# Theory puts new spin on IC spin current

HANCOCK, N.H. — A recent theoretical study of the quantum Hall effect (QHE), a type of superconductivity that occurs in semiconductors, suggests a new route to room-temperature quantum computers.

The researchers think they have discovered a spin current that is associated with holes rather than electrons in semiconductors. The predicted current would be able to inject spin momentum into quantum dots and would also interact with conventional electron currents, providing a bridge between electronics and spin-based quantum circuits.

Further, the spin current is completely reversible, minimizing power dissipation, and requires neither liquid-helium temperatures nor a magnetic field, said research partners Shuichi Murakami of the University of Tokyo and Shoucheng Zhang of Stanford University. At this point, the spin current is entirely theoretical, but Murakami and Zhang propose experiments to detect it based on their analysis.

Electron spin is a quantum mechanical variable that can take only two values, although like other such variables it can exist in a superposition of the two states until the spin is measured by an outside observer. Manipulating the spin of electrons in quantum dots has become a major thrust in the attempt to build quantum computers.

The pair's theoretical development, recently reported in the journal Science, was a surprising turn in a longstanding effort to understand the QHE, which was first observed by Klaus von Klitzing at the Grenoble (France) High Magnetic Field Lab in 1980. The QHE is a strange variant of the thoroughly prosaic Hall effect. The Hall effect occurs when a current of electrons is placed in a magnetic field. The electrons will begin to move in circles, while the center of the circles drifts in a direction perpendicular to the magnetic field and the original current. The result is the Hall current which, like any electric current, has a resistance associated with it.

Von Klitzing was studying the Hall current that is created in a two-dimensional electron gas at the interface of a heterojunction. He also began to turn down the temperature and discovered that as absolute zero is approached, the resistance of the Hall current begins to drop in discrete jumps. That quantum Hall effect became even more interesting to scientists when it was discovered that the resistance actually drops to zero, creating a superconducting current.

The problem for physicists was that the superconducting current differed in fundamental ways from the thoroughly studied low-temperature superconductivity. Von Klitzing's work created a sensation because this was the first time a different type of superconductivity had been discovered since the original discovery of low-temperature superconductivity at the beginning of the 20th century. High-temperature superconductivity had not yet made its debut.

More surprises were in store. Horst Stormer at Bell Laboratories and Daniel Tsui at Princeton University continued von Klitzing's work by increasing the magnetic field strength and lowering the temperature. They found that the Hall resistance begins to take on intermediate fractional values. This was a puzzle, since both the spin and the charge of electrons are indivisible constants.

The answer to the puzzle came from a mathematical model of the QHE created by Robert Laughlin, another Bell Labs researcher. Laughlin's model showed that electrons in a two-dimensional layer, at low temperature and in a high magnetic field, condense into a new kind of liquid, in which electrons clump together to create a quasiparticle with fractional charge.

Laughlin's wave function for the quasiparticles has turned out to be highly accurate and has withstood the test of time, providing an explanation of subsequent empirical work with QHE systems. But no one has found a way to generalize the model to three dimensions.

An important breakthrough came in 2001 when Zhang, working with Stanford colleague Jiangping Hu, found that Laughlin's two-dimensional model could be generalized to four dimensions. Thus it appeared that the QHE needed an even number of dimensions to exist.

Researchers had already probed the dimensionality question by showing that at the boundary of a 2-D QHE liquid, which is a one-dimensional realm, a new type of conductivity, called a Luttinger liquid, results from Laughlin's equations. That discovery coincided with the advent of carbon nanotubes and other types of one-dimensional quantum wires, and the mathematics has helped quantum wire researchers understand one-dimensional electron behavior, which is very different from the familiar, three-dimensional variety.

Murakami and Zhang, working with Naoto Nagaosa at the University of Tokyo's Applied Physics Laboratory, applied the same strategy to the four-dimensional model. Since the boundary of a four-dimensional region is three-dimensional, it is possible to look at what happens at the boundary of a four-dimensional QHE liquid to glean clues to novel electronic behavior in semiconductors.

The predictions for the 3-D boundary of a four-dimensional QHE liquid are specific. A particular band structure, found in silicon, germanium and gallium arsenide and some other compound semiconductors, is needed to support the 3-D model. Also, holes are essential to a physical realization of the phenomenon. Holes have generally been ignored in spintronic studies since they have a very short coherence lifetime.

The new theory predicts that in the spin current region, the holes can sustain coherence indefinitely. It is only when they reach a boundary that equilibrium is disturbed.

The predicted effect critically depends on spin-orbit coupling, which is very weak with electrons but turns out to be quite strong for holes. This is a quantum mechanical effect in which the angular momentum of the hole-its spin-is coupled to the momentum generated by its motion.

Spin-orbit coupling could turn out to be a convenient effect for designers of quantum computers. It would allow quantized spin information to be read electronically without disturbing quantum coherence, and it could also allow spin states to be injected into quantum dots.

Of course, all of this depends on whether experimenters can verify the mathematical model by actually finding the predicted spin current. And there maybe further problems along the road to practical applications. Nonetheless, the effect appears to be far more useful than the long-sought three-dimensional QHE.

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