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In popularizations, people tunnel through walls or doors. But what can really tunnel through a graphene sheet without tearing it?

According to Wikipedia, a single layer of graphene absorbs 2.3 % of white light, but 97% makes it through. It conducts electrons well enough to make a transistor.

I doubt that a baseball tunnels through a sheet of graphene without harming it.
But what about a Buckyball? or a smaller molecule? A helium atom? A bare proton?

This looks deceptively like the one dimensional finite barrier problem in elementary QM textbooks. Can we calculate the probability of a given projectile at a given velocity tunnelling through the graphene sheet? Is there any experimental data?

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Bloody Helium atoms get through all kinds of stuff, a fact which is a constant pain in the neck for particle experimenters. Especially as helium can have adverse effects on PMTs (see the "Handling precautions section of for instance). – dmckee Apr 28 '12 at 2:52
Yes, I knew that. But I don't know if or how fast they go through graphene. Also is that tunnelling or is it diffusion? Is there a difference? – Jim Graber Apr 29 '12 at 14:55
up vote 3 down vote accepted

Even helium atoms (at reasonable temperatures) do not tunnel through graphene, as the potential energy barrier is far too high. (source: Leenaerts et al. 2008)

However, suitably small holes may allow for tunneling of helium atoms through graphene-like materials at room temperature and below (source: Schrier 2010, Hauser and Schwerdtfeger 2012)

For protons, the barrier height is much lower, so tunneling can be appreciable. (source: Miao et al. 2013 )

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