Many-body effects on exciton dynamics and nonlinear optics in low-dimensional materials

In low-dimensional and nanostructured materials, the optical response is dominated by correlated electron-hole pairs---or excitons---bound together by the Coulomb interaction. By now, it is well-established that these large excitonic effects in low dimensions are a combined consequence of quantum confinement and inhomogeneous screening. However, many challenges remain in understanding dynamical processes following excitation. In particular, understanding exciton-phonon interactions and other exciton scattering processes is crucial for predicting the dynamics of exciton relaxation, lifetimes, and charge and energy transfer as well as interpreting pump-probe experiments in the ultrafast regime. In this talk, I will discuss three different frontiers related to the first principles understanding of exciton dynamics and nonlinear optics. Firstly, we will explore characteristics of the exciton bandstructure and the relation between dispersion and dimensionality. We have recently measured the exciton dispersion of a freestanding boron nitride monolayer, explicitly revealing the presence of massless excitons arising from the long-range exchange interaction in 2D, consistent with our previous theoretical predictions. These features of the exciton bandstructure have important implications for the coherence of exciton wavepackets. Secondly, we will explore first principles calculations of exciton-phonon interactions. I will show how exciton-phonon coupling controls exciton interband and intraband relaxation processes in materials that are candidates for multi-exciton generation and discuss the role of exciton-phonon interactions in hot exciton relaxation processes in transition metal dichalcogenides, focusing on relaxation from high energy states above the optical bandedge. Finally, computational cost is a considerable bottleneck in the first principles study of excited-state phenomena. I will present our recent work on data-driven and machine-learning methods for real-time calculations of nonlinear optical processes.