# Non-Hermitian Weyl Semimetals: Non-Hermitian Skin Effect and non-Bloch Bulk-Boundary Correspondence

## TL;DR

This paper explores the unique topological features of three-dimensional non-Hermitian Weyl semimetals, highlighting the breakdown of conventional bulk-boundary correspondence and establishing a non-Bloch framework that accurately predicts edge modes.

## Contribution

It introduces the non-Bloch bulk-boundary correspondence for non-Hermitian Weyl semimetals, resolving the breakdown of traditional bulk-boundary relations caused by the skin effect.

## Key findings

- Non-Hermitian skin effect causes breakdown of conventional bulk-boundary correspondence.
- Non-Bloch Chern numbers accurately predict Fermi-arc edge modes.
- Fermi-arc modes exhibit unidirectional edge motion.

## Abstract

We investigate novel features of three dimensional non-Hermitian Weyl semimetals, paying special attention to its unconventional bulk-boundary correspondence. We use the non-Bloch Chern numbers as the tool to obtain the topological phase diagram, which is also confirmed by the energy spectra from our numerical results. It is shown that, in sharp contrast to Hermitian systems, the conventional (Bloch) bulk-boundary correspondence breaks down in non-Hermitian topological semimetals, which is caused by the non-Hermitian skin effect. We establish the non-Bloch bulk-boundary correspondence for non-Hermitian Weyl semimetals: the Fermi-arc edge modes are determined by the non-Bloch Chern number of the bulk bands. Moreover, these Fermi-arc edge modes can manifest as the unidirectional edge motion, and their signatures are consistent with the non-Bloch bulk-boundary correspondence. Our work establish the non-Bloch bulk-boundary correspondence for non-Hermitian topological semimetals.