Always-Real-Eigenvalued Non-Hermitian Topological Systems
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 () 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 -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.
Cite
@article{arxiv.2111.02701,
title = {Always-Real-Eigenvalued Non-Hermitian Topological Systems},
author = {Yang Long and Haoran Xue and Baile Zhang},
journal= {arXiv preprint arXiv:2111.02701},
year = {2024}
}