Hall angle in high-T_c cuprates: Anomalous temperature dependence and anisotropic scattering

Abstract

The anisotropy of the scattering rates, 1/$\tau_{tr} \propto T$ and 1/$\tau_H \propto T^2$, implied effectively by the anomalous temperature dependence of the normal-state in-plane Hall angle, $\cot \theta \propto T^2$, observed in the high-T$_c$ layered cuprates is reasoned out to be a natural consequence of the semiclassical Boltzmann transport equation with crossed electric (E) and magnetic (H) fields. It is argued that while the scattering rate 1/$\tau_{tr}$ describes the longitudinal relaxation of the dipolar E-perturbations to the circular zero-field reference distribution function which is known to correspond to a non-Fermi liquid with 1/$\tau_{tr} \propto T$, the scattering rate 1/$\tau_H$ describes the transverse relaxation of the H-perturbations to the E-induced shifted reference distribution which is Fermi-liquid-like giving 1/$\tau_H \propto T^2$. Incorporation of impurity scattering gives $\cot \theta _H = aT^2 + b$ in agreement with the observed temperature dependence.