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A quantum-dot heat engine operating close to the thermodynamic efficiency limits


Cyclical heat engines are a paradigm of classical thermodynamics, but are impractical for miniaturization because they rely on moving parts. A more recent concept is particle-exchange (PE) heat engines, which uses energy filtering to control a thermally driven particle flow between two heat reservoirs1,2. As they do not require moving parts and can be realized in solid-state materials, they are suitable for low-power applications and miniaturization. It was predicted that PE engines could reach the same thermodynamically ideal efficiency limits as those accessible to cyclical engines3,4,5,6, but this prediction has not been verified experimentally. Here, we demonstrate a PE heat engine based on a quantum dot (QD) embedded into a semiconductor nanowire. We directly measure the engine’s steady-state electric power output and combine it with the calculated electronic heat flow to determine the electronic efficiency η. We find that at the maximum power conditions, η is in agreement with the Curzon–Ahlborn efficiency6,7,8,9 and that the overall maximum η is in excess of 70% of the Carnot efficiency while maintaining a finite power output. Our results demonstrate that thermoelectric power conversion can, in principle, be achieved close to the thermodynamic limits, with direct relevance for future hot-carrier photovoltaics10, on-chip coolers or energy harvesters for quantum technologies.

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Fig. 1: Experimental device and its operational principle.
Fig. 2: Electric and thermoelectric characterization of the device.
Fig. 3: Thermoelectric performance of the PE engine.
Fig. 4: Device operation at maximum power.


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We thank S. Lehmann for the structural imaging of the nanowires used in this study. We acknowledge financial support by the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7-People-2013-ITN) under REA grant agreement no. 608153 (PhD4Energy), by the Swedish Energy Agency (project P38331-1), by the Swedish Research Council (projects 621-2012-5122, 2014-5490, 2015-00619 and 2016-03824), by the Knut and Alice Wallenberg Foundation (project 2016.0089), Marie Sklodowska Curie Actions, Cofund, Project INCA 600398 and by NanoLund. The computations were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) at LUNARC.

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H.L. and M.L. designed and guided the study. E.A.H. and S.F. performed preliminary experiments. S.F. grew the nanowires. A.S., A.M.B. and C.T. designed and fabricated the devices and carried out the experiments. M.J. and M.L. performed the theoretical calculations. M.J. and A.S. analysed the data. All the authors contributed to writing and editing the manuscript.

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Correspondence to Heiner Linke.

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Josefsson, M., Svilans, A., Burke, A.M. et al. A quantum-dot heat engine operating close to the thermodynamic efficiency limits. Nature Nanotech 13, 920–924 (2018).

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