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.

References in corpus (19)

• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Topological Origin of Non-Hermitian Skin Effects
• Observation of topological valley transport of sound in sonic crystals
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Topological Transition in a Non-Hermitian Quantum Walk
• Topological properties of linear circuit lattices
• Acoustic non-Hermitian skin effect from twisted winding topology
• Non-Hermitian skin modes induced by on-site dissipations and chiral tunneling effect
• Experimental discovery of bulk-disclination correspondence
• Non-Hermitian route to higher-order topology in an acoustic crystal
• Anomalous topological edge states in non-Hermitian piezophononic media
• Higher-order exceptional point in a pseudo-Hermitian cavity optomechanical system
• Multi-orbital model reveals second-order topological insulator in 1H-transition metal dichalcogenide
• Non-Hermitian band topology with generalized inversion symmetry
• Real spectra in non-Hermitian topological insulators
• Topological band theory of a generalized eigenvalue problem with Hermitian matrices: Symmetry-protected exceptional rings with emergent symmetry
• Non-Hermitian Higher-Order Dirac Semimetals
• Non-Hermitian Higher-Order Weyl Semimetals

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