The Hall effect due to small polarons and conduction in narrow energy bands

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.