Extended topological group structure due to average reflection symmetry

Abstract

We extend the single-particle topological classification of insulators and superconductors to include systems in which disorder preserves average reflection symmetry. We show that the topological group structure of bulk Hamiltonians and topological defects is exponentially extended when this additional condition is met, and examine some of its physical consequences. Those include localization-delocalization transitions between topological phases with the same boundary conductance, as well as gapless topological defects stabilized by average reflection symmetry.

8 pages, 5 figures, 1 table; improved section 4 "Extended topological classification" incl. example of stacked QSH layers

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• Aperiodic Weak Topological Superconductors
• Scattering matrix invariants of Floquet topological insulators
• Classification of topological crystalline insulators based on representation theory
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• Anderson localization and the topology of classifying spaces
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• Coupled-layer description of topological crystalline insulators
• Topological Crystalline Phases in a Disordered Inversion-Symmetric Chain
• Topology and localization of a periodically driven Kitaev model
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• Quantum phase transitions and a disorder-based filter in a Floquet system
• Global and Local Topological Crystalline Markers for Rotation-Symmetric Insulators