  We investigate the pumped charge and spin at zero-bias by adiabatic
modulation of two control parameters using the full counting statistics with
quantum master equation approach. First we study higher order effects of the
pumping frequency in general Markov systems and show the equivalence between
our approach and the real-time diagrammatic approach. An adiabatic modulation
of the control parameters induces the Berry-Sinitsyn-Nemenman (BSN) phase. We
show that the origin of the BSN phase is a non-adiabatic effect. The
adiabatically pumped charge (spin) is given by a summation of (i) a time
integral of the instantaneous steady charge (spin) current and (ii) a geometric
surface integral of the BSN curvature, which results from the BSN phase. In
quantum dots (QDs) weakly coupled to two leads, we show that (i) is usually
dominant if the thermodynamic parameters are modulated although it is zero if
the thermodynamic parameters are fixed to zero-bias. To observe the spin
effects, we consider collinear magnetic fields, which relate to spins through
the Zeeman effect, with different amplitudes applying to the QDs and the leads.
For interacting one level QD, we calculate analytically the pumped charge and
spin by modulating the magnetic fields and the coupling strengths to the leads
in the weak and strong interacting limits. We show that the difference between
these two limits appears through the averages of the numbers of the electron
with up and down spin in the QD. For the quantum pump by the modulation of the
magnetic fields of the QD and one lead, the energy-dependences of linewidth
functions, which are usually neglected, are essential.
