Correlations and phase transitions in Dirac systems

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The electrically insulating or conducting behavior of many solid materials, such as cooper or aluminum, may be well understood by a quantum mechanical model which almost entirely neglects the repulsive interaction between the constituent electrons. However, there are also many known materials where such a simple picture fails, and the inclusion of interactions between electrons becomes paramount. This is particularly true in the so-called Dirac materials, which have their electronic structure similar to graphene; a truly two-dimensional single layer of carbon which holds a promise to revolutionize today's electronics. These Dirac solids have their number of electrons that can react to external probes reduced, which diminishes the usual "screening" of the electron-electron repulsion, and makes them more vulnerable to its feedback effects on the electrons themselves. These features are not necessarily detrimental to their conducting, magnetic, and other properties, but they do necessitate a new theoretical approach to this type of materials.