Almost 50 years ago, computer world expected Douglas Hofstadter to spread its wings butterfly in the world of quantum. Under the appropriate circumstances, small electrons in the quantum system can produce an energy spectrum consisting of a buffer, which are complex self -repetition structures “that would form a very amazing style that is a somewhat like a butterfly”, he wrote in Paper in 1976.
Many physicists have tried to create a “Hofstadter butterfly” in different formats, in varying degrees of success; the The first of these spectra appeared about 25 years ago. The difficulty in monitoring the effect was partly, because the initial prediction of Hofstadter assumes that it would require huge magnetic fields outside the reach of any laboratory. Most experimental efforts have sought to summon the butterfly in silico, within the limits of computer simulation, and those that depend on the physical quantum systems that have studied its properties using largely indirect measurements.
Now, however, what might be The first direct and realistic monitoring of the butterfly It appeared from the complex quantum dance of the electrons confined between two microscopic gravies. Recently published results in nature, It is more clear because they were unexpected – the researchers involved even tried to hatch the Hofstadter butterfly from Quantum Chrysalis.
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“I think it was a happy accident,” says the study author. Kevin NokoulsPhysical at the Massachusetts Institute of Technology. “I think this is common for physics experiences [in which] You see something strange. She spends a few hours on her and decides – like, “I will give her a few other days.”
At the time of their experience, both Nuckolls and its participating authors were part of the Brentston University laboratory itself, studying how the superior conductivity-the electric-free flow-free flow, is a two-dimensional formula formed by one layer of carbon atoms arranged in a hexagonal pattern. When two leaves of graphics are accumulated on top of another, with a slight rotation of about 1.1 degrees so that the hexagon does not overlap completely, the so -called formation of the magic angle is formed. When exposed to a magnetic field, the electrons in each sheet of roses go and forth between carbon atoms, and the superior conductivity and other strange properties appear.
The manufacture of such “twisted graphics of the binary layer” is a lot of art like science. DUDS is often produced outside the cars that do not contain the right angle. So for each attempt, the researchers examined their work by searching directly for the leaves using a tunnel scan microscope (STM). The resulting images show the flow of electrons through the material and can indicate whether any certain group has hit the magic angle.
“In general, when we make these devices, we do not know what the twisted corner of the twisted graphics is from it until we put it in our microscope,” explains Delon WongParticipating author of the study and a former researcher in Princeton. “Most of the time, at a completely wrong angle, we are disappointed.”
As expected, things happened wrongly this time as well – a first look showed that the graphics were less than the intended angle of 1.1 degrees. But because this dual -layer graphic He was Closer to another magic angle known but slightly smaller, Nuckolls decided to continue to photograph it anyway with STM.
This plot shows how the energies (vertical axis) of the electrons change as a function of the magnetic field (the horizontal axis), and collects in the separate Hofstadter electronic domains (multi -colored shaded areas). Nuckolls and his colleagues were able to determine how to repeat electrons energy levels on different standards, and it was expected that the case in the composition of the “Hofstadter”, a type of quantum fracture.
Nuckolls admits that the first pictures were not impressive, but as soon as the researchers enlarged them to see a complete picture of the system, they became more interested. They realized after only several days, however, that the confined electrons seem to meet the ancient Hofstadter forecasts. Delaying them is not very surprising, given that they were not looking for the pattern in the first place – and it became only clear through the careful tracking of the collective behavior of the electrons.
“The idea behind the Hofstadter butterfly is that you are looking at how [band structure of electrons] It moves when you have the magnetic field on one axis and electrons on the other hand, and painted on this graph, the band forms a butterfly -like Syrian structure. ” Myungchul ohHe studied a co -author and professor of physics at the Bohang University of Science and Technology in South Korea. The previous experiments were “indirect”, meaning that they did not look at actual energy transformations but rather the measurements of the agent, such as spatial distributions of electrons.
Once Nuckolls, Wong and OH decided that this particular system was worth the deepest scrutiny, they were commissioned Michael ShareBrencestone theoretical studies in the theoretical physics, to reach more powerful models of virtual reactions at work to understand what happened better and how.
Sher says that the Hofstadter butterfly is “a fingerprint.” “It is truly detailed, information and very well for the model that you have, on the other hand, for the materials you measure and material parameters.” Nuckolls adds that this interaction between theory and experience can reveal a “huge amount of information” that researchers can use to identify material properties. In other words, the study of the Hofstadter butterfly in the twisted bilateral layers can be a wider benefit, which opens the way for further investigations implemented for the phenomenon in other systems and materials.
He says: “One of the biggest advantages of this work is that … I really managed Christian Morris SmithPhysical is an intense issue at Utrecht University in the Netherlands, which did not participate in the new work. “What was very special was that [they] You can go to a position in which these small magnetic fields are [like those of an STM] It was enough to investigate what [they] “The investigation wanted,” she says, which should allow other groups to easily repeat and develop the experiment.
Hofstadter, now 80 years old, politely refused American scientificHe added that he is unlikely to understand the paper correctly – which he had no plans to read about half a century ago, noting that he rarely reconsidered the request for the comment about the new result, indicating that he rarely reconsidered his prediction half a century ago and it will be unlikely to understand the paper correctly – which he did not have any plans to read it. “Over the years, I saw many allegations of” symmetrical copies “from [predicted] He says, “Repetition,” but they are all very coarse granules, and none of them approached the discovery of a real intertwined structure. Perhaps this will happen in other decades – if humanity is still present at that point. “
However, the new action takes at least several steps (or wing paintings?) Towards Hofstadter’s predictions. OH says, this initial result is mature of follow -up studies, such as studying whether the Hofstadter butterfly will continue to fly in graphic sandwiches that are subject to much stronger magnetic fields. “I would like to see how and whether the Hofstadter style will be simulated in the upper magnetic fields,” he says.
“There is a very satisfactory thing about our work on this problem 50 years after the Hofstadter account,” says Nokouls. “On the original Hofstadter paper, it mainly concludes that” what I calculated and expected is really great, but no one will never see it because the necessary magnetic fields will never be achieved. “After 25 years, researchers began seeing the first evidence to support his accounts.