Strange things happen to electrons when they are confined to a thin layer of semiconductor, cooled to near absolute zero and subjected to a high magnetic field. Instead of behaving as independent particles, they act collectively to form entities called quasiparticles, which have counterintuitive properties such as fractional charges. The physics of this quantum-electronic flatland is known as the fractional quantum Hall effect and has been an extremely fertile area for experimenters and theorists alike. But nothing quite like this system has ever existed--even as a theory--in more than two dimensions. Now two physicists have generalized the two-dimensional theory to four dimensions, and to cap it off they have made a controversial conjecture that the result could have relevance for fundamental particle physics and quantum theories of gravity.
Shou-Cheng Zhang of Stanford University and his student Jiangping Hu worked out a four-dimensional version of a quantum Hall system that would exist on the surface of a sphere in five dimensions. The key idea for the new theory came to Zhang one hot summer day in 2000 while he was lecturing at Tsinghua University in China, with which he and Hu are also affiliated. The higher-dimensional sphere was already familiar to Zhang and his students; in 1996 he developed a theory of high-temperature superconductivity based on its symmetries. According to Robert B. Laughlin, also at Stanford and recipient of the 1998 Nobel Prize in Physics for devising the original theory of the two-dimensional fractional quantum Hall effect, "the discovery of the four-dimensional quantum Hall state is rather beautiful and a real breakthrough. I tried for years to do something similar with little success."
This article was originally published with the title Fractional Success.