Aug 16, 2025 07:58 PM
https://www.quantamagazine.org/new-physi...r-20250815
INTRO: The mystery was this: In the 1950s, a physicist at Bell Labs named George Feher was injecting silicon with tiny quantities of other elements, such as phosphorus or arsenic. When he put a little in, the electrons would move freely through the resulting material. But as he added more, the material’s internal structure became more random, impeding the electrons’ motion. Rather than happening gradually, as one might expect, this obstruction occurred suddenly when the concentration passed a particular point, trapping the electrons. Then their movement stopped entirely.
“It was conducting, conducting, conducting, and it no longer conducts,” said Yan Fyodorov(opens a new tab), a physicist at King’s College London. What was intriguing was that the sharp change in behavior was reminiscent of phase transitions like the sudden freezing of water at zero degrees Celsius. “Physicists love transitions,” said Fyodorov.
Soon, Philip W. Anderson — another Bell Labs physicist — developed a model to describe the puzzling behavior. He hoped to rigorously prove that his model behaved just as Feher’s experiments had. That is, he wanted to show that once a material’s structure was random enough, its electrons would shift from being free-moving, or “delocalized,” to being completely stuck, or “localized.”
Anderson would later win a Nobel Prize, in part for this work, and as he recounted in his Nobel lecture, his efforts to find this proof made him “a nuisance to everyone.” But a rigorous proof would ultimately elude him.
It has also eluded other researchers for decades, but this past year, researchers have posted a string of results that mark the most significant advances on the problem since the 1980s.
Their techniques aren’t just promising for analyzing models of electron behavior like Anderson’s. The work also taps into a longtime quest to understand systems that aren’t entirely random or entirely ordered.
“I’m actually very excited,” said Horng-Tzer Yau(opens a new tab) of Harvard University, who has been working on the problem for most of his career. When it comes to these challenging kinds of models, “I feel this is the first time we have a method that will have a huge impact.” (MORE - details)
INTRO: The mystery was this: In the 1950s, a physicist at Bell Labs named George Feher was injecting silicon with tiny quantities of other elements, such as phosphorus or arsenic. When he put a little in, the electrons would move freely through the resulting material. But as he added more, the material’s internal structure became more random, impeding the electrons’ motion. Rather than happening gradually, as one might expect, this obstruction occurred suddenly when the concentration passed a particular point, trapping the electrons. Then their movement stopped entirely.
“It was conducting, conducting, conducting, and it no longer conducts,” said Yan Fyodorov(opens a new tab), a physicist at King’s College London. What was intriguing was that the sharp change in behavior was reminiscent of phase transitions like the sudden freezing of water at zero degrees Celsius. “Physicists love transitions,” said Fyodorov.
Soon, Philip W. Anderson — another Bell Labs physicist — developed a model to describe the puzzling behavior. He hoped to rigorously prove that his model behaved just as Feher’s experiments had. That is, he wanted to show that once a material’s structure was random enough, its electrons would shift from being free-moving, or “delocalized,” to being completely stuck, or “localized.”
Anderson would later win a Nobel Prize, in part for this work, and as he recounted in his Nobel lecture, his efforts to find this proof made him “a nuisance to everyone.” But a rigorous proof would ultimately elude him.
It has also eluded other researchers for decades, but this past year, researchers have posted a string of results that mark the most significant advances on the problem since the 1980s.
Their techniques aren’t just promising for analyzing models of electron behavior like Anderson’s. The work also taps into a longtime quest to understand systems that aren’t entirely random or entirely ordered.
“I’m actually very excited,” said Horng-Tzer Yau(opens a new tab) of Harvard University, who has been working on the problem for most of his career. When it comes to these challenging kinds of models, “I feel this is the first time we have a method that will have a huge impact.” (MORE - details)