Electrons flow like falling cats: Deformations and emergent gravity in quantum transport

When cold electrons move in a perfect, static, and stable lattice, according to conventional wisdom, they move 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 the second order electrical conductivity in materials lacking inversion and time-reversal symmetry, which exhibits a mixed axial-gravitational anomaly. 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.

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