Orbital magnetoconductance in the variable-range-hopping regime

The orbital magnetoconductance (MC) in the variable-range-hopping (VRH) regime is evaluated using a model proposed by Nguyen, Spivak, and Shklovskii (NSS), which approximately takes into account the interference among random paths in the hopping process. The results are shown to be valid in more general situations. The MC is obtained using the critical-percolating-resistor method, which is proven to be equivalent to a modified logarithmic averaging. The behavior of the MC is analyzed in detail neglecting backscattering. The small-field MC is quadratic in H, is positive deep in the VRH regime, and changes sign when the zero-field conductivity is high enough. Very deep in the VRH regime a quasilinear intermediate-field dependence develops. The calculated MC is always positive for strong fields and is predicted to saturate at sufficiently large fields. This behavior and the relevant magnetic-field scale are in agreement with recent experiments.