Absence of variable range hopping hall conduction?

Abstract

The three site hopping theory of Holstein is extended to the case of electronic states with Gaussian overlap in strong magnetic fields for two dimensional conductors. The Hall ratior =σ xy /σ xx is determined using an expression from recent effective medium theories which is evaluated by a Mott optimization procedure. The result isr∝ exp (-c(T 0/T)1/2) withc=1/4 for symmetric andc=5/12 for asymmetric transition rates. As usual the Mott optimization procedure yields only a rough estimate for the pre-exponential factor ofr. It is easily seen, however, that the pre-exponential will be reduced as compared to the weak field case due to an oscillatory behaviour of the strong field transition rates. As a consequence the hopping Hall conductivity will be reduced as compared to the transverse conductivity by at least two orders of magnitude in the temperature range 9 mK<T<400 mK. This is consistent with the experimental results of Tausendfreund and v. Klitzing which demonstrate (within experimental accuracy of ∼10−2) the absence of any temperature dependence ofσ xy which could be interpreted as variable range hopping, in contrast toσ xx where such a temperature dependence was seen.