The Quantum Skin Hall Effect

TL;DR

This paper introduces the quantum skin Hall effect, a novel phenomenon where topological surface modes and invariants are localized by the skin effect in layered topological insulators, expanding the understanding of non-Hermitian boundary phenomena.

Contribution

It proposes the concept of a topological skin effect in layered topological insulators, demonstrating extensive surface modes and invariants, and extends the idea to various symmetry classes and experimental setups.

Findings

Topological modes are localized at surfaces due to the skin effect.

The quantum skin Hall effect exhibits extensive Hall conductance and chiral surface modes.

Hybrid 2D systems with corner modes are proposed for experimental realization.

Abstract

The skin effect, which is unique to non-Hermitian systems, can generate an extensive number of eigenstates localized near the boundary in an open geometry. Here we propose that in 2D and 3D other quantities besides charge density are susceptible to the skin effect. We show that 2D and 3D models that are a hybrid between topological insulators and skin-effect systems can have a topological skin effect where an extensive number of topological modes, and the corresponding bulk topological invariant, are pinned to the surface. A key example, which we call the quantum skin Hall effect is constructed from layers of Chern insulators and exhibits an extensive Hall conductance and number of chiral modes bound to surfaces normal to the stack of layers. The same procedure is further extended to other symmetry classes to illustrate that a variety of 1D and 2D topological invariants ($\mathbb{Z}$ or $\mathbb{Z}_2)$ are subject to the skin effect. Indeed, we also propose a hybrid 2D system that exhibits an extensive number of topological corner modes and may be more easily realized in meta-material experiments.