Spatiotemporal characteristics of spin transport in compensated metals with electron-hole exchange interaction

We develop a theory describing spatiotemporal behavior of spin transport in two-band metals by postulating a spin-exchange interaction between electrons and holes. Starting with the semiclassical Boltzmann equation, we derive a system of coupled diffusion equations and solve them analytically under steady-state conditions. The solutions reveal two types of electron-hole coupled-spin transport modes: a dissipative mode and a nondissipative mode with an infinite spin diffusion length. The two modes are the manifestations of two types of spin coupling channels. Besides the exchange interaction, we incorporate into our derivation the relaxation caused by the spin-orbit interaction to show how it affects the spin transport characteristics of the two modes.