Heat Flow Hits Quantum Limit

When a coffee cup or any other object heats up, a cacophony of tiny vibrations pass through it. Now physicists have found a fundamental quantum limit on the amount of heat each individual vibration can carry. Scientists and engineers working on machines with parts a few molecules thick will have to take these findings into account, otherwise the devices might overheat in a hurry.

Both electrons and heat vibrations are really quantum waves, so electricity and heat should behave in the same strange ways in supersmall quarters. Electrons in a wire only a few nanometers thick must travel in a handful of quantum channels, rather like the traffic lanes on a bridge. The lanes open one by one when voltage between the two ends of the wire increases, so the current passing through the wire climbs in a series of even steps. Heat traveling down microscopic girders and beams should behave in a similar way, but until now, daunting technical challenges prevented researchers from seeing quantum effects.

To catch heat's quantum movements, physicists Michael Roukes, Keith Schwab, and colleagues at the California Institute of Technology studied heat flow in beams of silicon nitride a mere 60 nanometers thick and 200 nanometers wide. They warmed each beam at one end and measured the temperature difference between the two ends with ultrasensitive thermometers. They then tracked the beam's thermal conductance, the rate of heating divided by the temperature difference, as they cooled the beam toward absolute zero. To pull the experiment off, the researchers had to apply less than a millionth of a billionth of a watt of heat to the beam, roughly the amount of power that would hit your eye from a lightbulb 60 miles away.

Below 1°C above absolute zero, the plummeting thermal conductance leveled off into a kind of modified, tilted step. Though not as pretty as its cousin, the first step in the electrical conductance staircase, the sloping step showed that only four of the infinity of vibrations remained. Moreover, the angle of the slope revealed a quantum limit on how much heat each vibration could carry. These last channels are the only ones that would carry heat away in atom-scale devices run at low temperatures. And four channels may not be enough to prevent supersmall machines from overheating, Roukes says.

The finding, reported in the 27 April issue of Nature, closely matches a prediction made 2 years ago by physicists George Kirceznow and Luis Rego of Simon Fraser University in Burnaby, Canada. "I was obviously hoping that they would see what we predicted," Kirceznow says, "but I'm stunned that the agreement was so good."