Hall effect in a quasi-unidimensional metal

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Abstract
A model calculation is presented for the dc Hall effect and the transverse mobility in an anisotropic two-band quasi-one-dimensional charge-transfer organic solid in a metallic regime. It is assumed that the longitudinal bandwidth is much larger than the transverse bandwidth so that the electronic motion along the chain is bandlike, whereas the interchain motion is diffusive, at a sufficiently high temperature. We consider three cases: parallel bands, crossing bands, and identical bands. For the first case the two bands are well separated in momentum space at the Fermi level, and the Hall current is due to phonon-assisted hopping. For the second case, however, the bands cross each other at the Fermi point (e.g., tetrathiafulvalenium tetracyanoquinodimethanide) and resonant tunneling is responsible for the Hall current. In this case the Hall mobility is expressed in terms of the product of the absolute thermopower along the chain and the transverse mobility. The sign of the Hall effect is negative, like that for ordinary conduction. It is found that the Hall mobility is of the same order of magnitude as the transverse mobility in all cases. The present experimental results show that the Hall mobility is 5-10 times larger than the transverse mobility. The temperature dependence and the magnitude of the transverse mobilities agree with experimental data.