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

Triplet superconductors such as Sr₂RuO₄ and Na_xCoO₂⋅yH₂O are now found to be p-wave (p_x ± ip_y) or f-wave ((p_x ± ip_y) cos cp_z) 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.