Spinor Boltzmann Equation with Two Momenta at the Fermi Level

Abstract

Based on the formalism of Keldysh's nonequilibrium Green function, we establish a two momenta spinor Boltzmann equation for longitudinal scalar distribution function and transverse vector distribution function. The longitudinal charge currents, transverse spin currents and the continuity equations satisfied by them are then studied, it indicates that both the charge currents and spin currents decay oscillately along with position, which is due to the momenta integral over the Fermi surface. We also compare our charge currents and spin currents with the corresponding results of one momentum spinor Boltzmann equation, the differences are obvious.