Coarse geometric approach to topological phases: Invariants from real-space representations

Christoph S. Setescak; Caio Lewenkopf; Matthias Ludewig

doi:10.1103/physrevb.111.104207

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arXiv · 2407.16494

Coarse geometric approach to topological phases: Invariants from real-space representations

Christoph S. Setescak·Caio Lewenkopf·Matthias Ludewig

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Abstract

We show that topological phases include disordered materials if the underlying invariant is interpreted as originating from coarse geometry. This coarse geometric framework, grounded in physical principles, offers a natural setting for the bulk-boundary correspondence, reproduces physical knowledge, and leads to an efficient and tractable numerical approach for calculating invariants. As a showcase, we give a detailed discussion of the framework for three-dimensional systems with time-reversal symmetry. We numerically reproduce the known disorder-free phase diagram of a tunable, effective tight-binding model and analyze the evolution of the topological phase under disorder.

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Christoph S. Setescak, Caio Lewenkopf, Matthias Ludewig. 2024-07-23. Coarse geometric approach to topological phases: Invariants from real-space representations. https://doi.org/10.1103/physrevb.111.104207

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