Kohn-Sham-Proca equations for ultrafast exciton dynamics

A longstanding problem in time-dependent density functional theory has been the absence of a functional able to capture excitonic physics under laser pump conditions. Here we introduce a scheme of coupled Kohn-Sham and Proca equations in a pump-probe setup that we show (i) produces linear-response excitonic effects in the weak pump regime in excellent agreement with experiment, but also (ii) captures excitonic physics in the highly nonlinear regime of ultrafast strong laser pumping. In particular ”bleaching” (i.e., reduction) of the excitonic weight and the appearance of excitonic side bands is demonstrated. The approach is a procedural functional—the Kohn-Sham and Proca equations are simultaneously time propagated—allowing the straightforward inclusion of, for example, lattice and spin degrees of freedom into excitonic physics. The functional is shown to have universal applicability to a wide range of materials, and we also establish a relation between the parameters used in the functional and the exciton Bohr radii of the materials.