Alexander V. Balatsky
Recently a new single-layer material—graphene—has been discovered. This is a material where particle behavior is described by the very same Dirac equation that governs the behavior of relativistic particles. The Dirac fermionic spectrum leads to very unusual properties of these materials, including electron transport and impurity states. I will argue that these properties are not unique to graphene but are universal consequences of the Dirac spectrum in the fermionic excitation sector. Other materials displaying similar spectra include d-wave superconductors, superfluid 3He, p-wave superconductors, and topological insulators, and a comparison of all these materials offers a unifying perspective. Among the similarities are response to defects, suppressed backscattering, and unusual transport properties. An advantage of having relativistic Dirac particles in condensed matter is that we can perform quantum imaging of these Dirac materials. I will show examples of quantum images of Dirac particles at extreme spatial resolution. I will discuss some observable effects, such as Kondo effect and impurity resonances, that differentiate Dirac materials from other classes.