Electrons flow like falling cats: Deformations and emergent gravity in quantum transport
When cold electrons move in a perfect and static lattice, according to conventional wisdom, they behave like almost free quasiparticles in flat space. Here, we present evidence that this is not entirely correct, and quasiparticles actually move in an emergent curved spacetime.To this end, we discuss both the semiclassical equations of motion and the Kubo formalism for materials lacking inversion and time-reversal symmetry, whose conductivity exhibits a mixed axial-gravitational anomaly at second order in the electric field. We can explain this surprising result in terms of dynamical deformations of the semiclassical wavepacket as it moves through the periodic lattice potential, thereby establishing a common framework for the appearance of anomalous terms in many response functions. Our proposition that quasiparticles behave essentially like quantum cats has powerful implications for all types of quantum transport and may allow to probe synthetic gravitational fields in a bulk condensed matter setting.