Topics in Modern Condensed Matter Theory II: Open Problems in the theory of metals & superconductor

We will begin by reviewing a modern perspective on the theory of conventional (BCS s-wave) and unconventional (e.g. d-wave) superconductors. We will then discuss a variety of issues that are of current interest, but which are either incompletely understood or entirely open problems in the field. Depending upon the interests of the class and the whims of the instructor, topics to be covered may include: quantum superconductor to insulator and superconductor to metal transitions, emergence of superconductivity from a non-Fermi liquid normal state, exotic superconducting phases of matter, interplay between superconductivity and other broken symmetry states (issues of ¿intertwined orders¿), and superconductivity in paradigmatic models of highly correlated electron systems, including problems in which there is an interplay between strong electron-electron and electron-phonon interactions. We will also touch on theoretical ideas - all of them currently still being explored and hence controversial - concerning theories of unconventional metallic states - i.e. metallic states that cannot be well described in the context of a theory of weakly interacting quasiparticles. While the subject matter of this course is motivated by ongoing experimental studies in a variety of quantum materials and devices, the principle focus of the class will be on a coherent understanding of what is known and on crisply identifying what is not known.