Thermoelectric effects in transport through quantum dots attached to ferromagnetic leads with noncollinear magnetic moments

Charge transport accompanied by heat transfer through a single-level quantum dot coupled to ferromagnetic leads with noncollinear magnetic moments is studied theoretically in the linear and nonlinear transport regimes. Calculations performed in the framework of nonequilibrium Green’s function formalism and the equation of motion method reveal a significant influence of Coulomb blockade on thermal transport processes. The thermopower $S$ and thermal efficiency described by the figure of merit $ZT$ depend on magnetic configuration of the system. Two physically different situations are considered; one appears when spin accumulation is excluded and the second one when spin accumulation is relevant. In the latter case we also calculate the corresponding spin thermopower. Apart from this, magnetothermopower is introduced and discussed.

Figure 1

(a) Linear electrical conductance $G$, (b) thermal conductance $\kappa$, (c) thermopower $S$, and (d) $ZT$ as a function of level position and temperature, calculated for $\Gamma =0.1\text{meV}$, $U=2\text{meV}$, and $p=0.2$.

Figure 2

(Color online) (a) Thermal conductance $\kappa$, (b) thermopower $S$, and (c) $ZT$ as a function of the level position for indicated values of the spin polarization $p$. The other parameters are: $\Gamma =0.1\text{meV}$, $U=2\text{meV}$, and $kT=0.1\text{meV}$.

Figure 3

(Color online) Lorentz ratio as a function of level position for indicated values of the spin polarization $p$. The other parameters are: $\Gamma =0.1\text{meV}$, $U=2\text{meV}$, and $kT=0.1\text{meV}$.

Figure 4

(Color online) Thermal conductance $\kappa$ (a) as a function of the level position ${\epsilon }_0$ and angle $\theta$ and (b) as a function of ${\epsilon }_0$ for indicated values of $\theta$. The other parameters are: $p=0.95$, $\Gamma =0.1\text{meV}$, $U=2\text{meV}$, and $kT=0.1\text{meV}$.

Figure 5

(Color online) (a) Thermopower for indicated values of $\theta$ and (b) magnetothermopower as a function of the level position. MTP $\left(\theta \right)$ for indicated values of ${\epsilon }_0$ (c). The other parameters are: $p=0.95$, $\Gamma =0.1\text{meV}$, $U=2\text{meV}$, and $kT=0.1\text{meV}$.

Figure 6

(Color online) (a) Lorentz ratio and (b) $ZT$ as a function of the level position for indicated values of $\theta$. Τhe other parameters are: $p=0.95$, $\Gamma =0.1\text{meV}$, $U=2\text{meV}$, and $kT=0.1\text{meV}$.

Figure 7

(Color online) Thermopower as a function of level position calculated under the condition of $I_{\sigma }=0$ for indicated spin polarization of the leads. The other parameters are: $\Gamma =0.1\text{meV}$, $U=2\text{meV}$, and $kT=0.1\text{meV}$.

Figure 8

(Color online) (a) Figure of merit $ZT$ and (b) $Z_{spin}T$ as a function of level position calculated under the condition of $I_{\sigma }=0$ for indicated values of $p$. The other parameters are: $\Gamma =0.1\text{meV}$, $U=2\text{meV}$, and $kT=0.1\text{meV}$.

Figure 9

(Color online) Differential thermopower (a) in the absence of spin accumulation and (b) with spin accumulation as a function of temperature difference for indicated level position and polarization $p$, calculated for the condition of (a) vanishing charge current and (b) spin and charge currents, $\Gamma =0.1\text{meV}$, $U=2\text{meV}$, and $k{T}_R=0.1\text{meV}$.