  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.
