Quantized pumped charge due to surface acoustic waves in a one-dimensional channel

The quantum-mechanical adiabatic current, pumped through an unbiased one-dimensional (1D) channel, connected to two 1D leads and subject to surface acoustic waves (SAW), is calculated exactly for noninteracting electrons. The resulting pumped charge (during each period of the SAW) exhibits a staircase structure, with integer values (in units of electronic charge). We also find staircases for higher harmonics of the current. The qualitative dependence of these staircases on many parameters is reminiscent of experimental observations.