In Fig we present the contour plot of the

The spin current and the heat generation varying as functions of the spin bias for different values of the system temperature are illustrated in Figs. 3(a) and 3(b), respectively. In the low temperature regime, the two plateaus and the phonon-induced sub-steps in the current are clearly visible. With raising temperature, the cures of both Js−VsJs−Vs and Q−VsQ−Vs become more smooth, with unchanged qualitative behaviors. Here one can also see that BMS-707035 unlike the current, the derivative of the curve of the heat generation with respective to the bias dQ/dVsdQ/dVs shows no phonon side peaks [7] and [8]. In Fig. 3(c) we show the dependence of the heat generation on the line-width function Γ0Γ0 for different values of dot level. The heat generation first increases with increasing Γ0Γ0, reaching a maximum and then decreases with further increased line-width function. The enhanced heat generation by increasing Γ0Γ0 can be attributed to the broadening of the dot level. In the case of Te=TphTe=Tph, the heat generation can be simplified to the following form [7] and [11],equation(7)Q=∑σωqλ2Γ˜LΓ˜R∫dω2πfLRσ(ω)fLRσ(ω¯)Tσ(ω)Tσ(ω¯), where fLRσ(ω)fLRσ(ω) and fLRσ(ω¯) are individually fLσ(ω)−fRσ(ω)fLσ(ω)−fRσ(ω) and fLσ(ω¯)−fRσ(ω¯). Obviously, larger line-width function will make the transmission spectrum wider and enlarge the overlaps of fLRσ(ω)Tσ(ω)fLRσ(ω)Tσ(ω) and fLRσ(ω¯)Tσ(ω¯). In this way, the heat generation is enhanced. With further increasing Γ0Γ0, however, the time of an electron spent in the QD will be shortened and then the heat generation will be decreased. Fig. 3(d) shows that the heat generation has a huge peak at U=ωqU=ωq. This peak is induced by the resonant phonon emitting process happening between the two real electron levels εdεd and εd+Uεd+U[8].