Maximally localized exciton Wannier functions: theory and applications

Since their introduction over 25 years ago, maximally localized Wannier functions (MLWFs), the most compact real-space representation of a group of Bloch bands, have transformed our understanding of single-particle electronic states in periodic systems. Building on this success, we introduced maximally localized exciton Wannier functions (MLXWFs) – a natural but unexplored Wannier representation of excitons, correlated electron-hole pairs excited upon photoexcitation [1]. This representation brings to the forefront key properties related to the exciton’s center-of-mass motion, often overlooked but critically important for understanding exciton band dispersion and topology as well as exciton dynamics.

In this talk, I will present our methodology for computing MLXWFs, starting from ab initio solutions of the Bethe-Salpeter equation for a variety of material systems, including wide bandgap insulators and two-dimensional semiconductors. I will compare MLXWFs to their single-electron counterparts, highlighting unique features like the emergent long-range dipolar interactions amongst them, which have no counterpart in single-particle MLWF theory. I will then demonstrate the utility of MLXWFs by showing how they can be used to: (1) construct tight-binding models that accurately reproduce first-principles results for low-energy exciton bands, (2) interpolate exciton-phonon matrix elements across the Brillouin zone, and (3) provide a realistic diabatic basis for studying exciton transport. I will conclude with a discussion of future directions and the role I envision for exciton Wannier functions in advancing our understanding of excitonic phenomena.