Pseudogauge field driven acoustoelectric current in two-dimensional hexagonal Dirac materials

Using a diagrammatic scheme, we study the acoustoelectric effects in two-dimensional (2D) hexagonal Dirac materials due to the sound-induced pseudo-gauge field. We analyze both uniform and {\em spatially dispersive} currents in response to copropagating and counterpropagating sound waves, respectively. In addition to the longitudinal acoustoelectric current, we obtain an exotic {\em transverse} charge current flowing perpendicular to the sound propagation direction owing to the interplay of transverse and longitudinal gauge field components $j_T\propto A_L A^\ast_T$. In contrast to the almost isotropic directional profile of the longitudinal uniform current, a highly anisotropic transverse component $j_T\sim\sin(6\theta)$ is achieved that stems from the inherited three-fold symmetry of the hexagonal lattice. However, both longitudinal and transverse parts of the dispersive current are predicted to be strongly anisotropic $\sim\sin^2(3\theta)$ or $\cos^2(3\theta)$. We quantitatively estimate the pseudogauge field contribution to the acoustoelectric current that can be probed in future experiments in graphene and other 2D hexagonal Dirac materials.