Superconducting and charge-density-wave orders in the spin-fermion model: A comparative analysis

We present a comparative analysis of superconducting and charge-density-wave orders in the spin-fluctuation scenario for the cuprates. That spin-fluctuation exchange gives rise to d-wave superconductivity is well known. Several groups recently argued that the same spin-mediated interaction may also account for charge-density-wave order with momenta (Q,0) or (0,Q), detected in underdoped cuprates. This has been questioned on the basis that charge-density-wave channel mixes fermions from both nested and antinested regions on the Fermi surface, and fermions in the antinested region do not have a natural tendency to form a bound state, even if the interaction is attractive. We show that antinesting is not an obstacle for charge order, but to see this one needs to go beyond the conventional Eliashberg approximation. We show that in the perfect nesting/antinesting case, when the velocities of hot fermions are either parallel or antiparallel, the onset temperatures in superconducting and charge-density-wave channels are of comparable strength for any magnetic correlation length ξ. The superconducting Tsc is larger than Tcdw, but only numerically. When the velocities of hot fermions are not strictly parallel/antiparallel, Tcdw progressively decreases as ξ decreases and vanishes at some critical ξ.