Charge pumping in a quantum wire driven by a series of local time-periodic potentials

We develop a method to calculate electronic transport properties through a mesoscopic scattering region in the presence of a series of time-periodic potentials. Using the method, the quantum charge pumping driven by time-periodic potentials is studied. Jumps in the pumped current are observed at the peak positions of the Wigner delay time. Our main results in both the weak pumping and strong pumping regimes are consistent with experimental results. More interestingly, we also observed the nonzero pumping at the phase difference $\phi =0\mathrm{}$ and addressed its relevance to the experimental result.