Local invariants identify topology in metals and gapless systems

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.

10 pages, 4 figures

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• Probing Chiral-Symmetric Higher-Order Topological Insulators with Multipole Winding Number
• Local and energy-resolved topological invariants for Floquet systems
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• Floquet Amorphous Topological Orders in a One-dimensional Rydberg Glass
• Family of Aperiodic Tilings with Tunable Quantum Geometric Tensor
• Gapless superconductivity and its real-space topology in quasicrystals
• Majorana-metal transition in a disordered superconductor: percolation in a landscape of topological domain walls
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