Nearly 50 years ago, the computer scientist Douglas Hofstadter A planned butterfly would spread his wings in the quantum world. Depending on the correct conditions, small electrons in a quantum system can create a fracture energy spectrum, that is, the intricate structure that would be a very striking model, “he wrote 1976 Seminal Paper.
Many physicists have tried to create a “Hofstadter butterfly” in different formats, with different levels of success; a The first spectrum was created about 25 years ago. The difficulty of observing impact, partly because Hofstadter had a positive initial prediction, should be a colossal magnetic field beyond any laboratories. Therefore, most experimental efforts wanted to call the silic butterfly, on the borders of computer simulations, and based on physical quantum systems they studied using indirect measurements of their properties.
Now, however, what can be Direct observation from around the world of butterfly Among the two microscopic layers of graphen, it has been created from the complex quantum dance of sandwiches. Results have recently been published Nature, They are noteworthy because they were all surprises: the participating researchers did not try to catch Hofstadter’s butterflies from Quantum Chrysalis.
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“I think he was happy to have been an accident,” says the author of study Kevin NuckollsA physicist at the Massachusetts Institute Institute of Technology. “I think that’s common for physics experiments (in which) you see something weird. You give a couple of hours and decide the decision mode,” I’ll give it a couple more days. ‘
At the time of the experiment, Nuckolls and his author were part of the Princeton University laboratory, the flux against the electricity, is not organized into a hexagonal pattern that consists of a two-dimensional crystal, a single carbon atom. When two graphene sheet accumulates on top of the other, with a small rotation compensation of around 1.1 degrees, hexagons are not exactly so called Magic angle The configuration is formed. When a magnetic field is suffered, the electron inside each sheet returns between carbon atoms and shows forward, superaculated and other strange properties.
The manufacture of “twisted looking graffene” is as much as the art of science. It gives dudes that don’t have the right one-free mile. For each attempt, researchers verify their work while testing the sheet directly Scanning tunnel microscope (Hot). The results of the results show the flow of electrons through the material and indicate whether any assemblies given is hit the magic angle.
“When we are doing these devices in general, we don’t know what angle twisted until this non-twisted graphene has joined our microscope,” explained Dillon WongResearch author and former researcher at Princeton. “And most of the time, the angle is wrong, and we must fail.”
As expected, things went wrong This time, at first glance they showed that the graphene was emphasizing an angle of 1.1 degrees. But because graphene is a particular look It was Closer to another known but smaller magical angle, Nuccolls, however, decided to represent Stm.
This soil shows how electrons (vertical axes) change the electrons as a function of magnetic field (horizontal axis), and separated bands in Hofstadter (multi-color shadows). Nuccolls and his colleagues could identify how they repeating the energy level of electrons, as it was repeated in different scales, as it was planned, the case would be the case in the formation of “Hofstadter’s Butterfly”.
The first images were not so spectacular, Nuccolls, but when researchers went to see the whole image of the system, they were more intrigued. However, several days later they realized, however, the sandwich electrons seemed to be filling a half-century announcement in Hofstadter. Their delay is not so amazing, in fact, in the first and foremost they did not seek the model, he only appeared through the careful monitoring of the collective behavior of electrons.
“It is the idea behind Hofstadter’s butterfly (band structures) when you are looking at the magnetic energy of the electrons, and depicted in this diagram, the band forms this structure that looks like a butterfly,” he explains Myungchul ohLearn the author of the author and now Professor Physics at Pohang Science and Technology at South Korean University. The past experiments were “indirect”, the usual, as they were not facing real energy transformation, proxy measurements, such as spatial distribution of electrons.
NUCKOLLS, Wong and Oh, and decided that this particular system was deeper, above Michael ScheerPrincetone’s theoretical physics student to find stronger models of work interaction, to better understand what happened.
Hofstadter’s butterfly “is like a fingerprint”, says Scheer. “It’s really accurate, accurate and very sensitive information, and on the other hand, the material you are measuring and its physical parameters.” This interaction between theory and the experiment may show “tremendous information” that researchers can use learning about material properties, adds NUCKOLLS. In other words, watching the twisted butterflies of Hofstadter could be wider availability, opening the way other systems and materials to clarify the phenomenon research.
“It’s one of the biggest merits of this work … He really got to go in a very special parameter regime to see new physics,” he says Cristiane Morais SmithCondensed physicist at the University of Utrecht, in the Netherlands, who did not participate in new work. “It was very special (them) the small magnetic fields (like those who are similar to the sounds) could be sufficient (they wanted to probe they wanted to” probe, “he said, as other groups should be easily repeated and practiced in the experiment.
Hofstadter, 80 years ago, is polite American scientificRequest to comment on the new result, without saying that his prediction was rarely reviewed, since he did it for about half a century, and would hardly understand the proper understanding of the role, which he did not have to read. “I’ve seen a lot of claims for the years (planned) recurrence”, “he said.” But they are very thick, none of them approached a real nest structure. That may happen in the other decades, if humanity is still at that moment. “
However, the new job requires humanity at least a few steps (or wing slopes) to carry out predictions of Hofstadter. This initial result is ripe for the follow-up study, OH, Hofstadter’s butterflies still examine the flight of sandwich graphene that has been more powerful magnetic fields. “I would love how and what the Hofstadter model is emulating in large-scale magnetic fields,” he noted.
“Hofstadter’s calculation has done and has been working very happy for 50 years,” says Nuckold. “It’s essentially concluding” Hofstadter’s original paper, but no one will ever be achieved because the necessary magnetic fields will never be able to see the first evidence that the researchers support its calculations. “
