Magnetoresistance in a two-dimensional impurity band

The magnetic field dependence (H<15 T) and the temperature dependence (380 mK<T<30 K) of hopping conduction have been measured in a quasi-two-dimensional impurity band formed in the inversion layer of a sodium-doped silicon metal-oxide-semiconductor field-effect. We find that the positive magnetoresistance observed in the weak-field regime is consistent with the prediction of Shklovskii, i.e., ln[σ(H,T)/σ(0,T)]=-C${\xi }_{c0}^3$ /(λα${)}^4$, where the conductivity at the percolation threshold in the absence of a field is σ(0,T)=${\sigma }_0$exp(-${\xi }_{c0}$), the exponent ${\xi }_{c0}$ is determined from a noninteracting single-particle hopping model, λ=(ch/eH${)}^{1/2}$, α is the exponential decay rate of the localized state, and C is a positive constant. This work represents the first comprehensive evaluation of Shklovskii’s percolation model for hopping magnetoresistance.