Anomalous Hall Response in Two Dimensional Topological Insulators due to the Stark Effect

It is shown that the presence of matrix dipole moments induced by external electric fields can modify the Hall response in two dimensional Topological insulators. In the case of the Quantum Anomalous Hall effect the induced transverse currents acquire an extra term being proportional to the Hall conductance and the time derivative of the applied electric field. In the case of the Quantum Spin Hall effect both a spin and charge transverse currents appear simultaneously. In virtue of the bulk-edge correspondence the coupling between the chiral edge channels and the electromagnetic field changes allowing for an extra non minimal coupling term. Both effects can be measured through transport and tunnelling experiments.