  In this Letter, we present a theoretical analysis to single-electron pumping
operation in a large range of driving frequencies through the time-dependent
tunneling barriers controlled by external gate voltages. We show that the
single-electron turnstile works at the frequency lower than the characteristic
frequency which is determined by the mean average electron tunneling rate. When
the driving frequency is greater than the characteristic frequency of electron
tunnelings, fractional electron pumping occurs as an effect of quantum
coherence tunneling.
