Abstract

The small polaron has proved useful in understanding the transport properties of such low-mobility solids as oxides, glasses, and amorphous semiconductors. Polarons and bipolarons are of interest in high-Tc superconductors. I will first briefly review the basic mechanism for the Hall effect found in the localized regime where transport is due to multi-phonon-assisted transitions between localized small polaron states. The temperature-dependence of the Hall mobility will be reviewed for the non-adiabatic, adiabatic and three- and four site cases. I will then indicate how the magnetic phase factors in the localized regime give the conventional magnetic Lorentz force in a description of polaron band motion or of purely electronic bands of narrow width. This narrow-band regime is more relevant to the normal state of high- Tc materials in which carrier motion is itinerant. I will then survey experimental evidence for the Hall effect due to small polarons and in the narrow-band regime for several materials and conclude with an example of the Hall effect in the normal state of the cuprate superconductors taken from David Emin.

The basic mechanism of the Hall effect in the localized regime

The model used is a straightforward two-dimensional generalization of the molecular crystal model of Holstein [1]. (This case admits only a small-polaron and free-particle solution and no large-polaron solution.) Briefly, the model consists of a site occupied by diatomic molecules with fixed centres of gravity and orientation but variable internuclear separation so that each acts like an Einstein oscillator with fixed frequency, ω0. The oscillators are subject to weak coupling giving rise to dispersion of the vibrational frequencies.