Time-dependent Density-Functional Approaches for Excitons: Linear Response Versus Real Time

University Of Missouri-Columbia, Columbia MO

Investigators

Abstract

NONTECHNICAL SUMMARY The Division of Materials Research and the Chemistry Division jointly fund this award on fundamental research and education to develop theoretical and computational methodology for the study of light-matter interactions in semiconducting and insulating materials. The interaction of light and matter is of fundamental importance in science and technology: it determines the characterization of materials through optical spectroscopy and forms the basis of photovoltaics as a renewable energy resource. The goal of this research is to develop theoretical and computational methods for light-matter interactions that are more accurate and efficient than existing approaches. When light gets absorbed in a material, negatively charged electrons are excited into higher states, leaving behind them a positively charged void that is called a "hole" state. Electrons and holes can team up to 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 are formed within the original material and are subject to the influence of all other electrons therein. This project will utilize a quantum-mechanical method called time-dependent density-functional theory (TDDFT), 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, specifically focusing on properties that are necessary for the accurate description of excitons in optical spectroscopy. Another research goal will be to adapt a computer code called Qb@ll that is capable of describing the real-time dynamics of complex electronic systems, to account for excitonic properties, and use it to study the optical properties of materials with defects and interfaces. The research activities will go hand-in-hand with educational efforts, consisting of training and mentoring of graduate students in theoretical and computational condensed-matter research, and the development of an online course in density-functional theory at the undergraduate and beginning-graduate level. Undergraduate students will be involved in the design and development of course materials and of hands-on computational exercises. TECHNICAL SUMMARY The Division of Materials Research and the Chemistry Division jointly fund this award on fundamental research and education to develop theoretical and computational methodology for the study of excitonic properties in semiconductors and insulators. Excitons dominate the optical properties of many materials in the spectral region around the absorption edge; they arise from the attractive screened interaction of electrons and holes created during optical excitations. At present, the Bethe-Salpeter equation is the standard method for calculating excitonic properties in solids, but at significant computational cost. The PI will develop and implement alternative approaches for excitons based on time-dependent density-functional theory (TDDFT). The key challenge for TDDFT is to account for exchange and correlation (XC) effects via suitable approximations; the accurate description of excitonic properties requires XC functionals with the proper long-range behavior and with proper screening. The first goal in this project is to develop more accurate excitonic XC functionals for linear-response TDDFT, using three key ideas: simple parametrizations of the matrix form of long-range-corrected XC kernels, approximations derived from many-body theory, and nonlocal exchange screened with model dielectric functions. These models will be assessed by comparing calculated exciton binding energies and spectral strengths with experimental data. The second goal is to adapt the Qb@ll computer code for exciton dynamics with the time-dependent Kohn-Sham equation for solids. Qb@ll is capable of massively parallel calculations with unit cells containing many atoms, which makes it suitable to treat complex systems. Applications to bound exciton complexes at defects and charge-transfer excitons in molecular crystals will be carried out. In addition, the Qb@ll code allows coupling of electronic and ionic degrees of freedom, which is key for describing relaxation and charge separation in photovoltaic processes from first principles. The research activities will go hand-in-hand with educational efforts, consisting of training and mentoring of graduate students in theoretical and computational condensed-matter research, and the development of an online course in density-functional theory at the undergraduate and beginning-graduate level. Undergraduate students will be involved in the design and development of course materials and of hands-on computational exercises. 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.