Geometrical theory of the shift current in presence of disorder and interaction

The electric field of light induces--in a non centrosymmetric insulator--a dc current, quadratic in the field magnitude, and called "shift current". When addressed from a many-electron viewpoint, the shift current has a simple explanation and a simple formulation as well, deeply rooted in quantum geometry. The basic formula is then specialized to the independent-electron case, first for a disordered system in a supercell formulation, and then for a crystalline system. In the latter case the known shift-current formula is retrieved in a very transparent way.