Enhancement of superconductivity at the onset of charge-density-wave order in a metal

We analyze superconductivity in the cuprates near the onset of an incommensurate charge-density-wave (CDW) order with momentum Q=(Q,0)/(0,Q), as observed in experiments. We first consider a semiphenomenological charge-fermion model in which hot fermions, separated by Q, attract each other by exchanging soft CDW fluctuations. We find that in a quantum-critical region near the CDW transition, Tc=Ag super(-)c, where g super(-)c is charge-fermion coupling and A is the prefactor, which we explicitly compute. We then consider the particular microscopic scenario in which the CDW order parameter emerges as a composite field made of primary spin-density-wave fields. We show that charge-fermion coupling g super(-)c is of the order of spin-fermion coupling g super(-)s. As a consequence, superconducting Tc is substantially enhanced near the onset of CDW order. Finally, we analyze the effect of an external magnetic field H. We show that, as H increases, the optimal Tc decreases and the superconducting dome becomes progressively more confined to the CDW quantum-critical point. These results are consistent with experiments.