Quasiparticle Spectra around a Single Vortex in ad-Wave Superconductor

Using the Bogoliubov—de Gennes equation, we study the quasiparticle spectra around a single vortex in a $d$-wave superconductor. 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 fourfold symmetry when the mixing of an $s$-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 a ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ monocrystal.