Intrinsic Hall conductivities induced by the orbital magnetic moment

Abstract

The intrinsic anomalous Hall effect is one of the most exciting manifestations of the geometric properties of the electronic wave function. The electronic wave-function's geometric nature also gives rise to a purely quantum-mechanical intrinsic (scattering time-independent) Hall conductivity in the presence of a magnetic field. Here, we demonstrate that the orbital magnetic moment and the anomalous Hall velocity can combine to generate a scattering time-independent contribution to the thermoelectric and thermal Hall effects in addition to the Lorentz force-induced scattering time-dependent ``classical'' contribution. Considering specific examples of two-dimensional and three-dimensional systems, we explicitly: (i) show that neglecting the intrinsic charge Hall conductivity leads to an underestimation of the charge-carrier density in Hall measurement, and (ii) explore the implications of intrinsic thermoelectric Hall conductivity on the Nernst coefficient and the magneto-Seebeck effect.