In a first, physicists have directly seen Hofstadter's butterfly—a long-sought-after fractal in the quantum realm
A team of scientists from Princeton University has measured the energies of electrons in a new class of quantum materials and has found them to follow a fractal pattern known as "Hofstadter's butterfly," which has long been predicted, but the new study marks the first time it has been directly observed experimentally in a real material. Almost 50 years ago, computer scientist Douglas Hofstadter predicted that a butterfly would spread its wings in the quantum world. Under the right conditions, tiny electrons in a quantum system could produce an energy spectrum composed of fractals, intricate self-repeating structures that would "form a very striking pattern somewhat resembling a butterfly," he wrote in a seminal 1976 paper. Many physicists have attempted to create "Hofstadter's butterfly" in different formats, with varying degrees of success; the first such spectra emerged about 25 years ago. The difficulty in observing the effect was, in part, because Hofstadter's initial prediction posited that it would require colossal magnetic fields beyond the reach of any laboratory. Most experimental efforts consequently sought to summon the butterfly in silico, within the confines of computer simulations, and those reliant on physical quantum systems studied its properties using largely indirect measurements. Now, however, what may be the first-ever direct, real-world observation of the butterfly has emerged from the complex quantum dance of electrons sandwiched between two microscopic layers of graphene. The results, published recently in Nature, are all the more remarkable because they were unexpected—the researchers involved weren't even trying to hatch Hofstadter's butterfly from its quantum chrysalis. On supporting science journalism If you're enjoying this article, consider supporting our award-winning journalism by subscribing. By purchasing a subscription you are helping to ensure the future of impactful stories about the discoveries and ideas shaping our world…