Interaction-induced charge and spin pumping through a quantum dot at finite bias

Abstract

We investigate charge and spin transport through an adiabatically driven, strongly interacting quantum dot weakly coupled to two metallic contacts with finite bias voltage. Within a kinetic equation approach, we identify coefficients of response to the time-dependent external driving and relate these to the concepts of charge and spin emissivities previously discussed within the time-dependent scattering matrix approach. Expressed in terms of auxiliary vector fields, the response coefficients allow for a straightforward analysis of recently predicted interaction-induced pumping under periodic modulation of the gate and bias voltage [Reckermann et al., Phys. Rev. Lett. 104, 226803 (2010)]. We perform a detailed study of this effect and the related adiabatic Coulomb blockade spectroscopy, and, in particular, extend it to spin pumping. Analytic formulas for the pumped charge and spin in the regimes of small and large driving amplitude are provided for arbitrary bias. In the absence of a magnetic field, we obtain a striking, simple relation between the pumped charge at zero bias and at bias equal to the Coulomb charging energy. At finite magnetic field, there is a possibility to have interaction-induced pure spin pumping at this finite bias value, and generally, additional features appear in the pumped charge. For large-amplitude adiabatic driving, the magnitude of both the pumped charge and spin at the various resonances saturates at values which are independent of the specific shape of the pumping cycle. Each of these values provides an independent, quantitative measure of the junction asymmetry.

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

“…The first is the Green's function approach to pumping [26][27][28]. The second is the real-time diagrammatic approach [29][30][31][32][33][34][35][36] (RT approach), which uses the generalized master equation (GME) that is equivalent [37,38] to the quantum master equation (QME) derived using the Nakajima-Zwanzig projection operator technique [39]. Particularly, Ref.…”

“…Particularly, Ref. [34] derived a geometric expression similar to the Brouwer formula and the Berry-Sinitsyn-Nemenman (BSN) vector explained later. The third is the full counting statistics [40][41][42] (FCS) with the quantum master equation (FCS-QME, which is also * tokura.yasuhiro.ft@u.tsukuba.ac.jp called generalized quantum master equation [42]) approach proposed in Ref.…”

“…Some recent papers [33,34,43] showed that the Coulomb interaction induces the quantum pump. In Refs.…”

“…[33,34], it was shown that in a one level interacting quantum dot (QD) weakly coupled to two leads, the pumped charge (also spin in Ref. [34]) induced by an adiabatic modulation of the energy level of the QD and the bias between the two leads vanishes in the noninteracting limit. In particular, Yuge et al [43] studied the pumped charge coming from the BSN curvatures by adiabatic modulation of the thermodynamic parameters (the chemical potentials and the temperatures) in spinless QDs weakly coupled to two spinless leads and showed that the BSN curvatures are zero in noninteracting QDs although they are nonzero for finite interaction.…”

“…II A). We then study the nonadiabatic effects in general Markov systems and clarified the relations between the FCS-QME approach and the RT approach [34] in Sec. II B. Additionally we show that the origin of the BSN phase is a nonadiabatic effect.…”