Negative Magnetoresistance of InP in the Hopping Region

Abstract

A characteristic feature of hopping conduction is a very large positive magnetoresistance caused by the field reducing the overlap of the impurity wave functions and giving rise to a resistivity dependent exponentially on H 2. There is however evidence of an initial negative magnetoresistance in GaAs, InP and Ge which reaches a maximum of up to 10% in a field of approximately 10 kG and then decreases rapidly as the effect is swamped by the positive effect. This effect occurs when the zero field resistivity, due to variable range hopping, varies with temperature as ρ = ρoexp(T o/T)x where X depends on the energy dependence of the density of states at the Fermi energy and the samples are in the localized or non-metallic region. Benzaquen et al. [1] have interpreted their results on GaAs using the mechanism proposed by Fukuyama and Yosida [2] who assume the field causes a Zeeman splitting of impurity states with a majority of carriers in the upper Zeeman state. This results in an increase in overlap of wave functions with neighbouring states. The relative magnetoresistance then becomes $$\begin{array}{*{20}c} {\frac{{\rho _H - \rho _0 }} {\rho }} & = & {\left( {\left[ {\left( {\cosh \,\left( {a_1 H} \right)} \right)^{ - 1} - 1} \right] + \left\{ {\exp \left( {K_2 H^2 } \right) - 1} \right\}} \right)} \\ \end{array} $$ ((1)) KeywordsZeeman SplittingZeeman EffectNegative MagnetoresistanceOrbital EffectPositive MagnetoresistanceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.