Thermoelectric properties of interacting double quantum dots

TL;DR

This work addresses thermoelectric transport through an interacting parallel double quantum dot in the Coulomb-blockade regime. It develops an analytical equation-of-motion framework that delivers closed-form steady-state charge and heat currents, as well as linear and nonlinear transport coefficients, under asymmetrical dot-lead couplings. Transport are governed by the pole structure of the retarded Green's function, producing gate- and bias-dependent stripe resonances, regions of negative differential thermal conductance, and interaction-induced efficiency gains at finite power. The study also provides compact analytic treatments of thermal rectification for both open and closed circuits, identifies operating points that maximize efficiency and power, and highlights practical implications for nanoscale thermoelectric devices driven far from equilibrium.

Abstract

We investigate the thermoelectric transport properties of an interacting parallel double quantum dot in the Coulomb-blockade regime. Building on an analytical solution based on an equation-of-motion technique, we extend the formalism for the asymmetrically coupled situation and provide compact closed-form expressions for steady-state currents together with the differential conductance, Seebeck coefficient, and thermal conductance. We determine the operating points that maximize efficiency and output power of the system, clarifying their relation to standard near-equilibrium ZT expressions. We further study the thermal rectification in both the open- and closed-circuit configurations and derive an expression for the open-circuit case. Interaction-induced resonances are understood in terms of the poles of the resulting Green's function, generating gate and bias dependent regions of enhanced efficiency at finite power, negative differential thermal conductance, and finite thermal rectification.

Figures (7)

• Figure 1: Schematic transport setup representation of the DQD system. The interacting dots are coupled to the leads at temperatures $T_\alpha$, and chemical potentials $\mu_\alpha$ through the coupling strengths $\boldsymbol{\Gamma}_{ii}^{\alpha}=\gamma_\alpha/2$, with $\alpha=L,R$.
• Figure 2: Differential conductance $\frac{G}{G_0}$ (panels b), and f)), differential Seebeck $S$ (panels c), and g)), and differential thermal conductance $\frac{\kappa}{G_0}$ (panels d), and h)) as a function of the gates $\varepsilon_1$ and $\varepsilon_2$ for $U_1=2$, $U_2=3$, $T=0.1$, $\gamma = 0.1$, $\Delta T=0$, and up) $V=0.5$ down) $V=1$. Panels a) and e) show the finite charge current contributions from the poles ($p_j \in \{p_{1,j},p_{2,j}\}$) as defined in \ref{['eq_I_pi']} in the low temperature limit. Energies in units of $U_{12}$.
• Figure 3: Differential conductance $\frac{G}{ G_0}$ (panels b), and e)), differential Seebeck $S$ (panels c), and f)), and differential thermal conductance $\frac{\kappa}{ G_0}$ (panels d), and g)) as a function of the gate $\varepsilon$ and the bias $V$ for $U_1=2.2$, $U_2=1.4$, $T=0.1$, $\gamma = 0.1$, and up) $\Delta T=0$ down) $\Delta T\to 2T$. Panel a) shows the finite contributions from the poles ($p_j \in \{p_{1,j},p_{2,j}\}$) corresponding to solutions of $p_{i,j} -V_\alpha = 0$, where the solid (dashed) lines correspond to site two (one) and the lines with positive (negative) slopes correspond to $V_L$ ($V_R$). Energies in units of $U_{12}$.
• Figure 4: Differential transport coefficients as a function of the gate level $\varepsilon$ and the thermal gradient $\Delta T$ for $U_1=U_2=1$, $V=0$, $T=0.1$, and $\gamma = 0.05$. Energies in units of $U_{12}$.
• Figure 5: Up: maximum thermoelectric efficiency $\eta_{max}$ and bias $V_0$ that maximizes the efficiency, and down: efficiency at maximum output power $\eta(P_{max})$ and bias $V_1$ that maximizes the output power as a function of the gate level $\varepsilon=\varepsilon_1=\varepsilon_2$ for different fixed thermal gradients. The dashed lines represent the results obtained from linear response, while the solid line corresponds to the expressions beyond the linear response. The parameters are $T=2\gamma=0.2$, and $U_i=1$. Energies in units of $U_{12}$.