Valley Chern numbers and boundary modes in gapped bilayer graphene

Electronic states at domain walls in bilayer graphene are studied by analyzing their four- and two-band continuum models, by performing numerical calculations on the lattice, and by using quantum geometric arguments. The continuum theories explain the distinct electronic properties of boundary modes localized near domain walls formed by interlayer electric field reversal, by interlayer stacking reversal, and by simultaneous reversal of both quantities. Boundary mode properties are related to topological transitions and gap closures, which occur in the bulk Hamiltonian parameter space. The important role played by intervalley coupling effects not directly captured by the continuum model is addressed using lattice calculations for specific domain wall structures.