Quantum Cafe: Steve Kivelson

Title: Superconductivity in the Hubbard Model

Abstract: Since the discovery of high temperature superconductivity in the cuprates, much of the discussion concerning the mechanism of unconventional superconductivity in these (and other) materials has involved stories about the behavior of the Hubbard model. Real materials are complicated, with observable behaviors that are sensitive to all sorts of microscopic details, leading to debates over what is essential and what is a herring of one color or another. However, as a theoretical minimum, conditions for the existence of superconductivity in the Hubbard model can be addressed seriously, using tools that are controlled and unambiguous in appropriate limits. While it is easy to show that the ground-state is generically superconducting for small U, at intermediate U (which is a necessary condition for “high temperature superconductivity”) the answer is much more complicated as superconductivity competes and more generally “intertwines” with various forms of density-wave order. Still there are some interesting corners of the phase diagram where superconductivity occurs – even at intermediate coupling.