Boundary states and edge currents for free fermions

TL;DR

This paper investigates how boundary states affect edge currents in 2+1D free fermion theories, revealing conditions for current divergence cancellation and partial Lorentz invariance restoration at low energies.

Contribution

It provides a detailed analysis of boundary-induced edge currents and identifies parameter restrictions ensuring physical consistency in low-energy solid state models.

Findings

Edge current divergences depend on boundary state deformations.

Parameter restrictions are necessary for divergence cancellation.

Partial Lorentz invariance can be recovered at low energies.

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.