Quantum Electronic Matter in Two Dimensions

Abstract

Most often, the electrical properties of a material are described as either "conducting" or "insulating". Copper, everyone knows, is a good conductor. It is the foundation of the electrical infrastructure of the nation. Glass, on the other hand, is an excellent insulator. But do these two words describe all the possibilities? The answer is emphatically no, and the basic subject of the research funded by this grant is aimed at fleshing out a more complete description of the electrical properties of materials. Many people are aware that there are also special materials called superconductors. A superconductor (e.g. aluminum when cooled to very low temperatures) is like a regular conductor except that it conducts electricity with no energy loss at all. Ordinary metals get hot when current flows through them; witness the toaster in your kitchen. In a superconductor something very special is going on: The electrons in the metal don't behave individually as they do in an ordinary conductor. Instead they act collectively. It is this collective aspect that makes superconductors so interesting to physicists. So now we have metals, insulators and superconductors. Is there anything else? We now know the answer is yes. In this research we examine special conducting materials, ones in which the mobile electrons are confined to move on a plane surface (as opposed to motion in all three directions). Examples of such "2D" materials include electrons confined to the interface between two otherwise insulating materials (as in the so-called "semiconductor heterostructures" used here) and the single atomic layer of carbon atoms now known as "graphene". Materials like these are not just museum curiosities; each of the billions of transistors in every smart-phone has a 2D electron system in it. In the work supported by this grant, the focus is on both collective conducting states in semiconductor heterostructures and on the conducting properties of graphene and its few-layer cousins. In particular, the exotic collective (and deeply quantum mechanical) electronic phases which develop when a large magnetic field is applied have been a major focus of effort. Significant results have been obtained from both ordinary electrical measurements and from more sophisticated thermoelectric studies of such systems. Related studies of few-layer graphenes have elucidated the transition from the two- to three-dimensional electrical properties of carbon-based conductors. Investigations like these expand our understanding of electronic materials general. While there are certainly immediate fundamental scientific pay-offs, it is also true that research of this kind ultimately leads to technological breakthroughs in the long term. By way of example, superconductivity was undoubtedly regarded as a useless novelty when it was discovered in 1911. Who could have known then that it would become crucial to the medical revolution brought about by magnetic resonance imaging decades later?