Quasi - particle spectra around a single vortex in a d - wave superconductor

Using the Bogoliubov-de Gennes equation, we study the quasi-particle spectra around a single vortex in a d-wave superconductor, where a magnetic field is parallel to the c-axis. In the temperature region where the Ginzburg-Landau theory is valid, we find that the local density of states preserves a circular symmetry when the symmetry of the superconducting order parameter is pure d-wave. It, however, exhibits a four-fold symmetry when the mixing of a s-wave component occurs. A peak with a large energy gap is found in the local density of states at the center of the vortex, which corresponds to the lowest bound state. Our results are consistent with a recent scanning tunneling microscopy experiment in an YBa 2 Cu 3 O 7−δ (YBCO) monocrystal. The breakdown of the Eilenberger theory in YBCO in particular and in the high-T c superconductors in general is discussed.