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 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 dependent quantities, for which the mesoscopic gradients of the former is uncovered as a source term, opening a new research area. The precise connection with the Kubo formula 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 quantum kinetic approach. Some important implications for the theory of orbital transport are also briefly discussed.