Theory of hopping magnetoresistance induced by Zeeman splitting

TL;DR

This paper develops a theoretical model for hopping magnetoresistance influenced by Zeeman splitting, revealing a universal scaling behavior of conductivity with magnetic field and temperature, supported by analytical and numerical solutions.

Contribution

It introduces a new theoretical framework for understanding hopping conductivity with multiple electron occupations, including an analytical approximation for the universal scaling function.

Findings

Conductivity exhibits a universal scaling function of magnetic field and temperature.

Analytical solutions for weak fields and a numerical simulation for the full behavior.

An approximate analytical method successfully describes the scaling function across regimes.

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 $\mu_BH$. We show that the conductivity behaves as $\ln\sigma= (T/T_0)^{1/4}F(x)$, where $F$ is a universal scaling function of $x=\mu_BH/T(T_0/T)^{1/4}$. We find $F(x)$ analytically at weak fields, $x \ll 1$, using a perturbative approach. Above some threshold $x_{\rm th}$, 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.