The Bulk boundary Correspondence in 3d non-Hermitian Semimetals

Recently, Both numerical and analytical methods are proposed
to calculate the generalized Brillouin zone (GBZ) and explore the bulk-coundary correspondence in
non-Hermitian systems. In this article, we apply these methods to the study of the bulk-boundary
correspondence of non-Hermitian semimetal model. Concretely, we take two non-Hermitian semimetal
models into account and assume open boundary condition in x, y and z directions. In each case, we
calculate the spectrums and GBZ with typical parameters and plot topological phase diagram with
unit-circle Brillouin zone. We nd that GBZ recover the manifest consistency between OBC and
PBC spectrums, and the topological phase diagram in x, y and z direction open boundary condition
is consistent with the projection of 3 dimensional (3d) topological phase diagram into corresponding
direction. Besides, we compare the topological phase diagrams calculated with unit-circle Brillouin
zone and GBZ, which clearly shows that GBZ recovers the bulk-boundary correspondence in non-
Hermitian systems. The GBZ phase diagrams in x-direction and y-direction open boundray cases,
there exist exceptional lines phases; and in z-direction open boundary case, we get the parameter
space for topological nontrivial phase with winding number w = 1.