Field dependence of the residual-resistivity anisotropy in sodium and potassium.

Abstract

Recent measurements of the low-field, induced torque in sodium and potassium by Elliott and Datars show that the resistivity anisotropy increases with increasing magnetic field. The zero-field resistivity anisotropy, unexpected for cubic symmetry, is explained by the charge-density-wave (CDW) structure. Due to the wave-function mixing caused by the CDW potential, the momentum transfer (by isotropic impurities) is much larger for electrons near the CDW energy gap. This is modeled by an anisotropic relaxation time in k\ensuremath{\rightarrow} space. The Boltzmann transport equation in a magnetic field can then be solved exactly. The computed resistivity anisotropy is higher for ${\ensuremath{\omega}}_{c}$\ensuremath{\tau}>1 compared with its zero-field value. The effect of the magnetic field is to ``stir'' the electron distribution f(k\ensuremath{\rightarrow}); this feeds electrons into the region of rapid relaxation and thereby increases the resistivity anisotropy.