Absolutely continuous edge spectrum of topological insulators with an odd time-reversal symmetry

TL;DR

This paper proves that two-dimensional topological insulators with odd time-reversal symmetry possess an absolutely continuous edge spectrum, highlighting the presence of ballistic edge modes using a specialized Wold decomposition.

Contribution

It introduces a time-reversal symmetric Wold decomposition to demonstrate the absolute continuity of edge spectra in certain topological insulators.

Findings

Edge spectrum is absolutely continuous in these insulators

Ballistic edge modes are identified via the decomposition

Provides a mathematical proof for spectral properties

Abstract

We show that non-trivial two-dimensional topological insulators protected by an odd time-reversal symmetry have absolutely continuous edge spectrum. The proof employs a time-reversal symmetric version of the Wold decomposition that singles out ballistic edge modes of the topological insulator.