# Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence

## TL;DR

This paper explores non-Hermitian higher-order topological phases, revealing a generalized biorthogonal bulk-boundary correspondence that explains boundary modes and their unique behaviors in dissipative systems.

## Contribution

It introduces a unifying biorthogonal framework for non-Hermitian higher-order topological phases, accounting for phenomena like the skin effect and boundary state emergence.

## Key findings

- Boundary modes appear at different parameters than phase transitions.
- Non-Hermitian extensions show richer phenomenology than Hermitian cases.
- Framework applies even with the non-Hermitian skin effect.

## Abstract

Non-Hermitian Hamiltonians, which describe a wide range of dissipative systems, and higher-order topological phases, which exhibit novel boundary states on corners and hinges, comprise two areas of intense current research. Here we investigate systems where these frontiers merge and formulate a generalized biorthogonal bulk-boundary correspondence, which dictates the appearance of boundary modes at parameter values that are, in general, radically different from those that mark phase transitions in periodic systems. By analyzing the interplay between corner/hinge, edge/surface and bulk degrees of freedom we establish that the non-Hermitian extensions of higher-order topological phases exhibit an even richer phenomenology than their Hermitian counterparts and that this can be understood in a unifying way within our biorthogonal framework. Saliently this works in the presence of the non-Hermitian skin effect, and also naturally encompasses genuinely non-Hermitian phenomena in the absence thereof.