Ab Initio Maximally-Localized Exciton Wannier Functions for Solids

Since their introduction nearly 25 years ago, maximally-localized Wannier functions (MLWFs) have contributed significantly to many areas of electronic structure theory, impacting our ability to understand both local (chemical bonding) and global (topological) properties of solid-state systems. However, to date the MLWF framework has been applied to single-particle excitations. Excitons, correlated electron-hole pairs, dominate the optical response in gapped materials and understanding these composite particles plays an important role in the design of next-generation optoelectronic devices. Here, we leverage the MLWF scheme to construct maximally localized exciton Wannier functions (MLXWFs), representations of two-particle electron-hole states where the gauge freedom is used to enforce localization in the average electron-hole coordinate. As a proof-of-concept, we apply our framework to low-lying singlet and triplet excitons, computed with the ab initio GW plus Bethe-Salpeter approach, in the ionic solid LiF. We plot the MLXWFs and detail the convergence of their spreads. Our work paves the way towards the ab initio construction of exciton tight binding models, efficient interpolation of the exciton-phonon vertices, computation of the Berry-curvature for exciton bands, and more.