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.
Highlights
Topological insulators (TI) are states of matter in which the bulk is gapped but which host protected gapless edge states [1, 2]
We have shown how the topological structure of single-particle systems is enhanced by the presence of average symmetries
We have focused on protection due to average reflection symmetry in the presence of disorder, a situation which occurs naturally in many condensed matter systems
Summary
Topological insulators (TI) are states of matter in which the bulk is gapped but which host protected gapless edge states [1, 2]. Its disordered phases are distinguished by a secondgeneration weak index, i.e., one which is two dimensions lower than the system dimension, even if the strong and 2d weak invariants don’t change We generalize these results to an arbitrary dimension and symmetry class, showing that ARS enlarges the topological classification of both bulk Hamiltonians and topological defects alike.
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