Adiabatic electron pumping through a quantum dot with a discrete level

An adiabatic electron pumping through a quantum dot with a discrete energy level under a magnetic field is investigated theoretically. Adiabatic spin pumping takes place under two time-dependent external sources, the Zeeman energy and the difference in the tunneling coupling to the dot between the left and right leads. The behavior of the pumped spin as a function of the amplitude of the magnetic field is different whether the dot level is above the Fermi level in leads.