A pr 1 99 7 Hall angle in high - T c cuprates : Anomalous tempera - ture dependence and anisotropic scattering

Hall angle in high-T c cuprates: Anomalous temperature dependence and anisotropic scattering Abstract. The anisotropy of the scattering rates, 1/τ tr ∝ T and 1/τ H ∝ T 2 , implied effectively by the anomalous temperature dependence of the normal-state in-plane Hall angle, cot θ ∝ T 2 , observed in the high-T c lay-ered 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/τ 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/τ tr ∝ T , the scattering rate 1/τ H describes the transverse relaxation of the H-perturbations to the E-induced shifted reference distribution which is Fermi-liquid-like giving 1/τ H ∝ T 2. Incorporation of impurity scattering gives cot θ H = aT 2 + b in agreement with the observed temperature dependence. The temperature dependence of the normal-state in-plane Hall angle θ H (T) observed in the layered cuprate superconductors is known 1−7 to be anomalous in that cot θ H (T) = a + bT 2 while the in-plane resistivity ρ ab (T) is T-linear and the Hall coefficient R H ∝ 1/T. This is in clear violation of the Kohler scaling rule, 6,7 known to be valid generally for conventional metals, to the Hall geometry. Here τ tr is the usual longitudinal relaxation time for 1