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 nonlinear and dynamical processes, especially when it comes to correlating complex experimental signatures with underlying physical phenomena using quantitatively predictive theories. 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. Secondly, we will consider the role of excitons in nonlinear optical response beyond the perturbative regime. We present a first principles approach for including exciton effects in high harmonic generation (HHG) and reveal a many-body enhancement of the transverse HHG and its relationship with the Berry curvature of the underlying bands in monolayer transition metal dichalcogenides (TMDs). Finally, computational cost is a considerable bottleneck in the first principles study of excited-state phenomena. Excited-state calculations are typically built on top of density functional theory (DFT), but the direct training of machine learning (ML) models for excited states from the DFT wavefunctions is unfeasible due to the high dimensional nature of the wavefunctions. We present a new approach for the unsupervised learning of low-dimensional representations of DFT wavefunctions that are more than 100 times more compact than previous feature engineering approaches, and apply them for downstream prediction of excited-state properties.
Diana Qiu is an assistant professor in the Department of Materials Science at Yale University. She received her Ph.D. in physics from UC Berkeley in 2017, followed by a postdoc in the Materials Science Division at Lawrence Berkeley National Lab. Her research interests focus on the development and application of ab initio methods to predict the excited-state properties of novel quantum materials, most notably excitons in 2D materials. Her work is supported by a Packard Fellowship, a DOE Early Career Award, NSF Career award, and a Presidential Early Career Award in Science and Engineering.