Towards mixed quantum-classical simulations of nonequilibrium phenomena in bulk and low-dimensional materials

The recent years have seen an increased interest in crystalline materials featuring strong coupling of electronic carriers to lattice vibrations, including monolayer transition-metal dichalcogenides. Strong electron-vibrational coupling has been well studied in molecular assemblies, where mixed quantum-classical dynamics (MQCD) has emerged as a prominent simulation tool. The equations of motion involved in MQCD are traditionally solved in real space, which is appropriate for molecules where excitations are localized and amenable to real-space truncations. For crystals with band-like properties, however, excitations are delocalized over large spatial domains. I will present our recent efforts aimed at reformulating MQCD within a reciprocal-space representation tailored to describing delocalized, Bloch-like excitations. Since such excitations tend to "localize" within the Brillouin zone (BZ), computations can be kept feasible by truncating the transformed electronic and vibrational bases to the BZ regions of interest. Results will be presented for both mean-field MQCD and surface hopping. The latter is shown to yield accurate short- and long-time behavior, offering exciting prospects for the simulation of nonequilibrium phenomena in bulk and low-dimensional materials.