Quasi-particle excitations around a pair of half-quantum vortices in p- wave superconductors

Triplet superconductors such as Sr2RuO4 and NaxCoO2.yH2O are now found to be p-wave (px ± ipy) or f-wave ((px ± ipy) cos cpz) superconductors. It was phenomenologically suggested that in these p-wave or f-wave superconductors, a pair of half-quantum vortices (HQVs) becomes stable. Using the Bogoliubov-de Gennes equation, previously we have analyzed quasi-particle excitations around an HQV at one end of a d-soliton for simplicity. In next study, we will investigate the stability of the pair of HQV's, which are connected by the d-soliton. For this purpose, we have developed a new numerical method to solve the Bogoliubov-de Gennes equation for two vortices state, using Mathieu functions.