Mixed axial-gravitational anomaly from emergent curved spacetime in nonlinear charge transport

In 3+1 dimensional spacetime, two vector gauge anomalies are known: The chiral anomaly and the mixed axial-gravitational anomaly. While the former is well documented and tied to the presence of a magnetic field, the latter instead requires a nonzero spacetime curvature, which has made it rather difficult to study. In this work, we show that a quantum anomaly arises in the second-order electrical response for zero magnetic field, which creates a dc-current that can be either longitudinal or transverse to electric field. Consequently, the continuity equation for the chiral current is not conserved at order $\tau^{-1}$, where $\tau$ is the quasiparticle relaxation time. We can identify the anomaly as a mixed axial-gravitational one, and predict a material in which the anomaly-induced current can be isolated in a purely electrical measurement. Our findings indicate that charge transport generically derives from quasiparticle motion in an emergent curved spacetime, with potentially far-reaching consequences for all types of response functions.