Topological band degeneracies are conventionally characterized by invariants defined on enclosing spheres over which the energy spectrum remains gapped. This program has been completed for minimal degeneracies in all ten Altland-Zirnbauer (AZ) …
The topological classification of a system depends on the discrete symmetries of its Hamiltonian. In Floquet photonic waveguide arrays, the abstract symmetries of the Altland--Zirnbauer (AZ) scheme -- chiral, particle-hole, and time-reversal (for …
We investigate $s$-wave superconductivity in negatively curved geometries, focusing on Cayley trees and the hyperbolic plane. Using a self-consistent Bogoliubov--de Gennes approach for trees and a BCS treatment of the hyperbolic continuum, we …
We study $s$-wave superconductivity in hyperbolic spaces using the Bogoliubov-de Gennes theory for discrete hyperbolic lattices and the Ginzburg-Landau theory for the continuous hyperbolic plane. Hyperbolic lattices maintain a finite fraction of …
The defining feature of topological insulators is that their valence states are not continuously deformable to a suitably defined atomic limit without breaking the symmetry or closing the energy gap. When the atomic limit is given by symmetric …