Quantum dot thermal machines -- a guide to engineering

TL;DR

This work develops a linear-response framework for SET-based quantum-dot thermal machines in the narrow-band regime, showing that four microscopic dynamics parameters—ΔS, γ, α, and Γ—control performance and can be collapsed into two effective controls, Γ and σ, to guide engineering. It provides explicit heat-engine and refrigerator relations, demonstrating that increasing entropy difference and introducing controlled detailed-balance breaking can boost power and cooling, while also analyzing noise and constancy via a dynamical approach. The results offer concrete design strategies, such as enhancing degeneracy to raise ΔS and employing spintronic or interference-based methods to break detailed balance, to achieve higher-performance nanoscale energy converters. The findings hold under linear response and minimal passive heat leakage, suggesting practical routes to optimize quantum-dot thermal machines through internal state engineering. Overall, the paper supplies actionable guidelines to tailor quantum states for improved power, efficiency, and stability in solid-state thermal devices.

Abstract

Continuous particle exchange thermal machines require no time-dependent driving, can be realised in solid-state electronic devices, and miniaturised to nanometre scale. Quantum dots, providing a narrow energy filter and allowing to manipulate particle flow between the hot and cold reservoirs are at the heart of such devices. It has been theoretically shown that by mitigating passive heat flow, Carnot efficiency can be approached arbitrarily closely in a quantum dot heat engine, and experimentally, values of 0.7ηC have been reached. However, for practical applications, other parameters of a thermal machine, such as maximum power, efficiency at maximum power, and noise - stability of the power output or heat extraction - take precedence over maximising efficiency. We explore the effect of internal microscopic dynamics of a quantum dot on these quantities and demonstrate that its performance as a thermal machine depends on few parameters - the overall conductance and three inherent asymmetries of the dynamics. These parameters will act as a guide to engineering the quantum states of the quantum dot, allowing to optimise its performance beyond that of the simplest case of a two-fold spin-degenerate transmission level.

Figures (7)

• Figure 1: All possible configurations of a SET and corresponding thermal operation regimes. a) $\mu_H>\mu_C$, b) $\mu_C>\mu_H$. Current direction (dominant tunnelling direction) is shown with black arrows, and the signs of heat changes of the baths marked beneath them. (Positive sign means heat being deposited in the bath).
• Figure 2: a) The general energy flow diagram for a heat engine. b) Two configurations of a SET heat engine, with electron (i) and hole (ii) dominated transport.
• Figure 3: a) The general energy flow diagram for a refrigerator. b) Two configurations of a SET operating as a refrigerator, with electron (i) and hole (ii) dominated transport.
• Figure 4: a) A general energy diagram for transport through a single energy level, with the rates involved labelled. b) The gate-dependent conductance (i) and thermoelectric susceptibility for several values of $\Delta S$. c) The power-efficiency diagrams for various values of $\Delta S$. The non-degenerate case is shown in red. d) The parameter plots of maximum power vs. efficiency at maximum power at varying load resistances for several values of $\Delta S$. e) (i) The maximum cooling power of an SET refrigerator as a function of temperature difference for several values of $\Delta S$. (ii) Cooling power of an SET refrigerator as a function of $\Delta S$ at fixed $\dd V$ and $\dd T$. f) The power-efficiency diagrams for a non-degenerate QD for increasing values of a coupling strength parameter, $A$ (see Eq.\ref{['eq-G-unnorm']}). As the absolute magnitudes of power and efficiency depend on many parameters: $\Delta T$, $A$, $R$, $\Delta V$, etc, the plots are designed to illustrate the qualitative dependence on the parameters and thus do not show absolute units.
• Figure 5: a) Normalised gate-dependent conductance (i) and thermoelectric susceptibility for several values of $\Delta S$. b) The power-efficiency diagrams for various values of $\Delta S$ (the positive and negative values of $\Delta S$ have the same dependence). The non-degenerate case is shown in red. c) The parameter plots of maximum power vs. efficiency at maximum power at varying load resistances for several values of $\Delta S$. d) The maximum cooling power of an SET refrigerator with normalised conductance as a function of temperature difference for several values of $\Delta S$. e) Cooling power of an SET refrigerator with normalised conductance as a function of $\Delta S$ at fixed $\Delta T$ and $\Delta V$. Similarly to Fig.\ref{['fig-deg']}, the plots are designed to illustrate the qualitative behaviour and thus the their scale can very.