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

TL;DR

This paper demonstrates that non-Hermitian physics phenomena, such as the skin effect and lateral wave shifts, can occur without gain or loss, arising from wave scattering at insulator boundaries, thus broadening experimental access to non-Hermitian topological effects.

Contribution

It introduces a gain- and loss-free mechanism for non-Hermitian phenomena based on boundary scattering, expanding the scope of non-Hermitian topological physics.

Findings

Reflected waves exhibit non-Hermitian skin effect without gain or loss.

Waves experience a lateral shift (Goos-Hänchen effect) due to non-Hermitian topology.

Expands experimental platforms for observing non-Hermitian topological phenomena.

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-H\"{a}nchen 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.