Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Measurement of the quantum of thermal conductance

Nature volume 404, pages 974–977 (2000)Cite this article

Abstract

The physics of mesoscopic electronic systems has been explored for more than 15 years. Mesoscopic phenomena in transport processes occur when the wavelength or the coherence length of the carriers becomes comparable to, or larger than, the sample dimensions. One striking result in this domain is the quantization of electrical conduction, observed in a quasi-one-dimensional constriction formed between reservoirs of two-dimensional electron gas1,2. The conductance of this system is determined by the number of participating quantum states or ‘channels’ within the constriction; in the ideal case, each spin-degenerate channel contributes a quantized unit of 2e2/h to the electrical conductance. It has been speculated that similar behaviour should be observable for thermal transport3,4 in mesoscopic phonon systems. But experiments attempted in this regime have so far yielded inconclusive results5,6,7,8,9. Here we report the observation of a quantized limiting value for the thermal conductance, Gth, in suspended insulating nanostructures at very low temperatures. The behaviour we observe is consistent with predictions10,11 for phonon transport in a ballistic, one-dimensional channel: at low temperatures, Gth approaches a maximum value of g0 = π2k2BT/3h, the universal quantum of thermal conductance.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Suspended mesoscopic device.
Figure 2: Simplified apparatus diagram.
Figure 3: Thermal conductance data.

References

  1. van Wees,B. J. et al. Quantized conductance of point contacts in a two-dimensional electron-gas. Phys. Rev. Lett. 60, 848– 850 (1988).

    Article  ADS  CAS  Google Scholar 

  2. Wharam,D. A. et al. One-dimensional transport and the quantization of the ballistic resistance. J. Phys. C 21, L209– L214 (1988).

    Article  Google Scholar 

  3. Pendry,J. B. Quantum limits to the flow of information and entropy. J. Phys. A 16, 2161–2171 ( 1983).

    Article  ADS  MathSciNet  Google Scholar 

  4. Maynard,R. & Akkermans,E. Thermal conductance and giant fluctuations in one-dimensional disordered systems. Phys. Rev. B 32, 5440–5442 (1985).

    Article  ADS  CAS  Google Scholar 

  5. Lee,K. L., Ahmed,H., Kelly,M. J. & Wybourne,M. N. Fabrication of ultra-thin freestanding wires. Phys. Rev. Lett. 69, 1427–1430 (1992).

    Article  Google Scholar 

  6. Seyler,J. & Wyborne,M. N. Acoustic wave-guide modes observed in electrically heated metal wires. Phys. Rev. Lett. 69, 1427–1430 (1992).

    Article  ADS  CAS  Google Scholar 

  7. Kwong,Y. K., Lin,K., Isaacson,M. S. & Parpia,J. M. An attempt to observe phonon dimensionality crossover effects in the inelastic-scattering rate of thin freestanding aluminium films. J. Low Temp. Phys. 88, 261–272 (1992).

    Article  ADS  CAS  Google Scholar 

  8. Potts,A. et al. Thermal transport in freestanding semiconducting fine wires. Superlatt. Microstruct. 9, 315–318 (1991).

    Article  ADS  CAS  Google Scholar 

  9. Hone,J., Whitney,M., Piskoti,C. & Zettl,A. Thermal conductivity of single-walled carbon nanotubes. Phys. Rev. B 59, R2514–R2516 (1999).

    Article  ADS  CAS  Google Scholar 

  10. Angelescu,D. E., Cross,M. C. & Roukes, M. L. Heat transport in mesoscopic systems. Superlatt. Microstruct. 23, 673–689 (1998).

    Article  ADS  Google Scholar 

  11. Rego,L. G. C. & Kirczenow,G. Quantized thermal conductance of dielectric quantum wires. Phys. Rev. Lett. 81, 232–235 (1998).

    Article  ADS  CAS  Google Scholar 

  12. Blencowe,M. P. Quantum energy flow in mesoscopic dielectric structures. Phys. Rev. B 59, 4992–4998 ( 1999).

    Article  ADS  CAS  Google Scholar 

  13. Klitsner,T., VanCleve,J. E., Fischer,J. E. & Pohl,R. O. Phonon radiative heat-transfer and surface scattering. Phys. Rev. B 38, 7576–7594 ( 1988).

    Article  ADS  CAS  Google Scholar 

  14. Nishiguchi,N., Ando,Y. & Wybourne,M. N. Acoustic phonon modes of rectangular quantum wires. J. Phys. Cond. Matter 9, 5751– 5764 (1997).

    Article  ADS  CAS  Google Scholar 

  15. Rego,L. C. G. & Kirczenow,G. Fractional exclusion statistics and the universal quantum of thermal conductance: A unifying approach. Phys. Rev. B 59, 13080–13086 (1999).

    Article  ADS  CAS  Google Scholar 

  16. Krive,I. V. & Mucciolo,E. R. Transport properties of quasiparticles with fractional exclusion statistics. Phys. Rev. B 60, 1429–1432 (1999).

    Article  ADS  CAS  Google Scholar 

  17. Caves,C. M. & Drummond,P. D. Quantum limits on bosonic communication rates. Rev. Mod. Phys. 66, 481– 537 (1994).

    Article  ADS  CAS  Google Scholar 

  18. Tighe,T. S., Worlock,J. M. & Roukes, M. L. Direct thermal conductance measurements on suspended monocrystalline nanostructures. Appl. Phys. Lett. 70 , 2687–2689 (1997).

    Article  ADS  CAS  Google Scholar 

  19. Schwab,K., Henriksen,E. A. & Roukes, M. L. Direct measurement of phonon transport in mesoscopic devices. Appl. Phys. Lett. (submitted).

  20. Leivo,M. M. & Pekola,J. P. Thermal characteristics of silicon nitride membranes at sub-Kelvin temperatures. Appl. Phys. Lett. 72, 1305–1307 ( 1998).

    Article  ADS  CAS  Google Scholar 

  21. Holmes,W., Gildemeister,J. M., Richards, P. L. & Kotsubo,V. Measurements of thermal transport in low stress silicon nitride films. Appl. Phys. Lett. 72, 2250–2252 (1998).

    Article  ADS  CAS  Google Scholar 

  22. Roukes,M. L., Freeman,M. R., Germain,R. S., Richardson,R. C. & Ketchen,M. B. Hot-electrons and energy-transport in metals at millikelvin temperatures. Phys. Rev. Lett. 55, 422–425 (1985).

    Article  ADS  CAS  Google Scholar 

  23. Roukes,M. L., Germain,R. S., Freeman,M. R. & Richardson,R. C. DC SQUID noise thermometry. Physica 126 B+C, 1177–1178 (1984).

    Google Scholar 

  24. Roukes,M. L. Hot Electrons and Energy Transport in Metals at mK Temperatures. Doctoral dissertation, Cornell Univ. (1985).

    Google Scholar 

  25. Ketchen,M. B. et al. Design, fabrication, and performance of integrated miniature SQUID suseptometers. IEEE Trans. Magn. 25, 1212–1215 (1989).

    Article  ADS  Google Scholar 

  26. Martinis,J. M., Devoret,M. H. & Clarke, J. Experimental test for the quantum behavior of a macroscopic degree of freedom: The phase difference across a Josephson junction. Phys. Rev. B 35, 4682–4698 (1986).

    Article  ADS  Google Scholar 

  27. Mohanty,P., Jariwala,E. M. Q. & Webb, R. A. Intrinsic decoherence in mesoscopic systems. Phys. Rev. Lett. 78, 3366–3369 (1997).

    Article  ADS  CAS  Google Scholar 

  28. Yacoby,A. & Imry,Y. Adiabatic mode selection and the accuracy of the quantization of the conductance of ballistic point contacts. Europhys. Lett. 11, 663–667 (1990).

    Article  ADS  Google Scholar 

  29. Kander,I., Imry,Y. & Sivan,U. Effects of channel opening and disorder on the conductance of narrow wires. Phys. Rev. B 41, 12941– 12944 (1990).

    Article  ADS  CAS  Google Scholar 

  30. Roukes,M. L. Yoctocalorimetry: phonon counting in nanostructures. Physica B 263–264 1–15 ( 1999).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank M. C. Cross, R. Lifshitz, G. Kirczenow, M. Blencowe, N. Wingreen and P. Burke for discussions, suggestions and insights, and N. Bruckner for assistance with silicon nitride growth. We thank M. B. Ketchen and members of the IBM Yorktown superconductivity group for advice, assistance and the d.c. SQUID devices employed in our cryogenic electronics. This work was supported by DARPA MTO/MEMS and NSF/DMR.

Author information

Author notes

  1. J. M. Worlock

    Present address: Department of Physics, University of Utah, Salt Lake City, Utah, 84112, USA

Authors and Affiliations

  1. Condensed Matter Physics 114-36, California Institute of Technology, Pasadena, 91125, California , USA

    K. Schwab, E. A. Henriksen, J. M. Worlock & M. L. Roukes

Authors
  1. K. Schwab
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. A. Henriksen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. M. Worlock
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. L. Roukes
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. L. Roukes.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Schwab, K., Henriksen, E., Worlock, J. et al. Measurement of the quantum of thermal conductance. Nature 404, 974–977 (2000). https://doi.org/10.1038/35010065

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/35010065

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing