Fermions, criticality and superconductivity

Abstract

By tuning control parameters like pressure, magnetic field or doping, a fermionic system can be driven to a state with vanishing Fermi energy and power law behavior in many observables. Such fermionic quantum critical states have been identified in systems including heavy fermions, cuprates and pnictides. We study the superconducting transition in such systems. We propose that the superconducting instability, which is marginal in Fermi liquids, becomes relevant, leading naturally to a high transition temperature. This picture has been verified numerically in the 2-dimensional Hubbard model by using the Dynamical Cluster Approximation. We also propose tunneling experiments which can distinguish our mechanism from others.