Optically Active Fractional Wannier-Center Displacement Drives Giant Second-Harmonic Generation

Abstract: Electric polarization is a static ground-state Berry-phase property, whereas second-harmonic generation (SHG) and shift current are dynamical optical responses. Their connection is encoded in the shift vector, whose Brillouin-zone average is governed by the band-resolved Berry-phase polarization difference between the optically connected initial and final states. Here we exploit this geometric relation in quantized formal polarization (QFP) crystals, where symmetry-quantized formal-polarization branches correspond to fractional Wannier-center sectors. First-principles screening identifies noncentrosymmetric QFP materials with giant SHG responses, including $\mathrm{InNbBr}_6$ and $\mathrm{InPS}_3$. Band-resolved Berry-phase analysis shows that their dominant optical transitions connect occupied and low-lying unoccupied states whose Wannier centers lie at distinct fractional Wyckoff positions, producing a large transition-resolved Wannier-center displacement. This displacement gives rise to a large shift vector and a dominant shift-vector-related intraband contribution to the static SHG susceptibility. Our results show that symmetry-quantized formal polarization can become optically active through transitions between fractional Wannier-center sectors, providing a symmetry-guided route to giant SHG and shift-current responses.