Acoustoelectric effect in nanostructures: Role of quasimomentum balance

Abstract

In a recent paper giant quantum oscillations of acoustoelectric current under gate voltage variation were predicted for ballistic transport in nanowires. In particular, it was shown that the oscillations should exist provided that the sound frequency $\omega$ exceeds a certain threshold value ${\omega }_{\mathrm{th}}$ and no acoustoelectric effect exists for $\omega <{\omega }_{\mathrm{th}}.$ The result seems to be in contradiction with a simple energy and quasimomentum balance considerations that in the bulk case lead to the so-called Weinreich relation for the acoustoelectric current. We discuss this paradox in detail and prove it to be related to the very nature of ballistic transport. We develop a theory of the acoustoelectric effect for $\omega <{\omega }_{\mathrm{th}}$ assuming that the transport is not purely collisionless.