Exceptional second-order topological insulators

TL;DR

This paper introduces a new class of non-Hermitian topological phases called exceptional second-order topological insulators, characterized by unique boundary states and hinge states stabilized by point-gap topology.

Contribution

It develops a classification scheme for second-order point-gap topological phases protected by reflection symmetry and proposes specific models of exceptional second-order topological insulators.

Findings

Discovery of 2D exceptional second-order topological insulator with corner states

Identification of 3D exceptional second-order topological insulator with hinge states

Enlargement of the family of point-gap topological phases in non-Hermitian systems

Abstract

Point-gap topological phases of non-Hermitian systems exhibit exotic boundary states that have no counterparts in Hermitian systems. Here, we develop classification of second-order point-gap topological phases protected by reflection symmetry. Based on this classification, we propose exceptional second-order topological insulators, exhibiting second-order boundary states stabilized by point-gap topology. As an illustrative example, we uncover a two-dimensional exceptional second-order topological insulator with point-gapless corner states. Furthermore, we identify a three-dimensional exceptional second-order topological insulator that features hinge states with isolated exceptional points, representing second-order topological phases intrinsic to non-Hermitian systems. Our work enlarges the family of point-gap topological phases in non-Hermitian systems.