The Physics of Correlated Insulators, Metals, and Superconductors

A naive distinction between metals and insulators rests on the single-electron picture: completely
filled or empty bands characterize insulators while metals have some partially filled
bands. Nature, however, offers a much richer variety of behaviors: Mott insulators would
be band metals in the absence of electron correlation while strongly-correlated metals behave
quasiparticle-like only in the Fermi-liquid regime. Correlated metals and insulators can be distinguished
by the gap in the spectral function. Superconductors form a class of their own, they
have a single-electron gap but are not insulators.
This year’s school addresses the rich physics of correlated insulators, metals, and superconductors.
Insulators show complex ordering phenomena involving charge, spin, and orbital
degrees of freedom. Correlated metals exhibit non-Fermi-liquid behavior except right at the
Fermi surface. Superconductors are dominated by the delicate interplay of coupling bosons and
quasiparticles. Along with the phenomena, the models and methods for understanding and classifying
them will be explained. The aim of the school is to introduce advanced graduate students
and up to the modern approaches for modeling strongly correlated materials and analyzing their
behavior.