Interaction effect on adiabatic pump of charge and spin in quantum dot

TL;DR

This paper studies adiabatic charge and spin pumping in quantum dots, revealing the roles of geometric phases and interactions, and providing analytical results for different regimes.

Contribution

It introduces a full counting statistics approach to analyze higher order effects and the origin of BSN phases in quantum dot charge and spin pumping.

Findings

The BSN phase is a non-adiabatic effect.

Charge and spin are influenced by magnetic field modulation.

Energy dependence of linewidth functions is crucial for spin pumping.

Abstract

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.