Measurement of the quantum of thermal conductance

The physics of mesoscopic electronic systems has been explored for more tha n 15 years. Mesoscopic phenomena in transport processes occur when the wave length or the coherence length of the carriers becomes comparable to, or la rger 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 gas(1,2 ). The conductance of this system is determined by the number of participat ing quantum states or 'channels' within the constriction; in the ideal case , each spin-degenerate channel contributes a quantized unit of 2e(2)/h to t he electrical conductance. It has been speculated that similar behaviour sh ould be observable for thermal transport(3,4) in mesoscopic phonon systems. But experiments attempted in this regime have so far yielded inconclusive results(5-9). Here we report the observation of a quantized limiting value for the thermal conductance, G(th), in suspended insulating nanostructures at very low temperatures. The behaviour we observe is consistent with predi ctions(10,11) for phonon transport in a ballistic, one-dimensional channel: at low temperatures, Gth approaches a maximum value of g(0) = pi(2)k(B)(2) T=3h, the universal quantum of thermal conductance.