Kotliar

Rather than haphazardly looking for and discovering materials and exploiting their properties, materials science's aim is to understand materials so that new materials with desired properties can be created. The development of   quantum mechanics ideas and density functional theory based computational methods,  has been extremely successful in this regard.  In the twentieth century, a “standard model” of solids has been established, and it provides qualitative and quantitative guidance in the field of material research. Correlated electron systems are outliers whose behavior do not fit within the standard model. They display remarkable phenomena ranging from metal to insulator transitions and  high temperature superconductivity to anomalous thermoelectricity and volume collapses. They continue to surprise us with their exceptional physical properties and the perspectives for new potential applications.

The discovery of interesting strongly correlated compounds so far has   been  the result of serendipity and the application of the Edisonian approach,  the most recent example provided by iron arsenide superconductors. From a theoretical perspective correlated electron systems are close to a localization-delocalization boundary. In this regime neither band theory (itinerant picture) nor atomic physics (localized picture) describes the physical properties of the materials  posing one of the most difficult non-perturbative problems in physics.

In the past two decades we achieved  significant progress in the description of the electronic structure of correlated materials through the development
of the dynamical mean field theory (DMFT) approach. In this lecture we  will give an elementary introduction to  the field  of strongly correlated electron systems and  to the ideas of  Dynamical Mean Field Theory (DMFT).    We will illustrate the methodology with some examples drawn from f and d electron systems.  We will conclude with an outlook of  the challenges ahead and the prospective for theory assisted  material design.