PD. Tunable Chirality-Dependent Nonlinear Electrical Responses in 2D Tellurium. NANO LETTERS 2023; 23:8445-8453. [PMID: 37677143 DOI: 10.1021/acs.nanolett.3c01797] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/09/2023]
Abstract
Tellurium (Te) is an elemental semiconductor with a simple chiral crystal structure. Te in a two-dimensional (2D) form synthesized by a solution-based method shows excellent electrical, optical, and thermal properties. In this work, the chirality of hydrothermally grown 2D Te is identified and analyzed by hot sulfuric acid etching and high-angle tilted high-resolution scanning transmission electron microscopy. The gate-tunable nonlinear electrical responses, including the nonreciprocal electrical transport in the longitudinal direction and the nonlinear planar Hall effect in the transverse direction, are observed in 2D Te under a magnetic field. Moreover, the nonlinear electrical responses have opposite signs in left- and right-handed 2D Te due to the opposite spin polarizations ensured by the chiral symmetry. The fundamental relationship between the spin-orbit coupling and the crystal symmetry in two enantiomers provides a viable platform for realizing chirality-based electronic devices by introducing the degree of freedom of chirality into electron transport.
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Affiliation(s)
- Chang Niu
- Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, United States
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, United States
| | - Gang Qiu
- Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, United States
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, United States
| | - Yixiu Wang
- School of Industrial Engineering, Purdue University, West Lafayette, Indiana 47907, United States
| | - Pukun Tan
- Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, United States
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, United States
| | - Mingyi Wang
- School of Industrial Engineering, Purdue University, West Lafayette, Indiana 47907, United States
| | - Jie Jian
- School of Materials Science and Engineering, Purdue University, West Lafayette, Indiana 47907, United States
| | - Haiyan Wang
- School of Materials Science and Engineering, Purdue University, West Lafayette, Indiana 47907, United States
| | - Wenzhuo Wu
- School of Industrial Engineering, Purdue University, West Lafayette, Indiana 47907, United States
| | - Peide D Ye
- Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, United States
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, United States
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