Acoustoelectric effects in quantum constrictions

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A dc current induced in a quantum constriction by a traveling acoustic wave (or by non-equilibrium ballistic phonons) is considered. We show that in many important situations the effect is originated from acoustically-induced scattering between the propagating and reflecting states in the constriction. Two particular regimes corresponding to relatively high and low acoustic frequencies are discussed. In the first regime, the acoustoelectric effect in a smooth constriction can be understood by semi-classical considerations based on local conservation laws. For the low frequency regime, we show that the acousto-conductance is closely related to the zero field conductance. The qualitative considerations are confirmed by numerical calculations both for smooth and abrupt channels.