Charge ordering in metals with antiferromagnetic spin correlations

Metals with antiferromagnetic spin correlations have an instability to the superconductivity of spin-singlet Cooper pairs with d symmetry (for the Fermi surface of the cuprates). Metlitski et al. (<a href="/abs/1005.1288">arXiv:1005.1288</a>) noted that in two dimensions, in the low energy continuum theory, this superconductivity is degenerate with a charge density wave ordering which has a local d symmetry under rotations about the lattice points. We present a momentum-space Hartree-Fock computation on a simple lattice model, and find that the d symmetry is dominant for a range of small ordering wavevectors including those observed in recent experiments. We propose a charge order parameter for the underdoped cuprates.