Gauge-invariant tight-binding approach to magnetotunneling in superlattices

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Abstract
We analyze the electronic structure of a superlattice in a magnetic field parallel to the layers using a tight-binding scheme where Wannier functions centered on each well are coupled to their nearest neighbors. Gauge and translational invariances impose the condition that, within a single conduction miniband, electrons are subjected to a one-dimensional periodic potential of magnetic origin whose overall amplitude equals the miniband width. Landau levels are thus nondispersive in this energy range, and remain quasiparabolic at higher energies. The influence of interface disorder is also studied. The valence dispersion curves of a superlattice are described in an original way which leads to calculation schemes quite simpler than those already published: k⋅p expansion along the layers, and k-dependent tight binding along the growth axis. The allowed energies when a transverse magnetic field is applied are then computed, with particular emphasis on the numerous anticrossings due to heavy- and light-hole coupling.