Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics

TL;DR

This paper reveals that time-reversal and particle-hole symmetries are fundamentally equivalent in non-Hermitian systems, leading to new topological phases absent in Hermitian physics, and establishes a unified symmetry framework.

Contribution

It demonstrates the topological equivalence of time-reversal and particle-hole symmetries in non-Hermitian systems, unifying their roles and revealing novel non-equilibrium topological phases.

Findings

Symmetries are topologically equivalent in the complex energy plane.

Emergence of unique non-Hermitian topological phases.

Unified framework for non-equilibrium topological phases.

Abstract

Topological phases are enriched in non-equilibrium open systems effectively described by non-Hermitian Hamiltonians. While several properties unique to non-Hermitian topological systems were uncovered, the fundamental role of symmetry in non-Hermitian physics has yet to be fully understood, and it has remained unclear how symmetry protects non-Hermitian topological phases. Here we show that two fundamental anti-unitary symmetries, time-reversal and particle-hole symmetries, are topologically equivalent in the complex energy plane and hence unified in non-Hermitian physics. A striking consequence of this symmetry unification is the emergence of unique non-equilibrium topological phases that have no counterparts in Hermitian systems. We illustrate this by presenting a non-Hermitian counterpart of the Majorana chain in an insulator with time-reversal symmetry and that of the quantum spin Hall insulator in a superconductor with particle-hole symmetry. Our work establishes a fundamental symmetry principle in non-Hermitian physics and paves the way towards a unified framework for non-equilibrium topological phases.