Quantum parametric pump in a quantum wire

The charge pumping is investigated in a quasi-one-dimensional quantum wire within an external perpendicular magnetic field. A formula of the pumped current at finite frequency is derived by using scattering matrix method. It is found that the pumped current oscillates with the magnetic field due to Aharonov-Bohm effect and the oscillating period is only dependent on the effective area enclosed by two pumping potentials. At a weak magnetic field, the pumped current also exhibits an approximate magnetic field inversion symmetry