Theory of hopping magnetoresistance induced by Zeeman splitting

Abstract

We present a study of hopping conductivity for a system of sites which can be occupied by more than one electron. At a moderate on-site Coulomb repulsion, the coexistence of sites with occupation numbers 0, 1, and 2 results in an exponential dependence of the Mott conductivity upon Zeeman splitting ${\mu }_{B}H$. We show that the conductivity behaves as $\ln \sigma =(T/T_0{)}^{1/4}F(x)$, where $F$ is a universal scaling function of $x={\mu }_{B}H/T(T_0/T{)}^{1/4}$. We find $F(x)$ analytically at weak fields, $x\ll 1$, using a perturbative approach. Above some threshold $x_{\mathrm{th}}$, the function $F(x)$ attains a constant value, which is also found analytically. The full shape of the scaling function is determined numerically, from a simulation of the corresponding ``two color'' dimensionless percolation problem. In addition, we develop an approximate method which enables us to solve this percolation problem analytically at any magnetic field. This method gives a satisfactory extrapolation of the function $F(x)$ between its two limiting forms.

16 pages, 2 figures available on request from [email protected]