Topological invariants for asymmetric transport
Location
Several asymmetric transport phenomena observed in materials science, superconductors, and geophysical fluid flows at an interface between insulating phases, can be given a topological origin. This asymmetry is characterized by a physical observable, which takes quantized values given by a topological invariant, and hence is immune to continuous perturbations of the system. In this talk, we consider Hamiltonians modeled by systems of partial differential equations. We associate to them several invariants given by indices of Fredholm operators. We show how to relate them to the physical observable, to bulk properties of the insulating phases (bulk-interface correspondence encoding a topological charge conservation that does not always hold), and how to compute them explicitly. We also characterize on a specific model how non-trivial topologies materialize as an obstruction to Anderson localization, a regime in which transport is strongly suppressed.