Wladimir A Benalcazar : Spatial Localizers: Where Electrons and Excitons Live in Quantum Matter

Speaker: Wladimir A Benalcazar, Assistant Professor of Physics, Emory University

Electron localization underlies chemical bonding, polarization, and band topology, yet beyond one dimension no general framework exists to determine where electrons sit in an insulator. I will introduce the spatial localizer, an operator whose spectrum locates electrons in two- and three-dimensional insulators, including those with boundaries, defects, and disorder. It yields a position-space bulk-defect correspondence for charge and maximally localized states that reduce to Wannier functions in atomic insulators and to Landau-level-like coherent states in Chern insulators. I will then extend this idea to excitons, where simultaneous localization of electron and hole is obstructed by the quantum geometric dipole. An exciton spatial localizer overcomes this, producing constituent-resolved exciton Wannier functions without gauge fixing or optimization.