Topological band theory for non-Hermitian systems from the Dirac equation

Zi-Yong Ge, Yu-Ran Zhang, Tao Liu, Si-Wen Li, Heng Fan, and Franco Nori
Phys. Rev. B 100, 054105 – Published 15 August 2019

Abstract

We identify and investigate two classes of non-Hermitian systems, i.e., one resulting from a Lorentz-symmetry violation (LSV) and the other from a complex mass (CM) with Lorentz invariance. The mechanisms to break, and approaches to restore, the bulk-boundary correspondence in these two types of non-Hermitian systems are clarified. The non-Hermitian system with LSV shows a non-Hermitian skin effect, and its topological phase can be characterized by mapping it to the Hermitian system via a noncompact U(1) gauge transformation. In contrast, there exists no non-Hermitian skin effect for the non-Hermitian system with CM. Moreover, the conventional bulk-boundary correspondence holds in this (CM) system. We also consider a general non-Hermitian system in the presence of both LSV and CM, and we generalize its bulk-boundary correspondence.

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  • Received 27 March 2019

DOI:https://doi.org/10.1103/PhysRevB.100.054105

©2019 American Physical Society

Physics Subject Headings (PhySH)

  1. Physical Systems
Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & OpticalParticles & Fields

Authors & Affiliations

Zi-Yong Ge1,2, Yu-Ran Zhang3,4,*, Tao Liu4,†, Si-Wen Li5, Heng Fan1,2,6,7,‡, and Franco Nori4,8

  • 1Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
  • 2School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
  • 3Beijing Computational Science Research Center, Beijing 100193, China
  • 4Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
  • 5Department of Physics, Dalian Maritime University, Dalian 116026, China
  • 6CAS Center for Excellence in Topological Quantum Computation, UCAS, Beijing 100190, China
  • 7Songshan Lake Materials Laboratory, Dongguan 523808, China
  • 8Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA

  • *yrzhang@csrc.ac.cn
  • tao.liu@riken.jp
  • hfan@iphy.ac.cn

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Issue

Vol. 100, Iss. 5 — 1 August 2019

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