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 $2e2/h$ 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 $g0 = π2k2T/3h,$ where k is Boltz‐mann's constant, T is the temperature and h is Planck's constant.