Non-Hermitian physics without gain or loss: the skin effect of reflected waves

Abstract

Physically, one tends to think of non-Hermitian systems in terms of gain and loss: the decay or amplification of a mode is given by the imaginary part of its energy. Here, we introduce an alternative avenue to the realm of non-Hermitian physics, which involves neither gain nor loss. Instead, complex eigenvalues emerge from the amplitudes and phase-differences of waves backscattered from the boundary of insulators. We show that for any strong topological insulator in a Wigner-Dyson class, the reflected waves are characterized by a reflection matrix exhibiting the non-Hermitian skin effect. This leads to an unconventional Goos-Hänchen effect: due to non-Hermitian topology, waves undergo a lateral shift upon reflection, even at normal incidence. Going beyond systems with gain and loss vastly expands the set of experimental platforms that can access non-Hermitian physics and show signatures associated to non-Hermitian topology.

6 pages, 4 figures + 4 pages, 2 figures supplemental material; published version

References in corpus (8)

• Topological Crystalline Insulators
• Non-Hermitian Physics
• Topological Origin of Non-Hermitian Skin Effects
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Goos-Hänchen and Imbert-Fedorov beam shifts: An overview
• Measurement of a topological edge invariant in a microwave network
• Judiciously distributing laser emitters to shape the desired far field patterns
• Non-Hermitian Topoelectrical Circuits: Expedient Tools for Topological State Engineering with Gain-Loss Modulation

Cited by in corpus (27)

• Topological Non-Hermitian skin effect
• Anomalous Skin Effects in Disordered Systems with a Single non-Hermitian Impurity
• Enhancement of Second-Order Non-Hermitian Skin Effect by Magnetic Fields
• Non-Hermitian Topological Phases: Principles and Prospects
• Observation of non-Hermitian topology in a multi-terminal quantum Hall device
• Imaginary gauge transformation in momentum space and Dirac exceptional point
• The non-Hermitian skin effect: A perspective
• Non-Hermitian Topology in Hermitian Topological Matter
• Anomalous Andreev Spectrum and Transport in Non-Hermitian Josephson Junctions
• Universal subdiffusive behavior at band edges from transfer matrix exceptional points
• Non-Hermitian topological ohmmeter
• Robust zero modes in non-Hermitian systems without global symmetries
• Emerging exceptional point with breakdown of skin effect in non-Hermitian systems
• Non-Hermitian Origin of Detachable Boundary States in Topological Insulators
• Unravelling the edge spectra of non-Hermitian Chern insulators
• Protection of all nondefective twofold degeneracies by anti-unitary symmetries in non-Hermitian systems
• Non-Hermitian skin effect enforced by nonsymmorphic symmetries
• Transmission across non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric quantum dots and ladders
• Topological Invariant for Multi-Band Non-hermitian Systems with Chiral Symmetry
• Scattering theory of delicate topological insulators
• Symmetry-driven Phononic Metamaterials
• Exceptional second-order topological insulators
• Non-Hermitian Hopf insulators
• Experimentally Probing Non-Hermitian Spectral Transition and Eigenstate Skewness
• Breakdown of Non-Bloch Bulk-Boundary Correspondence and Emergent Topology in Floquet Non-Hermitian Systems
• Unified Multipole Bott Indices for Non-Hermitian Skin Effect in Different Orders
• Liouvillian skin effects in two-dimensional electron systems at finite temperatures