Oscillations of the hopping magnetoresistance in a macroscopic homogeneous sample

We study the variable-range-hopping transport in a system of two parallel impurity planes. If the spacing between the planes is large enough, the transport is dominated by the in-plane hops. However, the electron, while tunneling between two impurities in one plane, can be scattered by the impurities from the other plane. In a magnetic field B parallel to the planes, the resistance of the system oscillates with B. The period of the oscillations is determined from the condition that the unit flux ${\mathrm{\ensuremath{\Phi}}}_{0}$=hc/e is equal to the magnetic flux through the area (${\mathit{dr}}_{\mathit{c}}$)/2, where d is the interplane distance and ${\mathit{r}}_{\mathit{c}}$ is the maximal length of Mott's hop.