Convenient Peierls phase choice for periodic atomistic systems under magnetic field

Hamiltonian models based on a localized basis set are widely used in condensed matter physics, as, for example, for the calculation of electronic structures or transport properties. The presence of a weak and homogeneous magnetic field can be taken into account through Peierls phase factors on the hopping Hamiltonian elements. Here, we propose simple and convenient recipes to properly determine such Peierls phase factors for quasi-one-dimensional systems that are periodic or with periodic subcomponents (as in Hall bars, for example), and periodic two-dimensional systems. We also show some examples of applications of the formulas, and more specifically concerning the electronic structure of carbon nanotubes in magnetic fields, the integer quantum Hall effect in six-terminal bars obtained in two-dimensional electron gases, and the electronic structure of bumped graphene superlattices in the presence of a magnetic field.