Three-terminal quantum-dot refrigerators

Based on two capacitively coupled quantum dots in the Coulomb-blockade regime, a model of three-terminal quantum-dot refrigerators is proposed. With the help of the master equation, the transport properties of steady-state charge current and energy flow between two quantum dots and thermal reservoirs are revealed. It is expounded that such a structure can be used to construct a refrigerator by controlling the voltage bias and temperature ratio. The thermodynamic performance characteristics of the refrigerator are analyzed, including the cooling power, coefficient of performance (COP), maximum cooling power, and maximum COP. Moreover, the optimal regions of main performance parameters are determined. The influence of dissipative tunnel processes on the optimal performance is discussed in detail. Finally, the performance characteristics of the refrigerators operated in two different cases are compared.

Figure 1

(a) The schematic diagram of a three-terminal quantum-dot refrigerator. (b) Available transition for the situation described in (a).

Figure 2

Charge currents $I$ and heat flows $\dot{Q}$ as a function of the voltage bias for $\lambda =0.1$. Inset (a): the partial enlarged detail.

Figure 3

The curves of charge currents $I$ and heat flows $\dot{Q}$ varying with the dissipation factor $\lambda$ for $q\Delta V/\left(\hslash \gamma \right)=45$.

Figure 4

Performance characteristics of a three-terminal quantum-dot refrigerator. (a) The cooling power and (b) the coefficient of performance as a function of the voltage bias for different values of the dissipation factor $\lambda$. (c) Characteristic curves for different values of dissipation factor $\lambda$. Inset (a): the partial enlarged detail.

Figure 5

The threshold voltage (solid line) and optimal voltage biases at the maximum cooling power (blue dot line) and maximum COP (red dash line) as a function of the dissipation factor $\lambda$.

Figure 6

(a) The maximum cooling power and (b) the COP at the maximum cooling power as a function of the temperature ratio $T_g/T_s$ for different values of the dissipation factor $\lambda$.

Figure 7

(a) The maximum COP and (b) the cooling power at the maximum COP as a function of the temperature ratio $T_g/T_s$ for different values of the dissipation factor $\lambda$.

Figure 8

The maximum cooling power (black line) and the COP at the maximum cooling power (blue line) as a function of the dissipation factor $\lambda$.

Figure 9

The maximum COP (black line) and the cooling power at the maximum COP (blue line) as a function of the dissipation factor $\lambda$.

Figure 10

The characteristic curves of the refrigerators in the cases of $T_g>T_s$ and $T_s>T_g$ for $\lambda =0.002$. Inset: the partial enlarged detail.

Figure 11

The maximum COPs as a function of the temperature ratio $\tau$ in the cases of $T_g>T_s$ and $T_s>T_g$ for $\lambda =0.01$. Inset: the partial enlarged detail.

Figure 12

The maximum COP (black line) and the cooling power at the maximum COP (blue line) as a function of the dissipation factor $\lambda$.