Quasi-particle structures around a pair of half-quantum vortices in chiral p-wave super conductors

Abstract

Quasi-particle structures around a pair of half-quantum vortices (HQVs) and two singly quantized vortices are investigated, using the Bogoliubov-de Gennes equation. For this purpose, a new numerical method, which incorporates the two phase singularity points, is developed, using elliptic coordinates and the (modified) Mathieu functions. We investigate the local density of states around two singly quantized vortices and a pair of HQVs in chiral p-wave superconductors. As a result, we found that there is a difference between them: Quasiparticle bound states interfere with each other for two singly quantized vortices case and do not for a pair of HQVs case.