Quantum theory of the nonlinear Hall effect

Z. Z. Du, C. M. Wang, Hai-Peng Sun, Hai-Zhou Lu, X. C. Xie

Published 2020-04-21Version 1

The nonlinear Hall effect is an unconventional response, in which a voltage can be driven by two perpendicular currents. It can survive under time-reversal symmetry and is sensitive to the breaking of discrete and crystal symmetries, which is unprecedented in the family of the Hall effects. The nonlinear Hall effect is quantum by nature because of its deep connection with the Berry curvature dipole. However, a full quantum description is still absent. Here we construct the quantum theory of the nonlinear Hall effect by using the diagrammatic techniques. We figure out totally 100 diagrams in 9 types that contribute to the leading nonlinear response in the weak-disorder limit. We show both qualitative and quantitative differences between the quantum theory and the semiclassical Boltzmann formulism. As an application of the diagrammatic results, we propose an experimental scheme to realize a pure electric detection of the Berry curvature distribution near the band edge. This work will be instructive for experimental and theoretical explorations of the topological physics beyond the linear regime.