Nonequilibrium multi-band spin quantum transport: Spin, pseudo-spin, and total charge coupling

Abstract

Using the superfield nonequilibrium Green’s function technique, the spatio-temporal spin magnetization quantum transport equations (SMQTEs) were derived for a two-band model of semiconductors. The results show that the multi-band real SMQTEs are coupled to the pseudo-spin magnetization transport equations. Thus the SMQTEs essentially consist of three group of terms describing the rate of change, namely, (1) a group of terms similar to the equation for particle quantum transport, (2) a group of terms describing various torques influencing the spin orientation and phase-space magnetization density, and (3) a group of terms expressing the coupling of the real spin magnetization with the pseudo-spin magnetization. Self-consistently, the pseudo-spin magnetization equations incorporate the pseudo-spin/real spin coupling, as well as the pseudo-spin coupling to the total charge.