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Superconductivity and bond order at the onset of spin-density-wave order in a metal
Andrey Chubukov  1@  
1 : University of Wisconsin-Madison  (UW-Madison)
1150 University ave, Madison, WI 53706 -  United States

We revisit the issues of superconductivity and charge bond order at the quantum-critical point (QCP) between a 2D paramagnet and a spin-density-wave 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 for the pairing is generally of order one, even when the actual interaction is smaller than fermionic bandwidth. Previous studies have found that the renormalizations of the pairing vertex are stronger than in BCS theory and hold in powers of \log^2 (1/T), like in color superconductivity. We analyze the full gap equation and argue that, for QCP problem, summing up of the leading logarithms does not lead to a pairing instability. Yet, we show that superconductivity has no threshold and appears because subleading logarithmical renormalizations diverge and give rise to BCS-like equation for Tc. We argue that the analogy with BCS is not accidental as superconductivity at a QCP at least partly comes from fermions which retain Fermi liquid behavior at criticality. We also study the interplay between superconductivity and charge bond-density-wave order. We show that the pairing temperature in bond density channel is only slightly lower that superconducting Tc, discuss the type of potential bond order, and comment on the scenatio of a pseudogap due to competition between superconductivity and bond order.


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