Spotting the Elusive ‘Hofstadter Butterfly’

A TEAM OF SCIENTISTS who set out to study a new type of material inadvertently confirmed a nearly 40-year-old physics theory that predicts a pattern of energy.

Researchers from CUNY and several other universities had been studying sheets of extraordinarily thin and strong mineral graphite, called a graphene. Only a single atom thick and nearly transparent, graphene is an excellent conductor of heat and electricity.

Cory Dean, City College physics professor.

Cory Dean, City College physics professor.

But the marvels of graphene, in this instance, are secondary to the wonders of scientific thought, where a prediction made decades earlier is at last confirmed.

While studying the ultrathin material, researchers observed a rare effect — a repeating, butterfly-shaped energy spectrum. It’s known as the “Hofstadter Butterfly,” named after the American scientist Douglas Hofstadter who developed a theory in 1976 to predict the behavior of electrons in a magnetic field.

But although there had been many attempts to prove the theory over the years, none had been successful.

“Like many interesting discoveries, it was accidental,” says City College physics professor Cory Dean, who is the author of the study “Hofstadter’s Butterfly and the Fractal Quantum Hall Effect in Moiré Superlattices.”

“We were studying properties of graphene . . . and once in a while we’d see features in our data that we didn’t understand. We ended up putting all the pieces together and realized it was a complete manifestation of Hofstadter’s prediction.”

The pattern arises naturally when a sheet of graphene sits atop a sheet of boron nitride at an angle. Once positioned properly, a secondary hexagonal pattern emerges on the overlapped sheets. “We were fortunate in our ability to discover a system that actually revealed [Hofstadter’s butterfly],” says Dean.

“I get asked a lot, ‘What’s the real-world application of this study?’ At this point we just don’t know. I can say with assuredness we have discovered a new type of material that is exhibiting a new type of property that hasn’t been explored,” says Dean.

However, there is certainly a possibility that the material will enable new optical electronics, says Dean. “Will this lead to flatter TVs? Possibly, but at some point one can only get so flat.”