Local density of states of high-Tc superconductors with long-range Coulomb interaction

The local density of state (LDOS) has been studied by solving the mean-field Bogoliubov-de Gennes equations based on a model Hamiltonian with competing antiferromagnetic (AF) and d-wave superconducting orderings in the presence of a long-range Coulomb interaction. The vortex-core state with energies slightly above and below the Fermi level shows a four-fold symmetry with two-dimensional modulations under small on-site repulsion strength U, whereas it has a stripe structure for large U. The four-fold symmetry modulation with a periodicity of 4a0 is recovered as a long-range Coulomb interaction has been included. Recent scanning-tunneling-microscopy experiments may be understood in terms of the present results.