Boundary states and edge currents for free fermions

Abstract

We calculate the ground state current densities for $(2 + 1)$-dimensional free fermion theories with local, translationally invariant boundary states. Deformations of the bulk wave functions close to the edge and boundary states both may cause edge current divergencies, which have to cancel in realistic systems. This yields restrictions on the parameters of quantum field theories which can arise as low-energy limits of solid-state systems. Some degree of Lorentz invariance for boosts parallel to the boundary can be recovered, when the cutoff is removed.