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Inspired by the physics of rare earth nickelates, we study the photoemission(PES) and resonant inelastic X-ray scattering (RIXS) spectra of a correlatedelectron system with two types of insulating sublattices. Sublattice A ischaracterized by a hybridization gap and a low-spin state, while sublattice Bfeatures a Mott gap and a local magnetic moment. We show how the coupling ofthese two qualitatively different insulating states affects the dynamics ofphoto-induced charge carriers and how the nonequilibrium states manifestthemselves in the PES and RIXS signals. In particular, we find that chargecarriers created on the B sublattice migrate to the A sublattice, where theycontribute to the creation of in-gap states in the PES signal, and tocharacteristic peaks in the nonequilibrium RIXS spectrum. While thecontributions from the two sublattices cannot be easily distinguished in thelocal photoemission spectrum, the weights of the RIXS signals in thetwo-dimensional $\omega_\text{in}$-$\omega_\text{out}$ space provideinformation on the local state evolution on both sublattices.

Time-resolved photoemission and RIXS study of a site-selective Mott insulator