Convenient Peierls phase choice for periodic atomistic systems under magnetic field

Abstract

Peierls phase factors multiplying the hopping elements of tight-binding-like Hamiltonians conveniently describe the effect of slowly varying magnetic fields on electrons. This paper provides practical recipes to determine Peierls phase factors such that they preserve the translation symmetry of periodic two-dimensional systems and of quasi-one-dimensional systems that are periodic or with periodic subcomponents, such as Hall bars, in the presence of a homogeneous magnetic field. This allows the applicability of convenient numerical techniques based on the spatial periodicity of the Hamiltonian as demonstrated here on some examples.