Influence of interference effects on thermoelectric properties of double quantum dots

Electron and thermal transport through a double quantum dot/artificial molecule is studied theoretically in the linear response regime with use of Green function formalism. Gradually changing the system geometry from the configuration in series toward parallel ones, we demonstrate interplay between interference processes and thermoelectric effects. If the tunnelling through the antibonding state is progressively reduced, electronic-thermal conductance exhibits features typical for Fano effect with a well-pronounced antiresonance, in which position and intensity depend on the system geometry. Moreover, there is a possibility to manipulate the conductance using an external magnetic field. Thermopower and thermoelectric efficiency, described by the dimensionless figure of merit (FOM) $ZT$, significantly increase because of interference effects. Interdot Coulomb interaction, described by the parameter $U$, strongly influences thermoelectric properties. Optimal conditions toward thermoelectricity with high $ZT$ can by fulfilled for relatively strong correlation $U$. However, dramatic changes can be observed in the region of small $U$, where efficiency is very low. Because in double dots the interdot electrostatic interaction can be varied in a controlled way, the resonant enhancement of efficiency can be attained.

Figure 1

(a,b) Electronic thermal conductance, (c,d) thermopower, and (e,f) FOM as a function of gate voltage for $\mathit{kT}$ $=$ 0.01$t$ (left panel) and $\mathit{kT}$ $=$ 0.15$t$ (right panel). Insets to figures (d) and (f) give $S$ and $ZT$, respectively, for α $=$ 0.15 and indicated temperatures. Other parameters are Γ $=$ $t$, $E_1$ $=$ $E_2$ $=$ 0, $U$ $=$ 0.

Figure 2

(a,b) Electronic thermal conductance, (c,d) Lorentz ratio, (e,f) thermopower, and (g,h) FOM as a function of gate voltage for indicated values of magnetic flux ϕ, α $=$ 0.15, and $\mathit{kT}$ $=$ 0.01$t$ (left panel) and $\mathit{kT}$ $=$ 0.15$t$ (right panel). Other parameters are the same as in Fig. 1.

Figure 3

$ZT$ in function of gate voltage and α for ϕ $=$ 0 and $\mathit{kT}$ $=$ 0.15t. Other parameters are the same as in Fig. 1.

Figure 4

(a) $ZT$ and (b) Lorentz ratio as a function of $\mathit{kT}$ for indicated values of gate voltage and α. Other parameters are the same as in Fig. 1.

Figure 5

Electronic-thermal conductance as a function of gate voltage for α $=$ 0.3 and indicated values of $U$. $\mathit{kT}$ $=$ 0.01$t$ (left panel) and $\mathit{kT}$ $=$ 0.15$t$ (right panel). Other parameters are Γ $=$ $t$, $E_1$ $=$ $E_2$ $=$ 0.

Figure 6

Electronic thermal conductance for indicated values of magnetic flux ϕ calculated as a function of gate voltage with α $=$ 0.3, (a) $\mathit{kT}$ $=$ 0.01$t$ and (b) $\mathit{kT}$ $=$ 0.15$t$, $U$ $=$ 7$t$. Other parameters are the same as in Fig. 5.

Figure 7

$ZT$ and $S$ (inset) in function of gate voltage for indicated values of α and kT. U $=$ 7t. Other parameters are the same as in Fig. 5.

Figure 8

$ZT$ in function of α and $U$ for $\mathit{kT}$ $=$ 0.15$t$, $V_g$ $=$ −1.5$t$. Other parameters are the same as in Fig. 5.

Figure 9

(a) FOM, (b) thermal conductance, (c) thermopower, and (d) Lorentz ratio as a function of $U$ for indicated values of α and $V_g$ $=$ −1.5$t$, $\mathit{kT}$ $=$ 0.15$t$. Other parameters are the same as in Fig. 5.

Figure 10

$ZT$ as a function of $V_g$ and $U$ for α $=$ 0.15. (a) ϕ $=$ 0 and (b) ϕ $=$ 2π. $\mathit{kT}$ $=$ 0.15$t$. Other parameters are the same as in Fig. 5.

Figure 11

(a) Thermal conductance, (b) Lorentz ratio, (c) thermopower, and (d) FOM as a function of $\mathit{kT}$ for indicated values of α and two different values of $V_g$, $U$ $=$ 7$t$. Other parameters are the same as in Fig. 5.

Figure 12

$ZT$ as a function of coupling strength Γ for (a) $U$ $=$ 0 and indicated values of (b) $U$. $\mathit{kT}$ $=$ 0.15$t$, $V_g$ $=$ −1.5$t$. Other parameters are the same as in Fig. 5.