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

Abstract

We investigate the pumped charge and spin at zero bias by a 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 in this limit the equivalence between our approach and the real-time diagrammatic approach. An adiabatic modulation of the control parameters induces the BerrySinitsyn-Nemenman (BSN) phase. We show that the origin of the BSN phase is a nonadiabatic effect. The 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 noninteracting and strong interacting limits. We show that the difference between these two limits appears through the instantaneous 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.

Gauge freedom in observables and Landsberg's nonadiabatic geometric phase: Pumping spectroscopy of interacting open quantum systems

“…This comparison allows us to resolve the important issue regarding the "adiabaticity" of the FCS going beyond the scope of [75]. Also, we show how within this physical nonadiabatic picture of the AR approach, the geometric nature of pumping can be fully understood, independent of the FCS formulation, thereby avoiding the nontrivial issue of its "adiabaticity."…”

“…three of these formulations, found in [37,38,40,43,44,75], respectively. Before we outline the key results of our paper, we sketch these three geometric approaches, taking note of many other density-operator based works [18,[27][28][29][30][31][32][33][34][35][36]39,41,42].…”

“…It was also used to demonstrate that thermodynamic vector potentials arise in slow but nonadiabatic transformations between nonequilibrium steady states [99] accounting for geometric heat and excess entropy production. In a recent paper [75], Nakajima et al addressed a possible point of confusion in the FCS approach: how can an "adiabatic" approach include physically nonadiabatic pumping? In the last part of this paper we will further clarify this issue, extending their observations.…”

“…AR ↔ FCS Nonadiabatic Landsberg phase (Sec. V C 4) equal to χ -linear part of FCS phase [75] 155431-3 pumping problems and is reviewed in [44]: applications range from molecular reactions [40,44,92] to heat transport through strongly anharmonic molecules [93,94], and strongly interacting quantum dots [75,[95][96][97][98]. It was also used to demonstrate that thermodynamic vector potentials arise in slow but nonadiabatic transformations between nonequilibrium steady states [99] accounting for geometric heat and excess entropy production.…”

Geometric fluctuation theorem for a spin-boson system

“…It is remarkable that there exists a net average current without dc bias in the geometric pumping. This phenomenon has been observed in various processes such as quantized charge transports [2][3][4][5][6][7][8][9][10][11][12], spin pumpings [13][14][15][16][17][18][19][20] and qubit manipulations [21]. Such systems can be described by classical master equations [22][23][24][25][26][27][28][29][30][31][32][33] or quantum master equations [15-17, 20, 21, 34-38].…”