Surface acoustic waves (SAWs) on piezoelectric insulators can generate dynamic periodic potentials inside one-dimensional and two-dimensional materials. These periodic potentials have been utilized or proposed for various applications, which I will review in this presentation. One such application is acoustoelectric charge pumping, which I have investigated in my experiments on specially fabricated graphene devices that have very low electrostatic disorder. By employing a graphite top gate on boron-nitride-encapsulated graphene, I adjust the graphene carrier concentration over a broad range, enabling us to examine the acoustoelectric signal in both mixed-carrier and single-carrier regimes. I will discuss the benefits of hBN-encapsulated graphene for charge pumping applications and introduce a model that describes the acoustoelectric signal across all carrier concentrations, including at the charge neutrality point. This quantitative model will support future SAW-enabled explorations of phenomena in low-dimensional materials and guide the design of novel SAW sensors.