Our understanding of simple solids, is firmly grounded on the Fermi
liquid concept and powerful computational techniques built around the
density functional theory. These ideas form the basis of our “standard
model” of solid state physics and have provided us with an accurate
description of many materials of great technological significance.
Correlated electron systems are materials for which the the standard
model of solid state physics fails dramatically. The best known example
being the copper oxide high temperature superconductors. Correlated
electron materials continue to be discovered accidentally and surprise us
with their exceptional physical properties and their potential for new
applications. The most recent example is provided by the iron arsenide
based high temperature superconductors.
From a theoretical perspective describing strongly correlated electron
systems pose one of the most difficult non-perturbative challenges in
physics. In this colloquium I will give an elementary introduction to the
field of strongly correlated electron materials and Dynamical Mean Field
Theory (DMFT) a non perturbative method which provides a zeroth order
picture of the strong correlation phenomena in close analogy with the
Weiss mean field theory in statistical mechanics. Applications materials
containing f and d electrons will be presented to show how the
anomalous properties of correlated materials emerge from their atomic
constituents.
I will conclude with an outlook of the challenges ahead and the
perspectives for a rational material design.