Disorder-driven Phase Transitions of Second-order Non-Hermitian Skin Effects

TL;DR

This paper explores how disorder induces a phase transition to higher-order non-Hermitian skin effects, characterized by boundary modes forming arcs in the complex energy plane, akin to mobility edges in disordered Hermitian systems.

Contribution

It demonstrates the disorder-driven transition to higher-order non-Hermitian skin effects and characterizes this transition using effective medium theory and numerical methods.

Findings

Disorder induces boundary modes forming arcs in the complex energy plane.

Localized corner and bulk modes coexist at the phase transition.

The behavior is analogous to mobility edge phenomena in disordered Hermitian systems.

Abstract

Non-Hermitian skin effect exhibits the collapse of the extended bulk modes into the extensive number of localized boundary states in open boundary conditions. Here we demonstrate the disorder-driven phase transition of the trivial non-Hermitian system to the higher-order non-Hermitian skin effect phase. In contrast to the clean systems, the disorder-induced boundary modes form an arc in the complex energy plane, which is the manifestation of the disorder-driven dynamical phase transition. At the phase transition, the localized corner modes and bulk modes characterized by trivial Hamiltonian coexist within the single-band but are separated in the complex energy plane. This behavior is analogous to the mobility edge phenomena in the disordered Hermitian systems. Using effective medium theory and numerical diagonalizations, we provide a systematic characterization of the disorder-driven phase transitions.