A fractal butterfly pattern produced by an unusual configuration of magnetic fields, first predicted almost 50 years ago, has been seen in detail for the first time in a twisted piece of graphene.
While a physics student in 1976, the computer scientist predicted that when certain two-dimensional crystals were placed in magnetic fields, their electronsā energy levels should produce a strange pattern that looks the same no matter how far you zoom in, known as a fractal. At the time, however, Hofstadter calculated that the atoms of the crystal would have to be impossibly close together to produce such a pattern.
In 2013, researchers experimental hints of this pattern, which became known as Hofstadterās butterfly, in a flat sheet of boron nitride, a material similar to graphene. Their measurements looked at the overall resistance of the material, which could give hints of what the electrons were doing, but they still didnāt know the exact energies of the electrons.
Advertisement
Now, at Princeton University and his colleagues have measured Hofstadterās butterfly in detail for the first time, using two twisted layers of graphene.
When one layer of graphene is rotated on top of another at a certain angle, called the magic angle, it produces unique repeating structural patterns and magnetic fields that can lead to unexpected properties, such as superconductivity. These conditions are similar to those in Hofstadterās original prediction, but the strong magnetic fields distort the grapheneās electrons, making them impossible to measure in detail with an electron microscope.
Yazdani and his colleagues were experimenting with a second magic angle, which leads to wider repeating patterns, when they realised it would produce weaker magnetic fields and leave the electrons free to measure, allowing the team to take detailed readings of their energies. āThe fact that we could go to these very low magnetic fields, and do this experiment, was a sweet spot that people hadnāt anticipated before,ā says Yazdani.
āItās a nice story that shows the predictive power that we have,ā says at Imperial College London. āWe really understand the fundamental laws of electrons, so much so that we can make a prediction and, even if it takes 50 years to verify it, at the end of the day it comes out the way it was predicted.ā
āI was very pleased by the basic findings of the paper,ā says Hofstadter. āI left physics about 50 years ago, and thus I really canāt offer any professional judgments about it. It goes without saying that I am always gratified when there are empirical confirmations of the structure that I predicted back in 1976.ā
Nature
