Non-Hermitian boundary spectral winding

TL;DR

This paper uncovers a new boundary spectral winding phenomenon in 2D non-Hermitian systems under open boundary conditions, revealing unique topological features and potential experimental detection methods.

Contribution

It introduces the concept of boundary spectral winding in 2D non-Hermitian systems and demonstrates its origin, properties, and detection in specific lattice models.

Findings

Boundary spectral winding exists in 2D non-Hermitian systems under OBC.

The winding originates from Hermitian boundary localization and non-Hermitian pumping.

A topological response to local driving fields can detect the boundary spectral winding.

Abstract

Spectral winding of complex eigenenergies represents a topological aspect unique in non-Hermitian systems, which vanishes in one-dimensional (1D) systems under the open boundary conditions (OBC). In this work, we discover a boundary spectral winding in two-dimensional non-Hermitian systems under the OBC, originating from the interplay between Hermitian boundary localization and non-Hermitian non-reciprocal pumping. Such a nontrivial boundary topology is demonstrated in a non-Hermitian breathing Kagome model with a triangle geometry, whose 1D boundary mimics a 1D non-Hermitian system under the periodic boundary conditions with nontrivial spectral winding. In a trapezoidal geometry, such a boundary spectral winding can even co-exist with corner accumulation of edge states, instead of extended ones along 1D boundary of a triangle geometry. An OBC type of hybrid skin-topological effect may also emerge in a trapezoidal geometry, provided the boundary spectral winding completely vanishes. By studying the Green's function, we unveil that the boundary spectral winding can be detected from a topological response of the system to a local driving field, offering a realistic method to extract the nontrivial boundary topology for experimental studies.