Hall Effect in the Polaron-Band Regime

Abstract

A Hall effect is calculated for the band motion of the small polaron. The basic approach is to construct classical, Bloch-type wave packets from plane-wave combinations of localized polaron states. In this connection, it is shown that the effects of the "magnetic phase factors," which multiply the electronic overlap integrals in the basic Hamiltonian, are contained entirely in the conventional magnetic part, $\left(\frac{e}{c}\right)[{\mathrm{v}}_{\sigma }\times \mathrm{H}]$, of the total Lorentz force. The solutions of the steady-state Boltzmann equation for representative lattice structures indicate that the Hall coefficient is larger than or comparable to the "normal" value ($R=-1/\mathrm{nec}$) according to whether or not three sites of the lattice are mutually nearest neighbors. Such a result was previously obtained in the alternate regime in which small polaron motion is due to hopping between local sites.