Always-Real-Eigenvalued Non-Hermitian Topological Systems

• URL: http://arxiv.org/abs/2111.02701v2
• Date: Tue, 15 Mar 2022 11:23:12 GMT
• Title: Always-Real-Eigenvalued Non-Hermitian Topological Systems
• Authors: Yang Long, Haoran Xue, Baile Zhang
• Abstract summary: Non-Hermitian Hamiltonians can exhibit real energy spectra under parity-time ($PT$) symmetry. Sufficiently strong non-Hermiticity will destroy the reality of energy spectra, a situation known as spontaneous $PT$-symmetry breaking. Our work develops so far the only theory that can guarantee the reality of energy spectra for non-Hermitian Hamiltonians.
• Score: 4.8668411144978885
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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