# Focus: Vibrations Skip Across Vacuum

Phys. Rev. Focus 26, 15
Heat-carrying vibrational waves can be transmitted across a small vacuum barrier between a metal point and a flat surface, according to a new experiment.

This story was slightly revised on 11 October in the description of the 2005 experiment.

The Sun warms the Earth by radiating heat across the emptiness of space, but the physics of heat transfer is not well understood for very short distances. An experiment reported in the 15 October Physical Review Letters demonstrates that a sharp metal point will emit heat at a rate many times greater than normal when brought within a few atom-lengths of a cold, metal surface. The warm tip transfers heat through its fluctuating electric fields, which jiggle electrons in the surface. The researchers call the effect “phonon tunneling” because quantized molecular vibrations called phonons seemingly hop over the forbidden vacuum gap. The phenomenon could be important for future nanoscale devices, the researchers say.

Heat can flow between two objects at different temperatures in three possible ways: conduction, convection, and radiation. Convection requires a medium, such as air, to carry the heat, whereas radiation refers to electromagnetic waves that can travel through a vacuum. Conduction only occurs when the objects are touching, when faster-vibrating atoms in the hotter body jiggle the slower atoms in the colder body. Researchers describe this process as transmission of phonons (quanta of vibration), and it would seem to be impossible between separated objects. “The vacuum is a forbidden zone for phonons,” says Igor Altfeder of the Air Force Research Laboratory at Wright-Patterson Air Force Base in Ohio.

But heat transfer at short range shows some surprises. In one recent experiment, a sharp point or “tip” was placed near a cold surface, and the heat flow did not match theoretical predictions at separations less than 10 nanometers. However, the experimental design did not permit a measurement of the temperature at the end of the tip.

To measure that temperature and better understand what was happening, Altfeder and his colleagues used a technique called inelastic electron tunneling spectroscopy (IETS). It involves applying a range of voltages between the tip and the surface and recording the current produced by electrons jumping across the gap. These electrons are affected by thermal vibrations in the materials, so measuring the current leads to the temperature, especially that of the very last atom or molecule on the tip.

Under high vacuum conditions, the team brought a platinum-iridium tip at 275 Kelvin to within 0.3 nanometers of a gold surface cooled to 90, 150 or 210 Kelvin. From the IETS data, they found the tip temperature but also discovered that a single carbon monoxide (CO) molecule had attached to the very end of their tip. This is not uncommon, Altfeder says, but it turned out to be fortuitous, because the CO molecule was thermally isolated to some extent from the rest of the tip. The team was surprised to find that the CO molecule had roughly the same temperature as the surface, implying that heat was escaping from the tip-end at an enormous rate, much faster than in the previous experiment.

The researchers explain the cooling as a result of electric fields that have influence across the narrow gap. The electric field from the CO molecule rearranges the top layer of electrons in the gold surface. From classical electrodynamics, this rearrangement can be represented more simply as a single “image charge” underneath the surface. The CO molecule and its image vibrate in unison, but the shaking of the image charge–or alternatively, the surface electrons–induces heat-carrying phonons inside the gold, assuming a strong electron-phonon coupling.

This transmission of vibrations across a forbidden gap has previously been called phonon tunneling because it mimics quantum tunneling–for example, when electrons cross this same vacuum gap, even though they lack the energy to escape the tip. But in past experiments, the gap was another material, rather than a vacuum. The authors calculate that the CO molecule dissipates heat ${10}^{10}$ times faster by generating phonons in the gold than by emitting radiation directly into the vacuum.

The proposed mechanism coincides with recent theoretical work by Mika Prunnila and Johanna Meltaus of the VTT Technical Research Centre of Finland, which predicted phonon tunneling between nearby piezoelectric materials that by definition have a strong coupling between phonons and electric field variations [2]. Prunnila thinks this research will be applicable in nanoelectronics and the development of devices that harvest energy from temperature gradients. “Acoustic phonons are the major heat carriers in many solids, and in this sense it is somewhat surprising that phonon tunneling didn’t receive more attention previously,” he says.

–Michael Schirber

Michael Schirber is a Corresponding Editor for Physics based based in Lyon, France.

## References

1. A. Kittel, W. Müller-Hirsch, J. Parisi, S.-A. Biehs, D. Reddig, and M. Holthaus, “Near-Field Heat Transfer in a Scanning Thermal Microscope,” Phys. Rev. Lett. 95, 224301 (2005)
2. M. Prunnila and J. Meltaus, “Acoustic Phonon Tunneling and Heat Transport due to Evanescent Electric Fields,” Phys. Rev. Lett. 105, 125501 (2010)

Nanophysics

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