Theory of time-resolved resonant inelastic x-ray scattering for studying material dynamics

With recent progress in the X-ray beamline and pump-probe instrumentation, time-resolved RIXS (tr-RIXS) promises to detect the nonequilibrium dynamics of collective modes, which play significant roles in quantum materials. Here we present a theory for evaluating the tr-RIXS cross-section. This time-domain theory is based on nonequilibrium linear response and can reproduce the common Kramers-Heisenberg formula at equilibrium. We numerically evaluated tr-RIXS cross-section for some example systems out of equilibrium, including a graphene nanoribbon and the 2D single-band Hubbard model. We show that tr-RIXS can capture the dynamics of multi-particle Floquet excitations in a momentum-resolved way, revealing underlying physics such as Floquet band renormalization, topological edge states, and pump-induced collective excitations.