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

Abstract

The effective low-energy excitations in a metallic or semimetallic crystalline system (i.e. electronic quasiparticles) always have a finite spatial extent. It is self-evident but virtually unexplored how the associated internal degrees of freedom manifest themselves in the quasiparticle response. Here, we investigate this question by illuminating an intimate connection between the theory of nonlinear response and the equations of motion of classical deformable bodies. This connection establishes that nth-order response in an external perturbation corresponds to nth-order derivatives of the quasiparticle motion, where the resulting motion is anomalous at every order due to the internal degrees of freedom. This new point of view predicts that quasiparticles necessarily move in an emergent curved spacetime, even in a homogeneous and defectless lattice. We underscore these concepts using recent results on the second order electrical conductivity, elucidating the associated anomalous acceleration that the quasiparticle exhibits. Based on our observations, we predict the existence of an infinite series of anomalous components of the quasiparticle motion, and propose a new mapping between response theory in flat space and a gravitational theory for the center-of-mass coordinate.

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

“…It allows, for the first time, to probe in the electrical conductivity the nontrivial emergent spacetime in which the electrons move when traversing a periodic lattice. This emergent curved spacetime is consistent with a classical picture of transport of deformable wavepackets flexing and bending while they squeeze through the lattice atoms [29]. These results offer the exciting perspective that dynamical effects of motion in a Riemannian curved spacetime could be engineered and accessed in a genuine bulk setting, and not by strain engineering [48,[66][67][68][69][70][71].…”

“…A much more detailed justification why and how the nonlinear conductivity implies a nontrivial effective metric is given elsewhere [29]. Here, we focus on the AGA caused by motion in a curved spacetime as it is encoded in the second order dc-conductivity σ (2) , corresponding to a static nonlinear current j c = σ (2) ab;c E a E b in response to an applied electric field E. We reveal that σ (2) manifests the AGA by using standard perturbation theory.…”

General nonlinear Hall current in magnetic insulators beyond the quantum anomalous Hall effect

“…These nonlinear effects are due to virtual interband transitions, which have been shown to appear beyond linear response even in insulators [22,23]. This is a testament to the fact that the Hall conductivity is a response function which can depend on the applied bias and which is not identical in physical content to the Chern number of the ground state [24]. An intuitive picture of these interband transitions is shown in Fig.…”