# Higher-order topological corner states induced by gain and loss

## TL;DR

This paper demonstrates that higher-order topological corner states can be induced in trivial phases by adding staggered gain and loss, establishing a bulk-corner correspondence in non-Hermitian systems with potential experimental realizations.

## Contribution

It introduces a biorthogonal nested-Wilson-loop and edge-polarization theory to characterize non-Hermitian higher-order topological phases with gain and loss.

## Key findings

- Higher-order topological corner states emerge from gain/loss in trivial phases.
- A general bulk-corner correspondence is established for non-Hermitian systems.
- Topological invariants for non-Hermitian multipole moments are defined.

## Abstract

The concept of topological phases has been generalized to higher-order topological insulators and superconductors with novel boundary states on corners or hinges. Meanwhile, recent experimental advances in controlling dissipation (such as gain and loss) open new possibilities in studying non-Hermitian topological phases. Here, we show that higher-order topological corner states can emerge by simply introducing staggered on-site gain/loss to a Hermitian system in trivial phases. For such a non-Hermitian system, we establish a general bulk-corner correspondence by developing a biorthogonal nested-Wilson-loop and edge-polarization theory, which can be applied to a wide class of non-Hermitian systems with higher-order topological orders. The theory gives rise to topological invariants characterizing the non-Hermitian topological multipole moments (i.e., corner states) that are protected by reflection or chiral symmetry. Such gain/loss induced higher-order topological corner states can be experimentally realized using photons in coupled cavities or cold atoms in optical lattices.