Resistance magneto-oscillations of superlattices

We study theoretically vertical transport in a superlattice in a magnetic field applied along the growth direction. The electron spectrum and the conductivity are characterized by the interplay of the width of the superlattice miniband without magnetic field, 4{Λ}, the energy separation between Landau levels, {}{Ω}, and the energy uncertainty due to scattering, {Γ}. When {}{Ω} is the largest of those energies there are gaps in the electron spectrum and strong magneto-oscillations can be observed. If {Λ}{}{Γ} the conductivity in the longitudinal direction is calculated with the help of the Boltzmann equation. In the opposite case, we use percolation arguments to estimate the conductivity and prove the existence of a mobility edge. When the magnetic field is small, {}{Ω}{}{Γ}, the magneto-oscillations are weak and the conductivity is calculated with the help of the self-consistent Born approximation.