# Topological phase transition in non-Hermitian quasicrystals

## TL;DR

This paper reveals topological phase transitions in non-Hermitian quasicrystals with $ ext{PT}$ symmetry, showing that the metal-insulator transition at symmetry breaking points is topological and characterized by a winding number.

## Contribution

It introduces a non-Hermitian extension of the Aubry-André-Harper model to study topological phases in quasicrystals, highlighting the topological nature of the phase transition.

## Key findings

- Topological phases exist in non-Hermitian quasicrystals with $ ext{PT}$ symmetry.
- The metal-insulating transition at $ ext{PT}$ symmetry breaking is topological.
- Winding number characterizes the topological phase transition.

## Abstract

The discovery of topological phases in non-Hermitian open classical and quantum systems challenges our current understanding of topological order. Non-Hermitian systems exhibit unique features with no counterparts in topological Hermitian models, such as failure of the conventional bulk-boundary correspondence and non-Hermitian skin effect. Advances in the understanding of the topological properties of non-Hermitian lattices with translational invariance have been reported in several recent studies, however little is known about non-Hermitian quasicrystals. Here we disclose topological phases in a quasicrystal with parity-time ($\mathcal{PT}$) symmetry, described by a non-Hermitian extension of the Aubry-Andr\'e-Harper model. It is shown that the metal-insulating phase transition, observed at the $\mathcal{PT}$ symmetry breaking point, is of topological nature and can be expressed in terms of a winding number. A photonic realization of a non-Hermitian quasicrystal is also suggested.