Gravitational anomaly in nonlinear charge transport

We show that the flow of electrons necessarily involves a deformation of the semiclassical wavepacket, and argue that the effective quasiparticle motion therefore takes place in non-Euclidian space. As an important application, we discuss the semiclassical equations of motion for materials lacking time-reversal symmetry, which exhibit a mixed axial-gravitational anomaly. We predict an anomaly current at second order in the electric field and without applied magnetic field.