S03E14: The Einstein Approximation

The hottest material in physics can be made with a pencil and Scotch tape.   That’s “hottest” in popularity, not temperature.  When a new, interesting, material is discovered, teams of physicists will race against each other to figure it out.   This decade’s material-of-the-century is graphene.

Graphene is merely chicken wire made with carbon atoms…chicken wire that is no thicker than a single atom.

Atomic chickenwire: A image of an actual sheet of graphene. Each little black dot is an empty space surrounded by six carbon atoms, forming a hexagon. (The width of the entire image is about one thouand times smaller than the width of a human hair.)

Carbon atoms love to form chains, as in alcohol, or even rings, as in chemicals found in gasoline.   Even more tangled-up connections of carbon create popular substances like diamonds and soot.  Physicists knew for decades that the existence of a single sheet of interconnected carbon atoms was possible, in principle.  But they also knew that such a structure could hardly be grown as a crystal since the structure tends to roll up and form three-dimensional bonds.

But only six years ago, in cutting-edge experiments (using Scotch tape and pencils), physicists succeeded in creating small quantities of graphene, smaller than a speck of dust.  Pencil lead, despite its name, has no “lead” in it.  Rather it is many layers of carbon sheets, like a deck of cards, stuck together called graphite (from the Greek “to write“).  The experimental heroes just stuck a little of the humble pencil graphite in a folded over piece of tape…and pulled, separating hundreds of atomic layers in two smaller stacks.   A student can repeat the process as many times as needed, until a single layer is  created.

The students transfer the single-sheet candidates from the tape to a silicon wafer for further study.  One of the researchers’  breakthroughs was to discover a quick way of identifying single layers from less interesting multiple layers.   Like oil floating on a puddle reflecting sunlight after the rain, the film thickness determines its color.   The thin, elegant, highly-sought single sheets of graphene appear pale pink, while their fatter cousins are blue.

The process produced perfect crystals, with no apparent defects.  Graphene would prove to be harder than diamond, yet flexible.  Graphene is not a metal, yet highly conductive.  Success having many mothers, after the discovery, claims of priority going back several decades have been staked.

Pity the poor condensed-matter theorists.  For over a century they have pushed pencils across their pads in search of new materials to propose.  Yet there graphene was, literally right under their noses, the entire time.

A few episodes ago, Sheldon took us in his mind to the fictional country of Flatland, where only two dimensions of motion are allowed.   Not at all fictional, graphene is a carbon Flatland with electrons fixed to move only in its two-dimensional world.  Lacking that one extra dimension turns most of the rules of materials on its head.  Graphene has captured the imagination of physicists with its potential applications.

High speed transistors:  The heart of computers and most other electronics are the fast switches called transistors.  The electrons in graphene are extremely mobile, able to cross thousands of carbon atoms without a single scatter.  So the idea, at least, has been put forward that graphene could be the basis of a new generation of higher speed, smaller integrated circuits.

Super-batteries:   Because its mass per area is as low as any imaginable material, graphene could revolutionize energy storage in batteries and the adoption of renewable energy.  Capacitors too, one of the basic building blocks of all electronics (they hold charge in circuits), could be replaced by far smaller graphene components.

Displays: Having the seemingly contradictory properties of transparency and conductivity at once, perhaps one day graphene sheets will produce large area touch-screens.  Now scientists only need discover what the iPad is good for.

Gas sensors:  Graphene’s low noise and high surface area could perhaps make it sensitive enough to detect even a single gas molecule adsorbed onto its surface causing a detectable step-like change in its electrical resistance.

Graphene could revolutionize electronics.

But what attracted Sheldon’s attention tonight is the theoretical description of electron motion in graphene.  By a mathematical coincidence, the equation that describes electron motion in graphene is almost the same as the fundamental equation of free electrons in relativistic quantum mechanics:  the famous Dirac Equation.   Because of the electrons’ interactions with the carbon nuclei, the electrons move as if they are massless.   So graphene can serve as a kind of laboratory for particle physics theorists, like Sheldon, to test their understanding of the mathematics they use every day under more abstract and less controllable conditions.

Graphene.  It’s the greatest thing since sliced pencil lead.

27 Responses to “S03E14: The Einstein Approximation”

  1. Jeff Edsell Says:

    So could you call graphene a room-temperature superconductor?

    • David Saltzberg Says:

      It is highly conductive but there is still *some* resistance at room temperature. So it is not a superconductor at room temperature.

  2. Jeff Edsell Says:

    Also, isn’t Sheldon’s epiphany when he sees the broken plates at the end a reference to Richard Feynman’s similar experience, seeing spinning plates dropped by a waiter and being inspired about rotation?

  3. PG Says:

    Sheldon should talk about superconductivity, wherein electrons form “Cooper pairs”. ;)

  4. Jay from Toronto Says:

    Hi Im not a scientist but enjoy reading your blog after the shows. Can you tell me what the problem Sheldon was trying to figure out was?

    You hinted at it at the end of the entry. I understand that various particles can act as a wave or as a particle and remember in school learning that even mass has a ‘wave equation’ associated with it. Here Sheldon sees that: “the equation that describes electron motion in graphene is almost the same as the fundamental equation of free electrons in relativistic quantum mechanics: the famous Dirac Equation. Because of the electrons’ interactions with the carbon nuclei, the electrons move as if they are massless” –in other words as a wave.
    1) Why wouldnt a theoritcal physicist think of it as a wave before any plates got broken. In other words he knows electrons can act as waves as well as particles with other materials –how come this would not have occured to him via electrons and graphene immediately?
    2) In terms of physics what is the importance if any that this observation would lead to in Sheldon’s current work (the work that changes on his board every show)?

    Pardon my ignorance but Im not a scientist at all –its just the intensity of “Dr Cooper” during this episode got me curious–I would like to know what he was trying to find out?

    • Icy Says:

      err, yeah, for a physicist with so many academic credentials, he conveniently forgot that electrons act as both a particle and waves. this is highly unrealistic.

      • David Saltzberg Says:

        I think the concept was that he realized they were a “supercollimated wave”. That is a more subtle point in graphene than just wave particle duality.

  5. Jay from Toronto Says:

    Ps love your blog and I hope you yourself appear on the show in the future maybe via a ‘run in’ with “Dr Cooper” as the Dr. Smoot did.

  6. Jay from Toronto Says:

    PPS my area is in the arts but your blog and the show tempt me to minor in science just to understand.

  7. shellorz Says:

    Hey, I love how this rather hot topic makes it on the show. Plus it’s both quantum physics and solid physics. Still I didn’t get Sheldon’s conclusion “it’s a wave!”. Well, everything is a wave and a particle, right ?As Feynamn would say, it’s all a question of reduction and rotation of the big main complicated wavefunction, right ? Is there some scientific thing I didn’t get or was it just “romanced” so the writers could come up with something that sounded connected to known facts ? congrats on the white board prop. Must have taken some time !

    • David Saltzberg Says:

      Maybe it was a “super-collimated” wave. That’s a hot topic in understanding graphene right now. (This is not canon.)

    • mike Says:

      It’s because the massless nature of electrons in graphene. They behave as Dirac (relativistic) particles with no effective mass. More info:


      Nature 438, 197 (2005)

      Two-dimensional gas of massless Dirac fermions in graphene

      K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos & A. A. Firsov

  8. Uncle Al Says:

    Electrons in graphene spontaneously propagate hard by the local speed of light, about c/300 (arxiv:0812.1116) – impressive!

    graphene optical absorption is (pi)(alpha), ~ 2.29%

    graphene is CVD growable to multiple mm^2 on copper

    Nature Physics 2 620 (2006)
    Somebody is always pulling a Sheldon

  9. uberVU - social comments Says:

    Social comments and analytics for this post…

    This post was mentioned on Friendfeed by gaiiden: any true nerd who loves The Big Bang Theory should also br reading The Big Blog Theory – http://ping.fm/uHyYK

  10. Graphene « Life doesn't make sense Says:

    [...] am writing this post because of the recent The Big Bang Theory episode. In it, Sheldon was pondering (abeit to a pretty serious degree) over why electrons behave [...]

  11. TBBT Fan Says:

    Shelly is so cute!!! err, I mean Sheldon. hehe

  12. Eric Says:

    My problem with this episode is that I’m not even a physicist, but an electrical engineer, and even I would know to start from diffraction patterns and effective mass etch when analysing graphene. Why did Sheldon start off considering electrons as particles?

    • David Saltzberg Says:

      Sometimes a particle treatment works easier, sometimes a wave treatment. Sometimes a hybrid approach of a “packet of waves” works best. It is all about what is easiest to calculate.

  13. HS Says:

    Has anybody spotted the error in the Hamiltonian yet? [The Hamiltonian is the 2x2 matrix in the lower left part of the white board, in the scene where Sheldon talks about unbalanced formulas. Hint: It should be hermitian.]

  14. HS Says:

    (lower right part, I meant…)

  15. NeoTechni Says:

    “until a single layers are created.”

    The letter/word a should be omitted.

  16. Tradução: “S03E14: The Einstein Approximation (A Aproximação de Einstein)” « The Big Blog Theory (em Português!) Says:

    [...] feita por Hitomi a partir de texto extraído de The Big Blog Theory, de autoria de David Saltzberg, originalmente publicado em 1º de Fevereiro de [...]

  17. Nathan Says:

    Ok.. here’s what I don’t get, Sheldon is supposed to have an IQ of 170+, and it takes him 3/4 sleepless nights to work out that diffraction is a wave property, something known by even the most simple physicists. You get taught this in A-level physics.

    • David Saltzberg Says:

      In my understanding of the backstory, Sheldon was realizing it was a supercollimated wave. That is a more subtle point in graphene than just wave particle duality.

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