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It has long been known that two-dimensional metals with antiferromagneticexchange interactions have a weak-coupling instability to the superconductivityof spin-singlet, d-wave electron pairs. We examine additional possibleinstabilities in the spin-singlet particle-hole channel, and study theirinterplay with superconductivity. We perform an unrestricted Hartree-Fock-BCSanalysis of bond order parameters in a single band model on the square latticewith nearest-neighbor exchange and repulsion, while neglecting on-siteinteractions. The dominant particle-hole instability is found to be anincommensurate, bi-directional, bond density wave with wavevectors along the(1,1) and (1,-1) directions, and an internal d-wave symmetry. The magnitude ofthe ordering wavevector is close to the separation between points on the Fermisurface which intersect the antiferromagnetic Brillouin zone boundary. Thetemperature dependence of the superconducting and bond order parametersdemonstrates their mutual competition. We also obtain the spatial dependence ofthe two orders in a vortex lattice induced by an applied magnetic field:"halos" of the bond order appear around the cores of the vortices.

Mean field theory of competing orders in metals with antiferromagnetic exchange interactions