50 Years of Physical Review B: Solid Hits in Condensed Matter Research

50 Years of Physical Review B: Solid Hits in Condensed Matter Research

R. Laughlin, Phys. Rev. B (1981)

Using one simple figure, Robert Laughlin provided an explanation for the quantum Hall effect, which was reported one year before.

Take a strip of metal, run an electrical current through it, and then pierce the strip with a magnetic field. The moving charges will veer off to the sides, producing a so-called Hall voltage that should go up continuously as the field is made stronger or the current higher.

However, a repeat of this basic experiment when the temperature was very low, the strip very flat, and the field very strong revealed an astounding effect. Instead of changing continuously, the voltage only budged in quantized steps, plateauing at an extremely precise value in between. Those steps, reported in 1980, showed that the Hall conductivity (the ratio of the current to the Hall voltage) could only assume integer multiples of

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What’s striking about the Hall conductivity is that it’s insensitive to impurities. That feature suggested the quantum Hall effect (QHE) was due to a “fundamental principle,” wrote Robert Laughlin, then at Bell Labs, in an elegant 1981 paper—one of the first to explain the QHE. The principle turned out to be the gauge invariance of localized and extended electronic states. Laughlin’s insight provided the groundwork for his explanation of another exceptional result, the 1982 observation of the fractional quantum Hall effect. (For this theoretical work, Laughlin was awarded the 1998 Nobel prize.)

The quantum Hall system came to be known as the first example of a topological material, which has properties that remain constant despite some continuously changing parameter, like an external field. Physicists have since uncovered numerous other forms of such materials, such as topological insulators, which might be useful for hosting robust qubits for quantum computing. Since 2005, Physical Review B alone has published more than 5000 papers that mention topological insulators. The vast interest in the topic today was “unpredictable,” says Laughlin, now at Stanford University. Realizing the possibility of topological insulators, he adds, “took a confluence of unlikely events and actions made by other people.”

One scientist who jumped in was Taylor Hughes, of the University of Illinois, Urbana-Champaign. “When I first started working in this field in 2005, we were really concerned that topological insulators were just a theorist’s playground,” he says. “However, in the last 15 years, so many new topological materials have been predicted and discovered that it is almost easier these days to list things that aren’t topological!” (See more on this topic in this 2015 Q&A with Hughes, Topologically Speaking.)

R. B. Laughlin, “Quantized Hall conductivity in two dimensions,” Phys. Rev. B 23, 5632(R) (1981).

–Jessica Thomas is the Editor of Physics.

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