Calculation Provides Insight Into Quantum Superconductivity Of Bizzare Particles

The composite fermion is a complex creature from the strange world of quantum physics. It can be thought of as a single electron surrounded by a number of tornado-like objects known as quantum-mechanical vortices, which themselves are formed by a swirling swarm of electrons. "The quantum-mechanical vortex has no analog in our familiar every-day world," Jain explains, but he says a simplistic way to imagine it is as a whirlpool in water or a tornado in air. "Just as a whirlpool that forms in a sea of water has no water in its center, a vortex that forms in a quantum-mechanical sea of electrons has no electrons at it center," Jain explains. When a single electron enters this empty space, the result is a composite particle called a composite fermion. "This composite particle behaves as a unit, just as, on the atomic scale, the union of two hydrogen atoms with one oxygen atom behaves as a single molecule of water," Jain explains.

To form composite fermions physicists must first confine electrons to two dimensions in "quantum wells," which can occur at the interface of two semiconductors. They then must cool the trapped electrons to extreme temperatures close to absolute zero and finally subject them to an incredibly strong magnetic field.

Physicists were skeptical when Jain first predicted the existence of the composite fermion in 1989, aiming to understand the well-known phenomenon known as "fractional quantum Hall effect," a 1982 discovery that later won the Nobel Prize in physics, but experiments eventually confirmed its presence and showed that its properties are surprisingly similar to those of simple electrons. "Composite-fermion systems exhibit absolutely marvelous properties, which are entirely unexpected and inexplicable when you think of them simply as a collection of weakly interacting electrons, but can be understood and modeled when you think of them as systems of composite particles," Jain says.

Using this approach in their paper to be published in the journal Nature, Jain and his colleagues now have calculated that a property known as a "Cooper instability," which produces superconductivity in electrons, can exist in composite fermions. This research suggests that composite fermions are capable of achieving quantum superconductivity.

This calculation was motivated by the enigmatic experimental discovery in 1987, before composite fermions were known, of a resistence-free state by R.L. Willett and colleagues at Lucent Technologies. Early theoretical work by M. Greiter, X.G. Wen, and F. Wilczek at the Institute for Advanced Study, and G. Moore and N. Read at Yale University suggested a pairing of composite fermions in this context, but further developments in theory proved necessary for a confirmation of this idea.

"There are two kinds of particles in nature: bosons and fermions," Jain says. "The bosons go into a superfluid state by each occupying the same quantum state, as in Bose-Einstein condensation in ultracold magnetically trapped atoms. The fermions, on the other hand, are not allowed to occupy the same state. They form a Fermi sea instead. However, they can superconduct by binding into pairs, called Cooper pairs, because a pair of fermions is a boson. The formation of these Cooper pairs causes an instability of the Fermi sea that catalyzes the material's transformation into a superconducting state."

Electrons in a high magnetic field form discrete energy levels, called "Landau levels," which require them to make a quantum leap from one energy level to another. The superconductivity, on the other hand, arises out of a Fermi sea with a continuous range of energy levels. Even though a high magnetic field is necessary for producing composite fermions, at certain values of the field the "composite fermions absorb all the incoming flux of the huge matnetic field so, in effect, they behave as if they do not experience the external magnetic field at all," Jain says. "That is why they form a Fermi sea, which is something particals normally can do only when they are free from any strong magnetic field." The Fermi sea of composite fermions was predicted theoretically by two groups‹B.I. Halperin at Harvard University, P.A. Lee at the Massachusetts Institute of Technology, and N. Read at Yale University, and by U.L. Kalmeyer and S.C. Zhang at Stanford University.

In addition to the Fermi sea, pairing also requires an attractive interaction between electrons. "Even though there normally is a strong repulsion between electrons, the effect of the quantum vortices in composite fermions is to make them slightly attractive to each other and to give them the ability to join together in pairs," Jain says. The new calculation provides convincing evidence that composite fermions do indeed form these magically mobile Cooper pairs, which could result in quantum superconductivity.

"Exactly why composite fermions form in the first place remains a mystery, Jain says. "We don't yet have a full understanding of why electrons would want to sit at the center of quantum vortices."

Jain says he does not expect to see superconducting electronic devices such as quantum computers made with composite fermions in the near future because of the extreme temperatures and magnetic conditions needed for their existence. But he says, "it is irresistible to imagine what uses could be found for composite fermions in the future."

This research was supported by the National Science Foundation.