Second-order nonlinear Hall effect in Weyl semimetals

We investigate the second-order nonlinear Hall effect of Weyl semimetals using a quantum theory, paying attention to the interband process and quantum interference effect. The Drude-type nonlinear Hall conductivity due to the intraband process is found for each Weyl node in the low-frequency regime (the photon energy of the incident field is much smaller than the chemical potential). While in the high-frequency regime with the interband process dominated, the nonlinear photoconductivity shows a two-photon resonant peak or double peaks due to inversion symmetry breaking. The peak splitting is determined by the chemical potential and tilt of the Weyl node. There is a nonmonotonic dependence of the nonlinear Hall current on the tilt of the Weyl node, and an optimal tilt for the maximum Hall current has been found. Moreover, with the help of quantum interference, the nonlinear Hall response can be effectively modulated by tuning the amplitude, phase, and polarization of the incident fields. In particular, in the presence of driving fields with frequencies ${\ensuremath{\omega}}_{0}$ and $3{\ensuremath{\omega}}_{0}$, the interplay between the optical processes of second-harmonic generation and different frequency generation leads to the chirality-selective generation of nonlinear Hall current under suitable conditions.