Nanofabrication techniques allow researchers to confine electrons in semiconductors to "mesoscopic" structures such as a 2-dimensional "quantum well", a 1D "quantum wire", or a 0D "quantum dot", which we like to call an "artificial atom". The mesoscopic scale is ten nanometers to ten microns at low temperatures: the length scale on which quantum mechanics holds sway, yet tens to thousands of mobile electrons are involved. The host semiconductor can be so clean and electronically simple that we are not limited by the foibles of a particular material, but instead measure the intrinsic properties of a few confined electrons. Beyond five or ten electrons, however, brute-force predictions of behavior are infeasible. The remarkable consequence: basic questions remain even for the simplest structures, and surprises keep popping up.
The Goldhaber-Gordon group studies simple, archetypical structures such as a quantum point contact -- a narrow constriction between two electron reservoirs, which can be thought of as a short 1-dimensional wire. To learn more about how electrons organize themselves in these well-studied (but still poorly-understood) structures, we either develop new measurement techniques or work with new materials in which electrons interact more strongly.
We also build designer Hamiltonians out of these simple building blocks. For example, we are working to build a two-channel Kondo system out of coupled quantum dots. Previous physical realizations of this intriguing theoretical model have been controversial because they have depended on poorly-characterized parameters of complex materials. By comparison, we can measure and electrically tune all the important parameters of our quantum dot building blocks.