23-03-2025
The butterfly effect: A misaligned experiment accidentally unfolds quantum wings
In a remarkable scientific breakthrough, researchers at Princeton University have observed a fractal energy pattern in quantum materials that had only been predicted on paper for nearly fifty years.
Known as Hofstadter's butterfly, this intricate design emerges from the behavior of electrons in certain conditions.
Originally theorized in 1976 by physicist Douglas Hofstadter, the pattern had never been directly observed in an actual material — until now.
The discovery came as a surprising outcome of research focused on superconductivity, where a small experimental mistake opened the door to this long-sought-after observation.
The discovery was made possible by recent developments in materials science, where scientists are able to stack and twist extremely thin layers of carbon atoms — known as graphene — into specific structures.
This twisting creates moiré patterns, a kind of interference design similar to overlapping fabrics.
'These moiré crystals provided an ideal setting to observe Hofstadter's spectrum when subjecting electrons moving in them to a magnetic field. These materials have been extensively studied, but up to now the self-similarity of the energy spectrum of these electrons had remained out of reach,' explained Ali Yazdani, James S. McDonnell Distinguished University Professor at Princeton.
Interestingly, the discovery happened by accident.
The research team, led by Yazdani, was originally studying superconductivity in twisted bilayer graphene.
'Our discovery was basically an accident,' admitted Andrew Nuckolls, one of the researchers. 'We didn't set out to find this.'
Dillon Wong, postdoctoral research associate and co-lead author of the paper, elaborated, 'We were aiming to study superconductivity, but we undershot the magic angle when we were making these samples.'
This misstep produced a longer moiré periodicity than planned — but exactly the right conditions for observing the fractal spectrum.
capable of imaging atoms by measuring the tiny quantum currents that flow between the microscope tip and the surface.
While using the STM, the team noticed unusual behavior in electron energy levels.
'The STM is a direct energy probe, which helps us relate back to Hofstadter's original calculations, which were calculations of energy levels,' said Myungchul Oh, a postdoctoral research associate and co-lead author.
Electrical resistance measurements in past studies had hinted at the butterfly pattern, but the STM allowed for direct visualization.
'Sometimes nature is kind to you,' said Nuckolls. 'Sometimes nature gives you extraordinary things to look at if you stop to observe it.'
The team's work also shed light on how electrons interact with each other in these complex materials.
While Hofstadter's original calculations did not account for electron interactions, this experiment showed that including these effects made the models more accurate.
'The Hofstadter regime is a rich and vibrant spectrum of topological states, and I think being able to image these states could be a very powerful way to understand their quantum properties,' said Michael Scheer, a graduate student and co-lead author.
Though immediate applications are unclear, this accidental discovery opens exciting new possibilities for understanding quantum materials.
The study was published in the journal Nature.
