Parametric study for optimal performance of Coulomb-coupled quantum dots


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In recent decades, quantum heat engines which is regarded as a heat-to-work device using thermoelectric effects at the mesoscopic scale, especially, the three or four terminal heat engines using the Coulomb coupled Quantum Dots, attracts a great interest.

Since Hicks, et al showed that the thermoelectric figure of merit can be increased in low dimensions and Mahan, et al showed that the best energy filters are also the best thermoelectric, the research into this field has further become active. Quantum dot has both low dimension and discrete energy, and the energy level and coupling strength to the reservoir are controlled by means of the gate voltage as well, thus the quantum dot has become an important candidate for developing high-efficient heat engines.

The earliest models of quantum dot heat engines were two-terminal devices, which consisted of single quantum dot coupled to two reservoirs at different temperatures and different electrochemical potentials. Recent experiments demonstrated that this engine can achieve much higher efficiency than the classical heat engines. But in this two-terminal geometry, the heat and charge flow are carried by the same particles. For applications, materials need to have high electrical conductance while at the same time low thermal conductance. Thus, the intimate coupling between the heat and charge flow in two-terminal devices poses a big problem.

To overcome this, multi-terminal heat engines have been proposed. These engines separate the system into a conductor and environment and control the interaction between the two subsystems. The three-terminal heat engine with Coulomb-coupled double quantum dots (CCQD) is one of the examples, especially, peculiar drag effects such as Coulomb drag and thermal drag make this device curious.

Sanchez, et al, first suggested the three-terminal setup and showed the behavior of power and efficiency. According to them, the efficiency of this heat engine depends linearly on the bias voltage, thus it can, in principle, achieve the Carnot efficiency by increasing the bias. The problem is that there is no one-to-one correspondence in this device and moreover in the Coulomb blockade region cotunneling effect appears and suppresses the efficiency and output power of the devices. therefore, it is very important to find the optimal conditions in terms of power and efficiency. These conditions are determined by several parameters such as Coulomb interaction, bias voltage, tunneling parameters and temperature difference.

To do this, we should use the optimization algorithms. Well-known optimization methods are genetic algorithm (GA), particle swarm optimization [37], etc. GA, one of the intelligent optimization algorithms, is based on the basic principles of natural evolution and optimal solution has evolved through following three steps; selection, crossover and mutation. MOGA is a sort of GA for multi-objective problems and in generally, the objective functions in multi-objective problem always contradict each other. The improvement of one objective function may result decreasing of others, therefore, it is impossible to optimize all objective functions simultaneously. In this case, the corresponding optimal solutions are certain "compromise" between those objective functions, while they get close to their optimum as much as possible. These corresponding optimal solutions are called Pareto optimal solution and the set of these optimal solutions in parameter space is called Pareto front.

Recently, we have investigated the optimal properties of three terminal heat engine with Coulomb coupled Quantum dots by using the MOGA. We have studied the efficiency and output power of this device and found the optimal properties in terms of parameters such as Coulomb interaction, tunneling parameter, bias voltage.

The result is given by the Pareto front and their corresponding parameters and objective functions. Every point in Pareto front has its own advantage and which is best can be chosen in experiments or engineering.

Our work has been published in "J. Phys.: Condens. Matter" (33 (2021) 375302) under the title of "Parametric study for optimal performance of Coulomb-coupled quantum dots" (