Featured Research

from universities, journals, and other organizations

First direct proof of Hofstadter butterfly fractal observed in moiré superlattices

Date:
May 15, 2013
Source:
Columbia University
Summary:
Scientists have directly observed a rare quantum effect that produces a repeating butterfly-shaped energy spectrum, confirming the longstanding prediction of this quantum fractal energy structure called Hofstadter's butterfly.

This is an artistic image illustration of a butterfly departing from a graphene moiré pattern formed on the top of an atomically thin boron nitride substrate. Electron energy in such a graphene moiré structure exhibits the butterfly like a self-recursive fractal quantum spectrum.
Credit: Columbia Engineering

A team of researchers from Columbia University, City University of New York, the University of Central Florida (UCF), and Tohoku University and the National Institute for Materials Science in Japan, have directly observed a rare quantum effect that produces a repeating butterfly-shaped energy spectrum, confirming the longstanding prediction of this quantum fractal energy structure, called Hofstadter's butterfly.

The study, which focused on moiré-patterned graphene, is published in the May 15, 2013, Advance Online Publication (AOP) of Nature.

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 (akin to a marble rolling on a sheet the shape of an egg carton) and a strong magnetic field. The Hofstadter butterfly is a fractal pattern -- it contains shapes that repeat on smaller and smaller size scales. Fractals are common in classical systems such as fluid mechanics, but rare in the quantum mechanical world. In fact, the Hofstadter butterfly is one of the first quantum fractals theoretically discovered in physics but, until now, there has been no direct experimental proof of this spectrum.

Previous efforts to study the Hofstadter butterfly, which has become a standard "textbook" theoretical result, attempted to use artificially created structures to achieve the required periodic potential energy. These studies produced strong evidence for the Hofstadter spectrum but were significantly hampered by the difficulty in creating structures that were both small and perfect enough to allow detailed study.

In order to create a periodic potential with a near-ideal length scale and also with a low degree of disorder, the team used an effect called a moiré pattern that 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. This work builds on years of experience with both graphene and BN at Columbia. The techniques for fabricating these structures were developed by the Columbia team in 2010 to create higher-performing transistors, and have also proven to be invaluable in opening up new areas of basic physics such as this study.

To map the graphene energy spectrum, the team 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 moiré-patterned graphene provides a new model system to explore the role of fractal structure in quantum systems," says Cory Dean, the first author of the paper who is now 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," adds 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 work from Columbia University resulted from collaborations across several disciplines including experimental groups in the departments of physics (Philip Kim), mechanical engineering (James Hone), and electrical engineering (Kenneth Shepard) in the new Northwest Corner building, using the facilities in the CEPSR (Columbia's Schapiro Center for Engineering and Physical Science Research) microfabrication center. Similar results are concurrently being reported from groups led by Konstantin Novoselov and Andre Geim at the University of Manchester, and Pablo Jarillo-Herrero and Raymond Ashoori at MIT.


Story Source:

The above story is based on materials provided by Columbia University. Note: Materials may be edited for content and length.


Journal Reference:

  1. C. R. Dean, L. Wang, P. Maher, C. Forsythe, F. Ghahari, Y. Gao, J. Katoch, M. Ishigami, P. Moon, M. Koshino, T. Taniguchi, K. Watanabe, K. L. Shepard, J. Hone, P. Kim. Hofstadter’s butterfly and the fractal quantum Hall effect in moiré superlattices. Nature, 2013; DOI: 10.1038/nature12186

Cite This Page:

Columbia University. "First direct proof of Hofstadter butterfly fractal observed in moiré superlattices." ScienceDaily. ScienceDaily, 15 May 2013. <www.sciencedaily.com/releases/2013/05/130515131554.htm>.
Columbia University. (2013, May 15). First direct proof of Hofstadter butterfly fractal observed in moiré superlattices. ScienceDaily. Retrieved September 2, 2014 from www.sciencedaily.com/releases/2013/05/130515131554.htm
Columbia University. "First direct proof of Hofstadter butterfly fractal observed in moiré superlattices." ScienceDaily. www.sciencedaily.com/releases/2013/05/130515131554.htm (accessed September 2, 2014).

Share This




More Matter & Energy News

Tuesday, September 2, 2014

Featured Research

from universities, journals, and other organizations


Featured Videos

from AP, Reuters, AFP, and other news services

Australian Airlines Relax Phone Ban Too

Australian Airlines Relax Phone Ban Too

Reuters - Business Video Online (Aug. 26, 2014) — Qantas and Virgin say passengers can use their smartphones and tablets throughout flights after a regulator relaxed a ban on electronic devices during take-off and landing. As Hayley Platt reports the move comes as the two domestic rivals are expected to post annual net losses later this week. Video provided by Reuters
Powered by NewsLook.com
Hurricane Marie Brings Big Waves to California Coast

Hurricane Marie Brings Big Waves to California Coast

Reuters - US Online Video (Aug. 26, 2014) — Huge waves generated by Hurricane Marie hit the Southern California coast. Rough Cut (no reporter narration). Video provided by Reuters
Powered by NewsLook.com
Chinese Researchers Might Be Creating Supersonic Submarine

Chinese Researchers Might Be Creating Supersonic Submarine

Newsy (Aug. 26, 2014) — Chinese researchers have expanded on Cold War-era tech and are closer to building a submarine that could reach the speed of sound. Video provided by Newsy
Powered by NewsLook.com
Breakingviews: India Coal Strained by Supreme Court Ruling

Breakingviews: India Coal Strained by Supreme Court Ruling

Reuters - Business Video Online (Aug. 26, 2014) — An acute coal shortage is likely to be aggravated as India's supreme court declared government coal allocations illegal, says Breakingviews' Peter Thal Larsen. Video provided by Reuters
Powered by NewsLook.com

Search ScienceDaily

Number of stories in archives: 140,361

Find with keyword(s):
 
Enter a keyword or phrase to search ScienceDaily for related topics and research stories.

Save/Print:
Share:  

Breaking News:
from the past week

In Other News

... from NewsDaily.com

Science News

Health News

Environment News

Technology News



Save/Print:
Share:  

Free Subscriptions


Get the latest science news with ScienceDaily's free email newsletters, updated daily and weekly. Or view hourly updated newsfeeds in your RSS reader:

Get Social & Mobile


Keep up to date with the latest news from ScienceDaily via social networks and mobile apps:

Have Feedback?


Tell us what you think of ScienceDaily -- we welcome both positive and negative comments. Have any problems using the site? Questions?
Mobile iPhone Android Web
Follow Facebook Twitter Google+
Subscribe RSS Feeds Email Newsletters
Latest Headlines Health & Medicine Mind & Brain Space & Time Matter & Energy Computers & Math Plants & Animals Earth & Climate Fossils & Ruins