Quantum Kinetic Theory of the Linear Response for Weakly Disordered Multiband Systems

A quantum kinetic theory of the linear response to an electric field is provided from a controlled expansion of the Keldysh theory at leading order, for a general multiband electron system with weak scalar disorder. The response is uniquely partitioned into intraband distribution functions and interband quantum coherences. A new explicit formula is provided for the latter, outlining their true nature as local slave quantities, for which the mesoscopic gradients of the former is uncovered as a new source term. The precise connection with the Kubo formula with vertex corrections in the ladder approximation is established. A pedagogical application to spin-orbit torque theory in the two dimensional electron gas demonstrates the striking efficiency of the new formalism. Some important implications for the theory of orbital transport are also briefly discussed.