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

by Tobias Holder, Daniel Kaplan, Roni Ilan, Binghai Yan

Submission summary

Authors (as registered SciPost users):

Tobias Holder

Abstract

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. Here, we show that a quantum anomaly arises in the second-order electrical response for zero magnetic field, which creates a dc-current that is both transverse and longitudinal to the electric field. We can identify this new anomaly as a mixed axial-gravitational one, and suggest an experiment in which the anomaly-induced current can be isolated in the second order electrical conductivity. Our findings demonstrate that the semiclassical picture of quasiparticle response needs to be updated: Charge transport generically derives from quasiparticle motion in an emergent curved spacetime, thereby indicating that Fermi liquid theory as it was originally conceived is incomplete beyond linear order.

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