Absolutely continuous spectrum for truncated topological insulators

TL;DR

This paper proves that truncating a topological insulator along a curve results in an edge system with absolutely continuous spectrum, combining bulk-edge correspondence and spectral analysis for straight edges.

Contribution

It introduces a novel approach combining bulk-edge correspondence and spectral analysis to establish absolutely continuous spectrum for truncated topological insulators.

Findings

Edge systems have absolutely continuous spectrum when truncated along sufficiently large curves.

The approach combines recent bulk-edge correspondence results with spectral analysis for straight edges.

The method applies to topological insulators truncated in specific geometric configurations.

Abstract

We show that if a topological insulator is truncated along a curve that separates the plane in two sufficiently large regions, then the edge system admits absolutely continuous spectrum. Our approach combines a recent version of the bulk-edge correspondence along curves that separates geometry and intrinsic conductance [DZ24], with a result about absolutely continuous spectrum for straight edges [BW22].