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

Abstract

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.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

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.

References

  1. 1.

    Scovil, H. & Schulz-DuBois, E. Three-level masers as heat engines. Phys. Rev. Lett. 2, 262–263 (1959).

    Article  Google Scholar 

  2. 2.

    Humphrey, T. E. & Linke, H. Quantum, cyclic, and particle-exchange heat engines. Physica E 29, 390–398 (2005).

    Article  Google Scholar 

  3. 3.

    Mahan, G. & Sofo, J. The best thermoelectric. Proceed. Natl Acad. Sci. USA 93, 7436–7439 (1996).

    CAS  Article  Google Scholar 

  4. 4.

    Humphrey, T. E., Newbury, R., Taylor, R. P. & Linke, H. Reversible quantum Brownian heat engines for electrons. Phys. Rev. Lett. 89, 116801 (2002).

    CAS  Article  Google Scholar 

  5. 5.

    Humphrey, T. E. & Linke, H. Reversible thermoelectric nanomaterials. Phys. Rev. Lett. 94, 096601 (2005).

    CAS  Article  Google Scholar 

  6. 6.

    Van den Broeck, C. Thermodynamic efficiency at maximum power. Phys. Rev. Lett. 95, 190602 (2005).

    Article  Google Scholar 

  7. 7.

    Curzon, F. & Ahlborn, B. Efficiency of a Carnot engine at maximum power output. Am. J. Phys. 43, 22–24 (1975).

    Article  Google Scholar 

  8. 8.

    Esposito, M., Lindenberg, K. & Van den Broeck, C. Universality of efficiency at maximum power. Phys. Rev. Lett. 102, 130602 (2009).

    Article  Google Scholar 

  9. 9.

    Esposito, M., Kawai, R., Lindenberg, K. & Van den Broeck, C. Efficiency at maximum power of low-dissipation Carnot engines. Phys. Rev. Lett. 105, 150603 (2010).

    Article  Google Scholar 

  10. 10.

    Limpert, S., Bremner, S. & Linke, H. Reversible electron–hole separation in a hot carrier solar cell. New J. Phys. 17, 095004 (2015).

    Article  Google Scholar 

  11. 11.

    Callen, H. B. Thermodynamics and an Introduction to Thermostatistics 2nd edn, Ch. 4 (John Wiley & Sons, New York, 1985).

  12. 12.

    Wong, W. A., Wilson, S., Collins, J. & Wilson, K. Advanced Stirling Converter (ASC) Technology Maturation Report NASA/TM-2016-218908 (National Aeronautics and Space Agency, 2016).

  13. 13.

    Nakpathomkun, N., Xu, H. Q. & Linke, H. Thermoelectric efficiency at maximum power in low-dimensional systems. Phys. Rev. B 82, 235428 (2010).

    Article  Google Scholar 

  14. 14.

    O’Dwyer, M. F., Humphrey, T. E. & Linke, H. Concept study for a high-efficiency nanowire based thermoelectric. Nanotechnology 17, S338–S343 (2006).

    Article  Google Scholar 

  15. 15.

    Esposito, M., Lindenberg, K. & Van den Broeck, C. Thermoelectric efficiency at maximum power in a quantum dot. Europhys. Lett. 85, 60010 (2009).

    Article  Google Scholar 

  16. 16.

    Staring, A. A. M. et al. Coulomb-blockade oscillations in the thermopower of a quantum dot. Europhys. Lett. 22, 57 (1993).

    CAS  Article  Google Scholar 

  17. 17.

    Svilans, A., Leijnse, M. & Linke, H. Experiments on the thermoelectric properties of quantum dots. C. R. Phys. 17, 1096–1108 (2016).

    CAS  Article  Google Scholar 

  18. 18.

    Prance, J. R. et al. Electronic refrigeration of a two-dimensional electron gas. Phys. Rev. Lett. 102, 146602 (2009).

    CAS  Article  Google Scholar 

  19. 19.

    Björk, M. T. et al. Few-electron quantum dots in nanowires. Nano Lett. 4, 1621 (2004).

    Article  Google Scholar 

  20. 20.

    Turek, M. & Matveev, K. Cotunneling thermopower of single electron transistors. Phys. Rev. B 65, 115332 (2002).

    Article  Google Scholar 

  21. 21.

    Gluschke, J. G., Svensson, S. F., Thelander, C. & Linke, H. Fully tunable, non-invasive thermal biasing of gated nanostructures suitable for low-temperature studies. Nanotechnology 25, 385704 (2014).

    CAS  Article  Google Scholar 

  22. 22.

    König, J., Schoeller, H. & Schön, G. Cotunneling at resonance for the single-electron transistor. Phys. Rev. Lett. 78, 4482 (1997).

    Article  Google Scholar 

  23. 23.

    Leijnse, M. & Wegewijs, M. Kinetic equations for transport through single-molecule transistors. Phys. Rev. B 78, 235424 (2008).

    Article  Google Scholar 

  24. 24.

    Gergs, N. M., Hörig, C. B., Wegewijs, M. R. & Schuricht, D. Charge fluctuations in nonlinear heat transport. Phys. Rev. B 91, 201107 (2015).

    Article  Google Scholar 

  25. 25.

    Dresselhaus, M. S. et al. New directions for low-dimensional thermoelectric materials. Adv. Mat. 19, 1043–1053 (2007).

    CAS  Article  Google Scholar 

  26. 26.

    Conibeer, G., Jiang, C. W., Green, M., Harder, N. & Straub, A. Selective energy contacts for potential application to hot carrier PV cells. Proc. 3rd World Conf. Photovolt. En. Conv. 3, 2730–2733 (2003).

    Google Scholar 

  27. 27.

    Persson, A. I., Fröberg, L. E., Jeppesen, S., Björk, M. T. & Samuelson, L. Surface diffusion effects on growth of nanowires by chemical beam epitaxy. J. Appl. Phys. 101, 034313 (2007).

    Article  Google Scholar 

  28. 28.

    Fröberg, L. E. et al. Transients in the formation of nanowire heterostructures. Nano Lett. 8, 3815–3818 (2008).

    Article  Google Scholar 

Download references

Acknowledgements

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.

Author information

Affiliations

Authors

Contributions

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.

Corresponding author

Correspondence to Heiner Linke.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Supplementary Information

Supplementary Sections 1–5

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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). https://doi.org/10.1038/s41565-018-0200-5

Download citation

Further reading

Search

Find nanotechnology articles, nanomaterial data and patents all in one place. Visit Nano by Nature Research