Graphene and the foundations of physics

Graphite, familiar from pencil leads, is a form of carbon consisting of stacks of sheets, each of which consists of a hexagonal mesh of atoms. The sheets are held together only weakly; this is why graphite is such a good lubricant, and when you run a pencil across a piece of paper the mark is made from rubbed off sheets. In 2004, Andre Geim, from the University of Manchester, made the astonishing discovery that you could obtain large, near-perfect sheets of graphite only one atom thick, simply by rubbing graphite against a single crystal silicon substrate – these sheets are called graphene. What was even more amazing was the electronic properties of these sheets – they conduct electricity, and the electrons move through the material at great speed and with very few collisions. There’s been a gold-rush of experiments since 2004, uncovering the remarkable physics of this material. All this has been reviewed in a recent article by Geim and Novosolev (Nature Materials, 6 p 183, 2007) – The rise of graphene (It’s worth taking a look at Geim’s group website, which contains many downloadable papers and articles – Geim is a remarkably creative, original and versatile scientist; besides his discoveries in the graphene field, he’s done very significant work in optical metamaterials and gecko-like nanostructured adhesives, besides his notorious frog-levitation exploits). From the technological point of view, the very high electron mobility of graphene and the possibility of shrinking the dimensions of graphene based devices right down to atomic dimensions make it very attractive as a candidate for electronics when the further miniaturisation of silicon based devices stalls.

At the root of much of the strange physics of graphene is the fact that electrons behave in it like highly relativistic, massless particles. This arises from the way the electrons interact with the regular, 2-dimensional lattice of carbon atoms. Normally when an electron (which we need to think of as a wave, according to quantum mechanics) moves through a lattice of ions, the effect of the way the wave is scattered from the ions and the scattered waves interfere with each other is that the electron behaves as it has a different mass to its real, free space value. But in graphene the effective mass is zero (the energy is simply proportional to the wave-vector, like a photon, rather than being proportional to the wave-vector squared, as would be the case for a normal non-relativistic particle with mass).

The weird way in which electrons in graphene mimic ultra-relativistic particles allows one to test predictions of quantum field theory that would be inaccessible to experiments using fundamental particles. Geim writes about this in this week’s Nature, under the provocative title Could string theory be testable? (subscription needed). Graphene is an example where, from the complexity of the interactions between electrons and a 2-d lattice of ions, simple behaviour emerges, that seems to be well described by the theories of fundamental high energy physics. Geim asks “could we design condensed-matter systems to test the supposedly non-testable predictions of string theory too?” The other question to ask, though, is whether what we think of as the fundamental laws of physics, such as quantum field theory, themselves emerge from some complex inner structure that remains inaccessible to us.

3 thoughts on “Graphene and the foundations of physics”

  1. Great Post!

    I found out about the Graphene discovery just 3 months ago searching the web about the Quantum Hall effect.

    Here is a link for those who do not have a Nature subscription for the Rise of Graphene:

    When you write ‘highly relativistic, massless particles’ are you refering to Quantum Hall effect?


  2. The fact that the electrons behave as highly relativistic massless particles does indeed mean that graphene has an anomalous quantum hall effect, but it’s more general than that – the electrons obey a Dirac equation rather than the Schrodinger equation, and from this many unusual consequences follow. Thanks for the link. I should note that the Nature Materials link is freely available without subscription, at least for now. The paper’s also available from Geim’s own site.

  3. Hi Richard

    Thanks for you very helpful reply!

    As this stuff is of very high intellectual caliber, it appears that for me to fully understand the fascinating phenomenon of quantum transport in Graphene will take some time…

    In particular, as you have pointed out the deeper relationship with Dirac’s equation, I will ponder the links between Graphene , Plasmonics and Spintronics!

    Thanks again for your post


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