Electrons in flat wonderland

Novel phases of matter can emerge when electrons are confined to two-dimensions, and have a significantly reduced kinetic energy relative to their interaction energy. The remarkable discovery of numerous interacting phases of matter, including superconductivity, in highly tunable devices made out of graphene and other semiconducting materials in recent years are challenging many of our established theoretical paradigms. I will begin by highlighting the conceptual difficulties with describing superconductivity in the limit where the electronic kinetic energy is quenched, where the standard theory due to Bardeen-Cooper-Schrieffer no longer applies. I will address the “universal” ingredients that set the superconducting transition temperature, in this non-perturbative limit. I will also revisit an old experimental puzzle in condensed matter physics, namely how a metal--an electrical conductor--transitions continuously into an electrical insulator with increasing strength of electronic interactions, inspired by experiments at Cornell.