Topological classification of defects in non-Hermitian systems

Chun-Hui Liu, Shu Chen

Published 2019-06-27Version 1

We classify topological defects in non-Hermitian systems with point gap, real line gap and imaginary line gap for all the Bernard-LeClair classes in all dimensions. The defect Hamiltonian $H(\bf{k}, {\bf r})$ is described by a non-Hermitian Hamiltonian with spatially modulated adiabatical parameter ${\bf r}$ surrounding the defect and belongs to any of 38 symmetry classes of general no-Hermitian systems. While the classification of defects in Hermitian systems has been explored in the context of standard ten-fold Altland-Zirnbauer symmetry classes, a complete understanding of the role of the general non-Hermitian symmetries on the topological defects and their associated classification are 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 non-trivial classes with point gap according to our classification table, and give explicitly the topological invariants for these classes. By studying some lattice or continuous models, we find the correspondence between zero modes at the topological defect and the topological number in our studied models.