Quantum critical superconductivity

Superconductivity (SC) is a remarkable realization of a macroscopic quantum state in the real world. Electrons are paired to coherently carry the current without resistance, and the quantum state is protected by formation of the superconducting gap. In conventional superconductors, the SC pairs are mediated by collective ionic motion or phonons and the SC order parameter (or the orbital wave-function of the pairs) is momentum independent (s-wave). Recently, new classes of unconventional superconductors have been discovered, where the SC order parameter is momentum dependent. This is highly suggestive of a completely different pairing mechanism, i.e., a non-phonon glue. The most well-known examples are high-Tc cuprates, organic superconductors, and heavy fermion superconductors, which are shown to have a d-wave pairing symmetry. Proximity of the unconventional superconductors to an antiferromagnetic ground state prompted a scenario that collective spin motion (spin waves), mediate the electron pairs and that the d-wave order parameter is a natural consequence of momentum dependent pairing interaction created by the spin waves. In this talk, we discuss recent progress in our understanding of unconventional superconductivity.