Effects of gap anisotropy upon the electronic structure around a superconducting vortex

An isolated single vortex is considered within the framework of the quasiclassical theory. The local density of states around a vortex is calculated in a clean type-II superconductor with an anisotropy. The anisotropy of a superconducting energy gap is crucial for bound states around a vortex. A characteristic structure of the local density of states, observed in the layered hexagonal superconductor $2H$-NbSe${}_2$ by scanning tunneling microscopy (STM), is well reproduced if one assumes an anisotropic $s$-wave gap in the hexagonal plane. The local density of states (or the bound states) around the vortex is interpreted in terms of quasiparticle trajectories to facilitate an understanding of the rich electronic structure observed in STM experiments. It is pointed out that further fine structures and extra peaks in the local density of states should be observed by STM.