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Measurement of the quantum of thermal conductance


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.

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


  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 

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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.

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Correspondence to M. L. Roukes.

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Schwab, K., Henriksen, E., Worlock, J. et al. Measurement of the quantum of thermal conductance. Nature 404, 974–977 (2000).

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