Always-Real-Eigenvalued Non-Hermitian Topological Systems

TL;DR

This paper introduces a systematic approach using non-reciprocal coupling to construct non-Hermitian topological systems with always-real energy spectra, regardless of the strength of non-Hermiticity, advancing the understanding of non-Hermitian topological physics.

Contribution

It develops the only known theory to guarantee real energy spectra in non-Hermitian Hamiltonians through non-reciprocal coupling, enabling new exploration of topological phases.

Findings

Real spectra in non-Hermitian systems regardless of non-Hermiticity strength

Non-reciprocal coupling drives topological phase transitions

Applicable to 1D and 2D non-Hermitian topological models

Abstract

The effect of non-Hermiticity in band topology has sparked many discussions on non-Hermitian topological physics. It has long been known that non-Hermitian Hamiltonians can exhibit real energy spectra under the condition of parity-time ($PT$) symmetry -- commonly implemented with balanced loss and gain -- but only when non-Hermiticity is relatively weak. Sufficiently strong non-Hermiticity, on the other hand, will destroy the reality of energy spectra, a situation known as spontaneous $PT$-symmetry breaking. Here, based on non-reciprocal coupling, we show a systematic strategy to construct non-Hermitian topological systems exhibiting bulk and boundary energy spectra that are always real, regardless of weak or strong non-Hermiticity. Such nonreciprocal-coupling-based non-Hermiticity can directly drive a topological phase transition and determine the band topology, as demonstrated in a few non-Hermitian systems from 1D to 2D. Our work develops so far the only theory that can guarantee the reality of energy spectra for non-Hermitian Hamiltonians, and offers a new avenue to explore non-Hermitian topological physics.