Research researchers create Hofstader butterfly in graphene

Published on May 20th, 2013 | by Tina Casey

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Elusive Graphene Butterfly Finally Spreads Its Wings

May 20th, 2013 by  

Graphene is an ultra-thin, ultra-conducting, ultra strong material that could spawn a whole new generation of ultra-efficient electronics, and hundreds if not thousands of researchers around the globe are racing to unlock the secrets behind its unique properties. It looks like the latest match will end in a draw, as two international research teams have both succeeded in manipulating graphene to produce a phenomenon that until now has only been known in theory, the Hofstadter butterfly.

Results for both teams have just been published back-to-back in the online edition of Nature.

researchers create Hofstader butterfly in graphene

Hofstadter butterfly courtesy of University of Manchester

The Elusive Hofstadter Butterfly

The Hofstadter butterfly is named after Douglas Hofstadter, a US physicist who first theorized the effect in 1976.

Hofstadter predicted that electrons in a two-dimensional sheet will form a distinctive “fractal” pattern in response to a strong magnetic field combined with periodic potential energy (fractal refers to a pattern that repeats in smaller and smaller shapes).

The occurrence of fractal patterns in quantum mechanics is relatively rare, and Hofstadter’s butterfly was among the first examples to be predicted. However, until now it has existed only in theory.

Columbia University’s Graphene Butterfly

One of the aforementioned teams consists of Columbia University, City University of New York, the University of Central Florida, and Tohoku University and the National Institute for Materials Science in Japan.

A major hurdle that the team tackled was the creation of perfectly scaled structures to generate the periodic potential energy required for creating the butterfly effect (think of periodic as a marble rolling around in an egg carton, and you’ve got the idea).

The solution was to use boron nitride, also known as “white graphene,” which shares a similar lattice structure with graphene.

Graphene is basically a sheet of carbon only one atom thick, and when the team layered it onto an atomically flat layer of boron nitride, the combination formed a moiré pattern (moiré refers to a ripple or washboard-like effect). The team used the National High Magnetic Field Laboratory to measure the electronic conductivity of the material, revealing the butterfly-like fractal pattern.

Manchester’s Graphene Butterfly

The other team, spearheaded by the University of Manchester, also includes the University of Lancaster in the UK, Instituto de Ciencia de Materiales de Madrid in Spain and National High-Field Laboratory in Grenoble, France.

Like Columbia University, the Manchester team worked with a two-layer sandwich of graphene and boron nitride to produce the butterfly effect.

Specifically, it involves replicating the unique pattern created by electricity-carrying electrons in graphene, called Dirac fermions, as the electrons move along the moiré pattern. These multiple Dirac clones form the Hofstadter butterfly.

On Beyond Graphene

Aside from solving a 40-year-old mystery, the two teams have added to a growing body of knowledge demonstrating that it is possible to create new classes of materials for electronic devices as well as new super-efficient photovoltaic devices, by layering graphene with other atomically thin materials.


Now that’s something to chew on, considering that the the unique properties of graphene alone appear to contain enough mysteries to keep an army of researchers busy for a lifetime (and don’t even get us started on its hydrogen-boosted variant, graphane).

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About the Author

specializes in military and corporate sustainability, advanced technology, emerging materials, biofuels, and water and wastewater issues. Tina’s articles are reposted frequently on Reuters, Scientific American, and many other sites. Views expressed are her own. Follow her on Twitter @TinaMCasey and Google+.



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  • James Wimberley

    I’ve read this and the Manchester press release several times, but remain completely baffled. What is a Dirac fermion?
    Don’t get me wrong, this sort of fundamental research is well worth doing, but the link to practical technology is handwaving. Physicists should not be asked to pretend that all knowledge has to be useful.

    • Wayne Williamson

      wikipedia states…

      In particle physics, all fermions in the standard model, except possibly neutrinos, are Dirac fermions.

      In condensed matter physics, low-energy excitations[clarification needed] in graphene and topological insulators, among others, are fermionic quasiparticles described by a pseudo-relativistic Dirac equation.

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