Nonlinear current response of Weyl semimetals in the ultraquantum regime

There are many recent studies on the linear magnetotransport of Weyl semimetals in the presence of a weak electric field. In this paper, we theoretically investigate the nonlinear current response of type-I Weyl semimetals to strong electric fields E in the ultraquantum regime (with strong magnetic field B parallel to E). Our nonperturbative approach based on the stochastic Liouville equation reveals the nonmonotonic dependence of the current on the electric field. In the weak-field regime, the time-average current < j > proportional to v(F) vertical bar B vertical bar(vertical bar E vertical bar tau). (with tau being the relaxation time) as a consequence of the chiral anomaly. In the strong-field regime,< j > proportional to v(F) vertical bar B vertical bar/(vertical bar E vertical bar tau). The current achieves the maximal value when the corresponding Bloch oscillation frequency matches the relaxation rate. Moreover, the nonlinear magnetotransport properties are independent of the tilting of the Weyl node. We also point out the difference between the lattice model and low-energy continuum model. Our study makes an important step toward the understanding of nonlinear magnetotransport in Weyl semimetals.