Quantum Geometric Exciton Drift Velocity

Excitons are bound particle-hole excitations of an insulating state which can carry dipole moment, allowing for coupling to an external electric field. We present a new quantum geometric quantity relevant to excitons that can uniquely determines which we call the dipole curvature. In addition to the anomalous drift velocity given by the Berry’s curvature, this new quantity arises naturally in the semiclassical equation of motion of the exciton and leads to a drift velocity in an electric field. This drift is known to occur in strong magnetic fields, with drift velocity E/B, and we show that its origin can be understood in terms of the dipole curvature to be a quantum geometric effect. When the band environments of the electron and hole are included, we show that the effective magnetic field associated with the drift velocity may be considerably different than the bare magnetic field, and in many circumstances will be present even if no real field is applied. We present estimates of the exciton dipole curvature for some van der Waals heterostructure systems.