Quasi-particle spectrum around a single vortex in gossamer superconductivity

We have established recently the high-Tc cuprate superconductors in the underdoped region is characterized as gossamer superconductivity (i.e. d-wave superconductivity in the presence of d-spin density wave (dSDW)). Here we first derive the Bogoliubov-de Gennes equation for gossamer superconductivity. Then we study the bound state spectrum around a vortex in the gossamer superconductivity. We find that the presence of the dSDW order parameter eliminate many low energy bound states, which is very consistent with Scanning Tunneling Spectroscopy (STS) data by Pan et al. Also the present model reproduces the checkerboard structure at the core of the vortex as seen by Hoffman et al., though for the precise description of this structure, it is necessary to choose the correct Q-vectors.