WannierNLQG: A Julia package for nonlinear optical responses and quantum geometry from Wannier tight-binding models

Abstract

Nonlinear optical responses and quantum geometry are central to modern condensed matter physics and are deeply intertwined. We introduce WannierNLQG, an extensible Julia framework for computing nonlinear optical responses and quantum geometric quantities from Wannier tight-binding models. Its gauge-consistent, degeneracy-aware architecture accommodates perturbative responses at arbitrary order and additional quantum geometric quantities. The current release evaluates ordinary, spin, and photon-drag injection and shift currents, as Brillouin-zone integrals and on k slices. For shift current, a unified interface exposes four complementary formulations: the conventional method, projector trace, generalized Wilson loop, and a finite-momentum geometric loop, with the last three explicitly accommodating degenerate subspaces. The framework also provides k-resolved Berry curvature, quantum metric, their multipoles, and additional quantum geometric and mixed momentum-spin quantities. Experimental symmetry workflows additionally support symmetry-adapted Wannier construction, symmetrization of tight-binding models and real-space operators, and reduction of spatially uniform response integrals to irreducible k-point orbits and invariant tensor components. The documentation covers formula conventions, the TaskConfig interface, and auditable output formats, with GeS and bilayer MoS2 case studies illustrating method comparison, degeneracy handling, quantum geometric analysis, and photon-drag responses. Together, these capabilities enable first-principles calculations of nonlinear response and quantum geometry in realistic multiband materials, connecting quantum geometry with quantitative materials modeling for optoelectronic, spintronic, and photovoltaic applications.