Teleportation of Berry curvature on the surface of a Hopf insulator
A. Alexandradinata, Aleksandra Nelson, Alexey A. Soluyanov
Abstract
The paradigm of topological insulators asserts that an energy gap separates conduction and valence bands with opposite topological invariants. Here, we propose that equal-energy bands with opposite Chern invariants can be spatially separated, onto opposite facets of a finite crystalline Hopf insulator. On a single facet, the number of Berry-curvature quanta is in one-to-one correspondence with the bulk homotopy invariant of the Hopf insulator; this originates from a bulk-to-boundary flow of Berry curvature which is not a type of Callan-Harvey anomaly inflow. In the continuum perspective, such nontrivial boundary states arise as nonchiral, Schr\"odinger-type modes on the domain wall of a generalized Weyl equation, describing a pair of opposite-chirality Weyl fermions acting as a dipolar source of Berry curvature. A rotation-invariant lattice regularization of the generalized Weyl equation manifests a generalized Thouless pump, which translates charge by one lattice period over half an adiabatic cycle, but reverses the charge flow over the next half.