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 ($PT$) 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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Cited by in corpus (7)

• Non-Hermitian skin effect and self-acceleration
• Zoology of non-Hermitian spectra and their graph topology
• Hybrid skin-topological effect induced by eight-site cells and arbitrary adjustment of the localization of topological edge states
• Hybrid higher-order skin-topological effect in hyperbolic lattices
• Detecting bulk and edge exceptional points in non-Hermitian systems through generalized Petermann factors
• Degenerate Topological Edge States in Multimer Chains
• Direct measurement of the quantum geometric tensor in pseudo-Hermitian systems