The Classical Phenomenon of Quantum Critical Superconductivity

One of the longest standing puzzles in condensed matter physics is so called “unconventional superconductivity”, which is a catchphrase for superconductivity that is not described by the (by now) well-established theory of Bardeen, Cooper and Schrieffer (BCS) of the binding of electrons into Cooper pairs with long-ranged coherence. One universal feature of many unconventional superconductors is that they appear in proximity to quantum phase transitions. I will describe an ongoing theoretical effort to explain how quantum critical fluctuations give rise to superconductivity. In my talk, I will point out how this framework emerges from fundamental ideas associated with BCS theory. In particular, I will try to stress the idea that quantum processes often give rise to emergent semiclassical behavior, and that this can serve as an organizing principle on which to build quantitative theories of unconventional superconductivity.