Pairing theory of striped superconductivity

Starting from a pairing Hamiltonian with an attractive interaction for electrons on nearest-neighbor sites on a square lattice we present a Hartree-Fock scheme which allows for spin and charge density order simultaneously with d-wave superconductivity. Specifically for filling 7/8 the stable groundstate solution is a striped superconductor with a stripe wavelength of eight lattice constants and $\pi$-shifted order parameters for d-wave pairing and antiferromagnetism. The superconducting state contains Cooper pairs with finite center of mass momenta ${\bf q}$ and $-{\bf q}$ corresponding to half the wavelength for the stripe pattern of the charge density. Despite the d-wave symmetry of the local pairing amplitude the striped superconductor is fully gapped. We characterize the striped superconducting state in real-space and in momentum space and discuss its possible relevance to La$_{1.875}$Ba$_{0.125}$CuO$_4$.