May 16, 2013
Researchers Discover First Direct Proof Of Hofstadter Butterfly Fractal
redOrbit Staff & Wire Reports - Your Universe Online
Researchers have for the first time directly observed a rare quantum effect that produces a repeating butterfly-shaped energy spectrum, confirming the longstanding prediction of the quantum fractal energy structure known as Hofstadter's butterfly.First predicted by American physicist Douglas Hofstadter in 1976, the Hofstadter butterfly emerges when electrons are confined to a two-dimensional sheet, and subjected to both a periodic potential energy and a strong magnetic field.
The Hofstadter butterfly is a fractal pattern, meaning it contains shapes that repeat on smaller and smaller size scales. Fractals are common in classical systems such as fluid mechanics, but are rare in the quantum mechanical world.
In fact, the Hofstadter butterfly is one of the first quantum fractals theoretically discovered in physics, although until now there has been no direct experimental proof of this spectrum.
Previous efforts to study the Hofstadter butterfly attempted to use artificially created structures to achieve the required periodic potential energy. These studies produced strong evidence for the Hofstadter spectrum, but were dramatically hindered by the difficulty in creating structures that were both small and perfect enough to allow detailed study.
In the current work, researchers from Columbia University, City University of New York, the University of Central Florida (UCF), Tohoku University, University of Manchester, MIT, and the National Institute for Materials Science in Japan used an effect called a moirÃ© pattern. This pattern arises naturally when atomically thin graphene is placed on an atomically flat boron nitride (BN) substrate, which has the same honeycomb atomic lattice structure as graphene but with a slightly longer atomic bond length. The researchers used this approach in order to create a periodic potential with a near-ideal length scale and also with a low degree of disorder.
To map the graphene energy spectrum, the researchers then measured the electronic conductivity of the samples at very low temperatures in extremely strong magnetic fields up to 35 Tesla (consuming 35 megawatts of power) at the National High Magnetic Field Laboratory.
The measurements show the predicted self-similar patterns, providing the best evidence to date for the Hofstadter butterfly, and providing the first direct evidence for its fractal nature.
"Now we see that our study of moirÃ©-patterned graphene provides a new model system to explore the role of fractal structure in quantum systems," said Cory Dean, the study´s lead author and an assistant professor at The City College of New York.
"This is a huge leap forward–our observation that interplays between competing length scales result in emergent complexity provides the framework for a new direction in materials design. And such understanding will help us develop novel electronic devices employing quantum engineered nanostructures."
"The opportunity to confirm a 40-year-old prediction in physics that lies at the core of most of our understanding of low-dimensional material systems is rare, and tremendously exciting," said Dean.
"Our confirmation of this fractal structure opens the door for new studies of the interplay between complexity at the atomic level in physical systems and the emergence of new phenomenon arising from complexity."
The study was published online May 15 in the journal Nature.