Local invariants identify topology in metals and gapless systems

TL;DR

This paper introduces a new approach using local invariants based on the spectral localizer to identify and measure topological properties in metals and gapless systems, expanding the scope of topological classification.

Contribution

It develops a spectral localizer-based theory to detect boundary states and topological protection in metallic and gapless systems, overcoming limitations of traditional topological band theory.

Findings

Method applies across symmetry classes in lattice systems

Topological features are robust to strong perturbations

Enables exploration of topological phenomena in new material classes

Abstract

Although topological band theory has been used to discover and classify a wide array of novel topological phases in insulating and semi-metal systems, it is not well-suited to identifying topological phenomena in metallic or gapless systems. Here, we develop a theory of topological metals based on the system's spectral localizer and associated Clifford pseudospectrum, which can both determine whether a system exhibits boundary-localized states despite the presence of degenerate bulk bands and provide a measure of these states' topological protection even in the absence of a bulk band gap. We demonstrate the generality of this method across symmetry classes in two lattice systems, a Chern metal and a higher-order topological metal, and prove the topology of these systems is robust to relatively strong perturbations. The ability to define invariants for metallic and gapless systems allows for the possibility of finding topological phenomena in a broad range of natural, photonic, and other artificial materials that could not be previously explored.