Linear and nonlinear Hall conductivity in presence of interaction and disorder

The theory of the nonlinear Hall effect has been established by I. Sodemann and L. Fu [Phys. Rev. Lett. 115, 216806 (2015)] in a semiclassical framework: therein, the effect appears as a geometrical property of Bloch electrons, originating from their anomalous velocity. Here I present a more general theory, addressing correlated and/or noncrystalline systems as well, where the expressions of both linear and nonlinear Hall conductivities originate from the many-electron anomalous velocity. The independent-electron results are retrieved as special cases.