Engineering non-Hermitian Second Order Topological Insulator in Quasicrystals

TL;DR

This paper introduces a non-Hermitian second-order topological insulator on a quasicrystalline lattice, demonstrating the emergence of gapless corner states with real or complex spectra, advancing topological phase engineering.

Contribution

It constructs a non-Hermitian extension of the BHZ model on a quasicrystal, revealing new second-order topological phases with customizable corner state localization and spectral properties.

Findings

Real spectra support helical edge states.

Corner states can be localized at specific corners.

Two variations of Wilson mass produce different spectral characteristics.

Abstract

Non-Hermitian topological phases have gained immense attention due to their potential to unlock novel features beyond Hermitian bounds. PT-symmetric (Parity Time-reversal symmetric) non-Hermitian models have been studied extensively over the past decade. In recent years, the topological properties of general non-Hermitian models, regardless of the balance between gains and losses, have also attracted vast attention. Here we propose a non-Hermitian second-order topological (SOT) insulator that hosts gapless corner states on a two-dimensional quasi-crystalline lattice (QL). We first construct a non-Hermitian extension of the Bernevig-Hughes-Zhang (BHZ) model on a QL generated by the Amman-Beenker (AB) tiling. This model has real spectra and supports helical edge states. Corner states emerge by adding a proper Wilson mass term that gaps out the edge states. We propose two variations of the mass term that result in fascinating characteristics. In the first variation, we obtain a purely real spectra for the second-order topological phase. In the latter, we get a complex spectra with corner states localized at only two corners. Our findings pave a path to engineering exotic SOT phases where corner states can be localized at designated corners.