Strongly enhanced nonlinear acoustic valley Hall effect in tilted Dirac materials

It has been recently established that a nonlinear valley current can be generated through propagating a surface acoustic wave (SAW) in two-dimensional Dirac materials. So far, the SAW-driven valley currents have been attributed to the warped Fermi surface or the Berry phase effect. Here, we demonstrate that the tilt mechanism can also lead to a nonlinear valley Hall current (VHC) when propagating SAWs in materials with the tilted Dirac cone placed on a piezoelectric substrate. It has been found that the nonlinear VHC exhibits a sin theta dependence on the orientation of the tilt with respect to the SAW. In addition, this tilt-induced nonlinear acoustic VHC shows independence of the relaxation time, distinguished from the contributions from the Berry phase or trigonal warping. Remarkably, the magnitude of the nonlinear acoustic VHC from the tilt mechanism in the uniaxially strained graphene is 2 orders larger than those reported in MoS2 stemming from the Berry phase effect and the warping effect.