Orbital magnetoconductance in the variable-range hopping regime

The orbital magnetoconductance (MC) in the variable-rangehopping (VRH) regime is evaluated by use, for definiteness, of a model proposed by Nguyen, Spivak, and Shklovskii, which approximately takes into account the interference among random paths in the hopping process. Instead of logarithmic averaging which is shown to be inadequate for this case, the MC is obtained by the critical percolating resistor method of Ambegaokar, Halperin, and Langer. The small-field MC is quadratic in H; it is positive deep in the VRH regime and changes sign when the zero-field conductivity is high enough. This behavior (except for the sign change) and the relevant magnetic field scale are in agreement with recent experiments. The calculated MC is always positive for strong fields and is predicted to saturate at sufficiently large fields.