Magnon-driven quantum dot refrigerators
Introduction
The specific low-dimensional structures are attracting much attention due to the advances in techniques for nanostructured materials [1], [2], [3]. Of particular interest, since the quantum-dot (QD) refrigerator was presented in 1993 by Edwards et al. [4], [5], [6], [7], are the nanothermoelectric setups using the quantum dot system.
Thus far, multi-terminal QD setups have been discussed in several references [8], [9], [10] because they allow for the crossed flows of the charge current and heat flow. Sánchez and Büttiker proposed a nano-sized structure consisting of two QDs coupled by the Coulomb interaction without particle exchange [8]. Entin-Wohlman et al. discussed a three-terminal thermoelectric setup composed of a resonant level, two electronic reservoirs, and a phonon source [9]. Li and Jia proposed a particle-exchange heat engine in which three QDs are coupled to two fermionic reservoirs and a bosonic reservoir [10].
The QD coupled to ferromagnetic reservoirs has underlying applications in spintronics, i.e., QD spin valves [11], [12], [13], [14]. Strasberg et al. proposed a model of an information driven current through a spin valve with which the Maxwell demon device can be physically realized [15]. Sothmann and Büttiker used two ferromagnetic reservoirs and a ferromagnetic insulator to generate a three-terminal QD setup with only one spin-splitting QD, which can convert part of the heat into an electron current [16]. It gives one type of multi-terminal setup, which can generate a spin-polarized charge current via a thermal gradient. The electron reservoirs of the conventional thermoelectric devices must be kept at different temperatures and chemical potentials [17], [18], [19], [20], whereas the magnon-driven QD setups can be operated between two ferromagnetic metals with identical temperature and used to exploit the heat of a ferromagnetic insulator reservoir [10], [16]. Based on the model in Ref. [16], we propose a refrigeration model to cool a bosonic reservoir. Note that when the irreversibility is taken into account, the refrigeration model is not the simple reverse operation of the heat engine model described in Ref. [16]. It includes not only the contribution of some crucial parameters such as the magnetic field, which was not discussed in Ref. [16], but also some applications that may be found in micromechanical systems [21], [22] and other fields.
In the present paper, the occupation probabilities of the QD are solved by using the model of a magnon-driven quantum dot refrigerator established here and the rate equation. The matter currents are analyzed, and several special cases are discussed. Both the cooling power and coefficient of performance (COP) are optimized by considering the influence of the external magnetic field and applied voltage. The effect of the temperature of the ferromagnetic insulator is considered. The performances of two magnon-driven quantum dot refrigerators with different cooling spaces are analyzed and compared.
Section snippets
Quantum dot refrigerator with a ferromagnetic insulator
Fig. 1(a) shows a refrigeration system consisting of a spin-splitting QD embedded in two ferromagnetic metallic leads at temperatures and and chemical potentials and and a ferromagnetic insulator at temperature . The two splitting levels are denoted as and . In Fig. 1(a), is the spin-dependent tunnel coupling strength between the ferromagnetic metallic lead r and the QD with spin σ. The density of state of the ferromagnetic metallic lead is spin-dependent. In
Performance characteristic analysis
First, the case of is considered. As a refrigerator, the heat needs to be absorbed from the cold reservoir and released to the hot reservoir. Because the spin-up electrons preferably tunnel between the left reservoir and the QD and the spin-down ones preferably tunnel between the right one and the QD, the direction of the flow of the matter current is from left to right, and consequently, the relation between the chemical potentials of the two leads should satisfy . By using Eqs. (6)
Conclusions
A magnon-driven QD refrigerator consisting of a spin-split QD coupled with two ferromagnetic leads and a ferromagnetic insulator has been established. The working conditions have been discussed in detail by using the spin-resolved currents. The case of is discussed in detail. The operating region is determined. The Carnot value of the COP is obtained in the case of . Moreover, the optimal region of the refrigerator in the case of is determined, the maximum values of the cooling
Acknowledgements
This work has been supported by the National Natural Science Foundation (No. 11175148), People's Republic of China.
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