Topological classification of defects in non-Hermitian systems

Chun-Hui Liu and Shu Chen
Phys. Rev. B 100, 144106 – Published 18 October 2019

Abstract

We classify topological defects in non-Hermitian systems with point, real, and imaginary gaps for all the Bernard-LeClair classes or generalized Bernard-LeClair classes in all dimensions. The defect Hamiltonian H(k,r) is described by a non-Hermitian Hamiltonian with a spatially modulated adiabatical parameter r surrounding the defect. While the non-Hermitian system with a point gap belongs to any of 38 symmetry classes (Bernard-LeClair classes), for non-Hermitian systems with a linelike gap, we get 54 nonequivalent generalized Bernard-LeClair classes as a natural generalization of point gap classes. Although the classification of defects in Hermitian systems has been explored in the context of the standard tenfold Altland-Zirnbauer symmetry classes, a complete understanding of the role of the general non-Hermitian symmetries on the topological defects and their associated classification is still lacking. By continuous transformation and homeomorphic mapping, these non-Hermitian defect systems can be mapped to topologically equivalent Hermitian systems with associated symmetries, and we get the topological classification by classifying the corresponding Hermitian Hamiltonians. We discuss some nontrivial classes with a point gap according to our classification table and give explicitly the topological invariants for these classes. We also study some lattice or continuous models and discuss the correspondence between the topological number and zero modes at the topological defect.

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  • Received 27 June 2019
  • Revised 15 September 2019

DOI:https://doi.org/10.1103/PhysRevB.100.144106

©2019 American Physical Society

Physics Subject Headings (PhySH)

General PhysicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Chun-Hui Liu1,2,* and Shu Chen1,2,3,†

  • 1Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
  • 2School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • 3Yangtze River Delta Physics Research Center, Liyang, Jiangsu 213300, China

  • *liuchunhui@iphy.ac.cn
  • schen@iphy.ac.cn

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Issue

Vol. 100, Iss. 14 — 1 October 2019

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