In order to investigate vortices, we usually use a Scanning Tunneling Microscope (STM) and observe local density of states (LDOS) of quasi-particles inside of the vortex core. Nishizaki found the deformation of bound states around a vortex core by STM when a vortex is trapped in a grain boundary. From his observation, bound states are extended along the grain boundary. On the other hand, Tamai and Kato self-consistently solve the Bogoliubov-de Gennes (BdG) equation with a impurity potential and found that bound states do not extended along the impurity potential (Fig. 1)[1]. They conclude that this phenomenon is caused by the Kramer and Pesch effect.

In order to resolve the contradiction between experimental and numerical results, we investigate dependence of quasi-particle bound states around a vortex core on the strength of potential of a grain boundary and other physical parameters.

Fig. 1  A bound state (E/E_c> 0) and a random impurity potential

[1] T. Tamai and M. Kato, Jour. Phys. Conf. Ser., 1590, 012001(2020)

Keywords: Vortex, Bogoliubov-de Gennes equation, Local density of states