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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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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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
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