  We have investigated the response of the acoustoelectric current driven by a
surface-acoustic wave through a quantum point contact in the closed-channel
regime. Under proper conditions, the current develops plateaus at integer
multiples of ef when the frequency f of the surface-acoustic wave or the gate
voltage Vg of the point contact is varied. A pronounced 1.1 MHz beat period of
the current indicates that the interference of the surface-acoustic wave with
reflected waves matters. This is supported by the results obtained after a
second independent beam of surface-acoustic wave was added, traveling in
opposite direction. We have found that two sub-intervals can be distinguished
within the 1.1 MHz modulation period, where two different sets of plateaus
dominate the acoustoelectric-current versus gate-voltage characteristics. In
some cases, both types of quantized steps appeared simultaneously, though at
different current values, as if they were superposed on each other. Their
presence could result from two independent quantization mechanisms for the
acoustoelectric current. We point out that short potential barriers determining
the properties of our nominally long constrictions could lead to an additional
quantization mechanism, independent from those described in the standard model
of 'moving quantum dots'.
