Absorption refrigerators based on Coulomb-coupled single-electron systems

Paolo Andrea Erdman, Bibek Bhandari, Rosario Fazio, Jukka P. Pekola, and Fabio Taddei

Phys. Rev. B 98, 045433 – Published 31 July 2018

Abstract

We analyze a simple implementation of an absorption refrigerator, a system that requires heat and not work to achieve refrigeration, based on two Coulomb-coupled single-electron systems. We analytically determine the general condition to achieve cooling-by-heating, and we determine the system parameters that simultaneously maximize the cooling power and cooling coefficient of performance (COP) finding that the system displays a particularly simple COP that can reach Carnot's upper limit. We also find that the cooling power can be indirectly determined by measuring a charge current. Analyzing the system as an autonomous Maxwell demon, we find that the highest efficiencies for information creation and consumption can be achieved, and we relate the COP to these efficiencies. Finally, we propose two possible experimental setups based on quantum dots or metallic islands that implement the nontrivial cooling condition. Using realistic parameters, we show that these systems, which resemble existing experimental setups, can develop an observable cooling power.

Received 4 May 2018

DOI:https://doi.org/10.1103/PhysRevB.98.045433

Physics Subject Headings (PhySH)

Coulomb blockade Heat transfer Mesoscopics Quantum transport Thermoelectric effects Transport phenomena

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Paolo Andrea Erdman^1,*, Bibek Bhandari¹, Rosario Fazio^1,2, Jukka P. Pekola³, and Fabio Taddei⁴

¹NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56127 Pisa, Italy
²ICTP, Strada Costiera 11, I-34151 Trieste, Italy
³QTF Centre of Excellence, Department of Applied Physics, Aalto University School of Science, P.O. Box 13500, 00076 Aalto, Finland
⁴NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, I-56126 Pisa, Italy

^*paolo.erdman@sns.it

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Vol. 98, Iss. 4 — 15 July 2018

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Images

Figure 1
Panel (a): schematic representation of the system. Panel (b): the Fermi distribution of the leads (red upper left, gray upper right, and blue lower left) is shown vertically. The thick black lines represent the transition energies $Δ U_{1} (n_{2})$ and $Δ U_{2} (n_{1})$ [Eq. (2)] that are measured with respect to the common chemical potential of the leads (black dashed line). Panel (c): sequence of system states and electron transitions that provide cooling when conditions (7) and (8), represented by the red crosses, are satisfied. The black horizontal lines represent the actual transition energies as determined by the occupation of the other QD, while the gray horizontal lines represent the transition energies when the other QD has opposite occupation. $δ Q_{α}$ , for $α = L, R, C$ , represents the heat extracted from reservoir $α$ during the corresponding electron transition.
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Figure 2
The coefficient of performance, COP, [panel (a)] and the heat currents in units of $Γ k_{B} T$ [panels (b) and (c)] are plotted as a function of $θ_{1}$ , when Eqs. (7) and (8) are satisfied. Panel (b) refers to $Δ T_{C} = 0$ , while panel (c) refers to $Δ T_{C} = Δ T / 5$ . The parameters are $Γ_{C}^{out} (0) = Γ_{C}^{in} (1) = Γ_{L}^{out} (0) = Γ_{R}^{in} (1) \equiv Γ, θ_{2} = 1, E_{I} = 6 k_{B} T$ , and $Δ T / T = 1 / 10$ . Since all rates are proportional to $Γ$ , the heat currents depend linearly on the rate, so the plots in panels (b) and (c) do not depend on the value of $Γ$ .
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Figure 3
Left: schematic representation of the system, where 1, 2, and 3 represent either QDs or MIs. Right: representation of the transition energies in the case of the system with QDs. See Fig. 1 for details.
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Figure 4
Cooling power $I_{C}^{h}$ , relative to the system containing three QDs and represented in Fig. 3, under resonant condition $[Δ U_{3} = Δ U_{1} (0)]$ . $I_{C}^{h}$ is plotted as a function of $θ_{1}$ for the case $Δ T_{C} = 0$ (solid black curve) and the case $Δ T_{C} = Δ T / 10$ (dashed red curve), setting $θ_{2} = 1 / 2$ and imposing $θ_{3} = θ_{1}$ . The parameters are of the order of the experimental ones reported in Ref. [44] and read: $E_{I} = 0.72$ meV, $γ_{L} = γ_{R} = γ_{C} = 0.036$ meV, $t = 0.016$ meV, and $T = Δ T = 4.17$ K.
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Figure 5
Cooling power, relative to the setup depicted in Fig. 3 for MIs, as a function of $θ_{1}$ for two different values of $Δ T_{C}$ , and setting $θ_{2} = 1 / 2$ and $θ_{3} = θ_{1} + 1 / 2$ . The parameters used are experimentally relevant (see, for example, Refs. [28, 57]) and read: $E_{I} = 25 μ eV$ , $Δ = 35 μ eV$ , $γ = 10^{- 3} μ eV$ , $T = 100$ mK, $Δ T = 200$ mK, and $R_{α ν} = 10 k Ω$ for all barriers.
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Figure 6
The efficiencies $η_{D}$ and $η_{C}$ are plotted as a function of $θ_{1}$ starting from $θ_{1} = θ_{1}^{*}$ for the case $Δ T_{C} = Δ T / 5$ . The parameters are the same as in Fig. 2.
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