Graphene is the darling of nanotechnologists because it is tough, easy to make and a very good conductor of both heat and electricity. The fact that it is one atom thick also makes it an ideal system for exploring the often bizarre properties of “two-dimensional” electrons.

Perhaps the most curious property of graphene is that it appears to behave like both a metal and a semiconductor. If electrodes are placed at either end of a sheet and a gate voltage is applied across the surface, the electrical conductance along the sheet will be different for different values of the gate voltage -- just like a semiconductor. But unlike a semiconductor the conductance does not go to zero when the gate voltage drops below a certain value -- something that you would expect of a metal. In the past when physicists have tried to measure this minimum conductance, however, they have found that it is a factor of pi (about 3.14) greater than predicted by theory.

While some worried that the theory could be wrong, others began to wonder if the minimum value was also related to the size and shape of the graphene sheet. Now, Chun Ning Lau and colleagues at the University of California at Riverside have showed this to be the case.

The team measured the minimum conductance of 14 different graphene rectangles with widths and lengths in the 300 to 8000 nm range. For samples with lengths smaller than 500 nm, the team discovered that the minimum conductance approached the theoretical value when the width of the rectangle was more than twice its length. However, when the width became any smaller than this, the conductance rose beyond the theoretical value. The team also found that in sheets longer than about 3000 nm, the conductance was always greater than the theoretical value, even when the width was greater than twice the length.

Lau told physicsworld.com that the experiment shows that the theory only applies to very small pieces of graphene, and that the minimum conductance is dependent upon the shape of the sheet.

According to Carlo Beenakker, a theoretical physicist at Leiden University in the Netherlands who studies graphene, Lau’s data agree with theoretical predictions regarding the relationship between conductance and the width and length of the sample. He told physicsworld.com that Lau’s work “closes a chapter on graphene.”