Geometric Response and Disclination-Induced Skin Effects in Non-Hermitian Systems

TL;DR

This paper explores how geometric defects in three-dimensional non-Hermitian crystalline systems with specific symmetries induce unique skin effects and zero modes, enriching the topological field theory of such systems.

Contribution

It reveals the connection between disclination lines and non-Hermitian skin effects, providing a field theoretic description and topological response actions for these phenomena.

Findings

Disclination lines induce nontrivial point-gap topology.

Disclination-induced skin modes are zero modes of surface Dirac fermions.

Field theoretic description via Euclidean Wen-Zee action.

Abstract

We study the geometric response of three-dimensional non-Hermitian crystalline systems with nontrivial point-gap topology. For systems with fourfold rotation symmetry, we show that in the presence of disclination lines with a total Frank angle which is an integer multiple of $2\pi$, there can be nontrivial one-dimensional point-gap topology along the direction of the disclination lines. This results in disclination-induced non-Hermitian skin effects. By doubling a non-Hermitian Hamiltonian to a Hermitian three-dimensional chiral topological insulator, we show that the disclination-induced skin modes are zero modes of the effective surface Dirac fermion(s) in the presence of a pseudomagnetic flux induced by disclinations. Furthermore, we find that our results have a field theoretic description, and the corresponding geometric response actions (e.g., the Euclidean Wen-Zee action) enrich the topological field theory of non-Hermitian systems.