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Hamiltonian models based on a localized basis set are widely used incondensed matter physics, as, for example, for the calculation of electronicstructures or transport properties. The presence of a weak and homogeneousmagnetic field can be taken into account through Peierls phase factors on thehopping Hamiltonian elements. Here, we propose simple and convenient recipes toproperly determine such Peierls phase factors for quasi-one-dimensional systemsthat are periodic or with periodic subcomponents (as in Hall bars, forexample), and periodic two-dimensional systems. We also show some examples ofapplications of the formulas, and more specifically concerning the electronicstructure of carbon nanotubes in magnetic fields, the integer quantum Halleffect in six-terminal bars obtained in two-dimensional electron gases, and theelectronic structure of bumped graphene superlattices in the presence of amagnetic field.

Convenient Peierls phase choice for periodic atomistic systems under magnetic field