Nonreciprocal Directional Dichroism Induced by the Quantum Metric Dipole

We identify the quantum metric dipole as the geometric origin of the nonreciprocal directional dichroism which describes the change in the refractive index upon reversing the light propagation direction. Specifically, we find that the static limit of the nonreciprocal directional dichroism corresponds to a quadrupolar transport current from the quantum metric dipole, in response to a quadrupolar electric field. Moreover, at a finite frequency, we demonstrate that the steepest slope of the averaged quantum metric dipole gives rise to a peak in the differential refractive index between counterpropagating lights. Finally, we illustrate both features in a low-energy model.