Feedback of superconducting fluctuations on charge order in the underdoped cuprates

Metals interacting via short-range antiferromagnetic fluctuations are unstable to sign-changing superconductivity at low temperatures. For the cuprates, this leading instability leads to the well known $d-$wave superconducting state. However, there is also a secondary instability to an incommensurate charge density wave, with a predominantly $d-$wave form factor, arising from the same antiferromagnetic fluctuations. Recent experiments in the pseudogap regime of the hole-doped cuprates have found strong evidence for such a charge density wave order and, in particular, the predicted $d-$wave form factor. However, the observed wavevector of the charge order differs from the leading instability in Hartree-Fock theory, and is that of a subleading instability. In this paper, we examine the feedback of superconducting fluctuations on these different charge-density wave states, and find that over at least a small temperature window, they prefer the experimentally observed wavevector.