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O: Fachverband Oberflächenphysik

O 40: Poster: Topological Materials

O 40.6: Poster

Tuesday, March 19, 2024, 18:00–20:00, Poster D

The Coarse Geometric Origin of Topological Phases — •Christoph S. Setescak¹ and Matthias Ludewig² — ¹Institute of Experimental and Applied Physics, University of Regensburg, Universitätstraße 31, 93080 Regensburg, Germany — ²Faculty of Mathematics, University of Regensburg, Universitätstraße 31, 93080 Regensburg, Germany

Topological phases of matter rely on the concept that the ensemble of occupied bulk energy bands of a translationally invariant Hamiltonian can be classified by topological invariants by making use of internal electronic symmetries. Non-trivial invariants give rise to exceptional electronic states at the boundary. This approach falls short when dealing with disorder induced by prevalent crystal defects. We propose that one should work in a coarse geometric framework, where the invariant can be defined in the presence of disorder. This construction is physically motivated, provides a natural setting for the bulk-boundary correspondence and furthermore provides a numerical efficient way to calculate the invariants. We apply this approach to a low energy tight-binding model of a three dimensional topological insulator with time reversal symmetry. We discuss the phase diagram in the disorder-free case and analyze the evolution of the topological phase upon the introduction of disorder.

Keywords: Topological Phases; Topological Insulators; Topological Invariants; Coarse Geometry; Numerical Methods