The Heat Flow through Nanoscale Wires Faces a Fundamental Limit

If a conducting wire is sufficiently narrow, the electrical conductance through it is quantized, increasing in steps of ${\text{2e}}^2\mathrm{/h}$ with the width of the wire. Does an analogous quantization apply to another type of transport—the conduction of heat by phonons? The theoretical answer is “yes.” A narrow, thermally insulating wire should be able to carry no more heat per mode than $g_0{\mathrm{\hspace{0.17em}=\hspace{0.17em}\pi }}^2{k}^2\text{T/3h,}$ where k is Boltz‐mann’s constant, T is the temperature and h is Planck’s constant.

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