Electronic Liquid Crystal Phases in Strongly Correlated Systems

Abstract: In this lectures I discuss the electronic liquid crystal (ELC) phases in correlated electronic systems, what these phases are and in what context they arise. I will go over the strongest experimental evidence for these phases in a variety of systems: the two-dimensional electron gas in magnetic fields, the bilayer material Sr$_3$Ru$_2$O$_7$ (also in magnetic fields), and a set of phenomena in the cuprate superconductors (and more recently in the pnictide materials) that can be most simply understood in terms of ELC phases. Finally we will go over the theory of these phases, focusing on effective field theory descriptions and some of the known mechanisms that may give rise to these phases in specific models.