We numerically study the parametric pumped current when magnetic field is applied both in the adiabatic and nonadiabatic regimes. In particular, we investigate the nature of pumped current for systems with resonance as well as antiresonance. It is found that, in the adiabatic regime, the pumped current changes sign across the sharp resonance with long lifetime, while the nonadiabatic pumped current at finite frequency does not. When the lifetime of the resonant level is short, the behaviors of the adiabatic and nonadiabatic pumped currents are similar with sign changes. Our results show that, at the energy where complete transmission occurs, the adiabatic pumped current is zero, while the nonadiabatic pumped current is nonzero. Different from the resonant case, both the adiabatic and nonadiabatic pumped currents are zero at antiresonance with complete reflection. We also investigate the pumped current when the other system parameters such as magnetic field, pumped frequency, and pumping potentials are varied. Interesting behaviors are revealed. Finally, we study the symmetry relation of the pumped current for several systems with different spatial symmetries upon reversal of magnetic field. Different from the previous theoretical prediction, we find that a system with general inversion symmetry can pump out a finite current in both the adiabatic and nonadiabatic regimes with an approximate relation $I\left(B\right)\approx I(-B)$ at small magnetic field. It has been shown theoretically that for systems with reflection symmetry, the pumped current satisfies the relation $I\left(B\right)=I(-B)$ in the adiabatic regime. Our results show that even for systems evolving from the inversion to reflection symmetry, the pumped current still obeys the relation $I\left(B\right)=I(-B)$ in the adiabatic regime at small magnetic field.

• Received 28 September 2011

DOI:https://doi.org/10.1103/PhysRevB.84.245323