1210.2408 (Yuxuan Wang et al.)

Superconductivity at the onset of spin-density-wave order in a metal    [PDF]

Yuxuan Wang, Andrey V. Chubukov

We revisit the issue of superconductivity at the quantum-critical point between a 2D paramagnet and a spin-density-wave (SDW) metal with ordering momentum (\pi,\pi). This problem is highly non-trivial because the system at criticality displays a non-Fermi liquid behavior and because the effective coupling constant \lambda for the pairing is generally of order one, even when the actual interaction is smaller than fermionic bandwidth. Previous study [M. A. Metlitski, S. Sachdev, Phys.Rev.B 82, 075128 (2010)] has found that the leading renormalization of the pairing vertex contains \log^2, like in color superconductivity. We analyze the full gap equation and argue that summing up \log^2 term does not lead to a pairing instability. Yet, superconductivity has no threshold, even if \lambda is set to be small: the subleading \log terms give rise to BCS-like T_c \propto e^{-1/\lambda}. We argue that the analogy with BCS is not accidental as superconductivity at a QCP is a Fermi liquid phenomenon -- it comes from fermions which retain Fermi liquid behavior at criticality. We computed T_c for the actual \lambda and found a good agreement with the numerical results.

View original: http://arxiv.org/abs/1210.2408