Strongly nonlinear thermovoltage and heat dissipation in interacting quantum dots

We investigate the nonlinear regime of charge and energy transport through Coulomb-blockaded quantum dots. We discuss crossed effects that arise when electrons move in response to thermal gradients (Seebeck effect) or energy flows in reaction to voltage differences (Peltier effect). We find that the differential thermoelectric conductance shows a characteristic Coulomb butterfly structure due to charging effects. Importantly, we show that experimentally observed thermovoltage zeros are caused by the activation of Coulomb resonances at large thermal shifts. Furthermore, the power dissipation asymmetry between the two attached electrodes can be manipulated with the applied voltage, which has implications for the efficient design of nanoscale coolers.

Figure 1

(a) Current-voltage characteristics of a dc-biased single-level Coulomb-blockaded quantum dot (see the sketch) for the indicated gate voltages (level positions). Inset: dot occupation as a function of the voltage bias. (b) Differential conductance versus level position and bias voltage. (c) Thermocurrent of a single-level Coulomb-blockaded quantum dot as a function of the temperature difference shown in the sketch. (d) Differential thermoelectric conductance versus level position and bias voltage. Solid (dashed) lines indicate positive (negative) values. Parameters: charging energy $U=10$ and background temperature $k_{B}T=0.1$. All energies are expressed in terms of ${\Gamma }_L={\Gamma }_R=\Gamma /2$.

Figure 2

Left: energy diagram corresponding to the current states of the right panel. $E_F$ $\left({\varepsilon }_d\right)$ is indicated with dashed (dotted-dashed) lines. Right: thermocurrent as a function of the temperature difference for ${\varepsilon }_d=-3U/4$ as taken from Fig. 1. Note that the electron flow from the left (right) electrode at point $A$ $\left(C\right)$ dominates but exactly cancels out for point $B$.

Figure 3

(a) Thermovoltage as a function of the temperature difference for the indicated values of the gate voltages (level positions). (b) Differential thermopower $S=d{V}_{th}/d\theta$ in units of $k_B/e$. Parameters: $U=10,k_{B}T=0.1$ and energy is given in units of ${\Gamma }_L={\Gamma }_R=\Gamma /2$.

Figure 4

Heat current as a function of applied voltage in the isothermal case $\theta =0$. Dot level positions are also indicated. Inset: Detail of the dissipated power around zero voltage. (b) Asymmetric dissipation versus voltage bias for the same gate voltages. Parameters: $U=10,k_{B}T=0.1$ and energy is given in units of ${\Gamma }_L={\Gamma }_R=\Gamma /2$.