Semiclassical theory of the perpendicular magnetoresistance in superlattices.

Abstract

The motion of the Bloch electron in the crossed electric, F, and magnetic B fields is studied for the case of the anisotropic band structure that exists usually in superlattices. The electron trajectories are calculated from the so-called effective Hamiltonian with an electric field applied in the growth direction of a superlattice and a magnetic field parallel to layers. We solve the kinetic equation and calculate the electric current for the case when the miniband width is much smaller than the characteristic kinetic energy of electrons. If the magnetic field is strong enough, only electrons that have a velocity component perpendicular to both the electric and magnetic field equal to the drift velocity, ${\mathit{v}}_{\mathit{A}}$=F/B, contribute into the current. The current reaches its maximum value when ${\mathit{v}}_{\mathit{A}}$ is close to the Fermi velocity ${\mathit{v}}_{\mathit{F}}$ or to the thermal velocity ${\mathit{v}}_{\mathit{T}}$, whatever is larger. However, as the magnetic field goes to zero the current peak position goes to its limit ${\mathit{F}}_{\mathrm{th}}$ like ${\mathit{B}}^{2}$. The magnetoresistance at low magnetic field changes its sign at the field ${\mathit{F}}_{\mathrm{th}}$/ \ensuremath{\surd}3 . The quantitative agreement with experiment is obtained for these results without fitting parameters. We also find that electric current is independent of the relaxation time in some interval of the applied field. This can be called the effect of a collisionless conductivity.