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In 3+1 dimensional spacetime, two vector gauge anomalies are known: Thechiral anomaly and the mixed axial-gravitational anomaly. While the former iswell documented and tied to the presence of a magnetic field, the latterinstead requires a nonzero spacetime curvature, which has made it ratherdifficult to study. In this work, we show that a quantum anomaly arises in thesecond-order electrical response for zero magnetic field, which creates adc-current that can be either longitudinal or transverse to electric field.Consequently, the continuity equation for the chiral current is not conservedat order $\tau^{-1}$, where $\tau$ is the quasiparticle relaxation time. We canidentify the anomaly as a mixed axial-gravitational one, and predict a materialin which the anomaly-induced current can be isolated in a purely electricalmeasurement. Our findings indicate that charge transport generically derivesfrom quasiparticle motion in an emergent curved spacetime, with potentiallyfar-reaching consequences for all types of response functions.

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