Spin-Orbit Assisted Variable-Range Hopping in Strong Magnetic Fields

It is shown that in the presence of strong magnetic fields, spin-orbit scattering causes a sharp increase in the effective density of states in the variable-range hopping regime when temperature decreases. This effect leads to an exponential enhancement of the conductance above its value without spin-orbit scattering. Thus an experimental study of the hopping conductivity in a fixed, large magnetic field, is a sensitive tool to explore the spin-orbit scattering parameters in the strongly localized regime. Typeset using REVTEX 1 While the effects of spin-orbit scattering in the weakly localized regime are well understood [1], much less is known on how spin-orbit scattering affects the transport in the strongly localized regime. Several different effects due to spin-orbit scattering have been suggested [2–6], with different, and sometimes contradicting predictions. All of these works rely on the measurement of the magnetoresistance, just as in the weakly localized regime, in order to explore the spin-orbit effects. However, the interplay of the different mechanisms leading to magnetoresistance in the strongly localized regime ambiguates the experimental results, leading to indefinite conclusions. In this work we propose a different approach which will allow determination of the spin-orbit scattering parameters without relying on magnetoresistance measurements. In particular, we show that in the presence of strong magnetic field, spin-orbit scattering leads to a temperature dependence of the effective density of states, ρ, in the Mott variable-range hopping law, R ∼ exp{(T0/T )1/(d+1)}, with T0 ∼ 1/ρξ, and ξ the localization length. Thus spin-orbit scattering will lead to an exponential change in the resistance, with a crossover temperature determined by the spin-orbit scattering and by the magnetic field. The sensitivity of the variable-range hopping resistance to spin-orbit scattering stems from an effect, first pointed out by Kamimura and coworkers [7]. At zero magnetic field each impurity state can be either unoccupied, singly occupied or doubly occupied. Hopping processes can occur from a singly or doubly occupied state to an unoccupied or singly occupied state. However, a strong magnetic field (