Corrections to the Hall mobility

We present the solution of the linear transport problem for a charged particle undergoing quantum diffusion a$iga— la Caldeira-Leggett in a two-dimensional translationally invariant system subject to an external magnetic field. The analysis provides a general framework in which to understand corrections to the classical form of the Hall mobility of an isolated carrier, when the current relaxation takes an arbitrary form. The Drude forms of the mobilities ${\mathrm{\sigma }}^{\mathit{x}\mathit{x}}$(ω) and ${\mathrm{\sigma }}^{\mathit{x}\mathit{y}}$(ω) are recovered for all relative values of the cyclotron frequency, frictional lifetime τ, and driving frequency ω as a limiting case of the model, when the upper cutoff on the dissipative bath spectral density is set to infinity. We make a quantitative estimate of the effect of a finite cutoff (${\mathrm{\Omega }}_{\mathit{c}}$) on the Hall coefficient. The Hall coefficient decreases in the presence of a finite cutoff; the correction grows as ∼-(${\mathrm{\Omega }}_{\mathit{c}}$τ${)}^{\mathrm{-}1}$ until (${\mathrm{\Omega }}_{\mathit{c}}$τ)∼1. We argue that this effect may account for part of the temperature-dependent Hall coefficient found in cuprate superconductors.