Nanotubes Unfolded

Two-dimensional carbon, or graphene, has many of the interesting properties possessed by one-dimensional carbon (in the form of nanotubes): electrons can move at high speed and suffer little energy loss. According to Walt deHeer (Georgia Tech), who spoke at this week's meeting of the American Physical Society (APS) in Baltimore, graphene will provide a more controllable platform for integrated electronics than is possible with nanotubes, since graphene structures can be fabricated lithographically as large wafers.

Single sheets of graphene were only isolated in 2004 by Andre Geim (University of Manchester). In graphene, electron velocity is independent of energy. That is, electrons move as if they were light waves; they act as if they were massless particles. This extraordinary property was elucidated in November 2005 through experiments (see background article in the Jan. 2006 Physics Today) using the quantum Hall effect (QHE), in which electrons, confined to a plane and subjected to high magnetic fields, execute only prescribed quantum trajectories. These tests were conducted by groups represented at the APS meeting by Geim and Philip Kim (Columbia University).

The QHE studies also revealed that when an electron completes a full circular trajectory in the imposed magnetic field, its wavefunction (encapsulating the electron's quantum wave nature) is shifted by 180 degrees. This modification, called "Berry's phase," acts to reduce the propensity for electrons to scatter in the backwards direction; this in turn helps reduce electron energy loss.

Geim reported a new twist to this story. Studying QHE in graphene bilayers he observed a new version of QHE, featuring a doubled Berry's phase of 360 degrees. Also, Geim drew a comparison to certain cosmologies in which multiple universes can co-exist, each with its own set of physical constants; in graphene, he said, where electrons move in a light-like way, with a fast speed -- but one somewhat less than the speed of light in vacuum -- the parameter which sets the scale of the electromagnetic force, namely, the fine structure constant (defined as e²/hc), has a value of roughly 2.0 rather than the customary 1/137.

The goal now is to learn more graphene physics and then worry about applications. For example, Walt deHeer reported that a plot of resistance versus applied magnetic field had a fractal shape. DeHeer said that has so far has no explanation for this. As for applications, he said that on an all-graphene chip, linking components with the usual metallic interconnects, which tends to disrupt quantum relations, would not be necessary. Thus the wave nature of electrons could be more fully exploited for quantum-information purposes.

De Heer's group so far has been attempting to build circuitry in this way; they have made graphene structures (including a graphene transistor) as small as 80 nanometers (80 billionths of a meter) and expect to get down to the 10-nanometer size.