Linear and nonlinear exciton dynamics with time-dependent density-functional theory

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NON-TECHNICAL SUMMARYThe interaction of light and matter is of fundamental importance in science and technology: it determines the characterization of materials through optical spectroscopy, forms the basis of photovoltaics as a renewable energy resource, and opens up new technologies in the area of quantum information. This award supports research and education activities with an aim to develop theoretical and computational methods for modeling light-matter interactions that are more accurate and efficient than existing approaches.When light gets absorbed in a material, electrons are excited into higher states, leaving positively charged “hole” states behind. The electrons and holes can team up and form pairs, called excitons, which give rise to characteristic spectroscopic features and often dominate the optical properties of materials. The theoretical and computational description of excitonic effects is challenging, since the electron-hole pairs exist within a solid-state environment of many electrons, and are influenced by subtle interaction effects between them. This project will especially focus on such interactions in two-dimensional materials.This project will utilize a quantum-mechanical method called time-dependent density-functional theory, which has been very successful in describing the dynamics of interacting electronic systems in many areas in physics, chemistry and materials science. Within this theoretical framework, the PI will develop new ways of accounting for the quantum behavior of many-electron systems in two-dimensional materials. Another focus will be on a real-time description of light-matter interactions that explicitly accounts for fast dynamical effects which allow the simulation of experiments probing exciton dynamics on very short time scales in 2D materials.The research activities will go hand in hand with educational efforts focusing on the training and mentoring of graduate students and postdocs and the development of innovative teaching methods. An open-source library of computer simulations will be developed, to be used as teaching tools for introductory courses in density-functional theory. This addresses a clear need to make these advanced quantum mechanical topics more accessible to learners from various backgrounds.TECHNICAL SUMMARYThis award supports theoretical and computational research and education activities with an aim to develop and apply time-dependent density-functional theory (TDDFT) based approaches for excitons in the linear and nonlinear regime. The first research goal is to extend the long-range corrected and the dielectrically screened hybrid functional based approaches to describe excitons at finite momentum and in two-dimensional (2D) materials. This requires the development of long-range corrected exchange-correlation functionals with explicit matrix form in reciprocal space, and of hybrid functionals that use momentum-dependent dielectric screening models. These methods will be applied to describe dark excitons, which are potential candidates for qubits in future quantum information devices. The second goal is to describe ultrafast and nonlinear excitonic effects in real time via the time-dependent Kohn-Sham equation for solids. This will be accomplished through a time-dependent version of the long-range corrected exchange-correlation functional, suitably modified to enforce the so-called zero-force theorem, and via hybrid functionals with explicitly time-dependent dielectric screening. These methods will be developed and tested with the help of 2D model systems, and they will be implemented in two codes, INQ and Octopus. Applications will address exciton formation and dynamics in 2D materials, the dynamical Franz-Keldysh effect, and excitonic effects in high-harmonic generation. The research activities will go hand in hand with educational efforts focusing on the training and mentoring of graduate students and postdocs and the development of innovative teaching methods. An open-source library of Python-based computer simulations will be developed, to be used as teaching tools for introductory courses in density-functional theory. This addresses a clear need to make TDDFT more accessible to learners from various backgrounds.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.