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 (opens a new tab), 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 (opens a new tab) that mark the most significant advances (opens a new tab) on the problem since the 1980s.
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