Research at Boston University

The Physics of Fractions

by Neil Savage

While many of his colleagues are busy slamming energetic particles into each other at very high speeds, Claudio Chamon, a professor of condensed matter physics, is concentrating on the opposite extreme. Much of his research involves electrons with very low energy, brought to near absolute zero temperature. But the work might one day save a lot of wasted electricity or lead to vastly more powerful computers.

Chamon studies a phenomenon called the fractional quantum Hall effect. Discovered by Edwin Hall in 1879, its predecessor, the Hall effect, occurs when a magnetic field is applied perpendicular to the direction of flow of an electrical current; it pushes the electrons to the side, increasing electrical resistance. It is often used to make sensors, for instance to measure rotating parts in a car engine.

In 1980, scientists discovered the quantum Hall effect: When electrons are cooled to within a few degrees of absolute zero and confined to two dimensions, they can flow across a layer of a semiconductor—like that used in computer chips—as if they were a fluid. When a high magnetic field is applied, the electrical resistance increases in distinct steps, or quanta.

Two years later, other scientists using colder temperatures and stronger magnets discovered the fractional quantum Hall effect. It turned out the conductance changed in steps that were just a fraction of those in the previously discovered effect. When a magnetic field is applied, it might take, say, three units of magnetic flux to match up with each electron. To turn up the magnetic field, you’d expect to have to add three more units of flux to match another electron, because an electron is a fundamental particle; it can’t be broken into smaller pieces. But, surprisingly, if you add just one more unit of flux, the electrical charge around it increases by one third, as if there were just a fraction of an electron present. “It’s as if the fundamental particle has a charge of one third,” Chamon says. “It’s really like the electron fell apart.”

The effect turns out to be a result of the fluid-like nature of the very cold electrons. “When you put many electrons together, they dance in such a way that they leave these ‘quasiholes,’” Chamon says. These quasiholes behave like fundamental particles with a fractional charge. “It really shook the way that people think about many-electron systems.”

Another researcher figured out that getting the original quantum Hall effect didn’t require a magnetic field. Instead, choosing the right topological features—controlling the properties of the semiconductor crystal on a nanoscopic level—would give rise to the same effect. So Chamon and his colleagues set out to find if the same was true of the fractional effect. As it turns out, it was. The researchers found that by creating the right topological features in energy levels and partially filling them with the fluid of electrons, they could get the fractional effect and the fractional particles with no magnetic field.

All this may seem a bit esoteric, and in fact no one has built a physical experiment to demonstrate what Chamon and his colleagues have worked out in theory. But a better understanding of how electrons flow could, in time, lead to practical results. “What we think is that we found a bit of the missing link,” Chamon says. “Maybe it will give us hints of how to approach theoretically other many-electron problems, like high-temperature superconductivity.”

Superconductors carry electrical current with no resistance at low temperatures. But despite two decades of work, researchers have been unable to produce superconductivity at close to room temperature. Superconductors could save a lot of the energy lost when electricity is delivered over power lines, perhaps lowering the demand for power plants that produce greenhouse gases and warm the planet.

Even without superconductors, being able to produce the fractional quantum Hall effect at higher temperatures could prove useful. Perhaps, says Chamon, materials scientists could produce a material that didn’t achieve superconductivity, but still had much lower resistance than copper, again reducing energy loss. Electrical resistance is one of the bottlenecks preventing computer chips, which have to move signals among many transistors, from operating at faster speeds, so a better conductor would be helpful there as well.

Other researchers have proposed using the fractional charges in quantum computing, which would be exponentially more powerful than today’s digital computing. Instead of the ones and zeros generated by turning an electrical current on and off, quantum computers could use fractions of electrons to do more complex calculations.

Chamon thinks it could take many years for his basic research to translate into practical applications, if it ever does, but says the possibility is real. “I think it will take a lot of research,” he says. “I don’t really see a reason why we couldn’t get there, but I can’t predict the timescale.”