Kinetic theory of infrared Hall effect in simple metals

A kinetic theory is developed for the infrared (IR) Hall effect. The dynami c transport coefficients including the conductivity sigma, cot theta(H) (th eta(H) = Hall angle) and the Hall coefficient RH for a system of conduction electrons ("electrons" or "holes") are shown to be obtained by applying th e conversion rule: gamma(0) --> gamma(omega) - i omega to the expressions f or the static coefficients, where gamma(0) [gamma(omega)] are static (dynam ic) scattering rates which depend on the frequency w and temperature T. If the real (Re) and imaginary (Im) parts of sigma(delta) are measured, the ra tio Re[sigma(omega)]/Im[sigma(omega)] is equal to gamma/omega, which direct ly gives the dynamic rate gamma(omega,T). The ratio Re[cot theta(H)]/Im[cot theta(H)] = -gamma(H)(omega,T)/omega yields the dynamic Hall rate gamma(H) (omega,T). The IR Hail effect experiments give a remarkable result: gamma(H ) (omega,T) = gamma(H,0)(T), that is, the dynamic Hall scattering rate is e qual to the static rate up to mid-IR similar to 1000 cm(-1).