Quasi-particle excitations around a half-quantum vortex in p- and f- wave superconductors

Triplet superconductors such as Sr₂RuO₄ and Na_xCoO₂·yH₂O are now found to be p-wave (k_x ± ik_y) or f-wave ((k_x ± ik_y)cos ck_z) superconductors. Kee phenomenologically suggested that in these p-wave or f-wave superconductors, two half-quantum vortices (HQVs) become stable. Using Bougoliubov–de Gennes equation with the Fourier-Bessel expansion, we analyze quasi-particle excitations around an HQV at one end of the d-soliton for both p-wave and f-wave superconductors. We find that the bound state peak in the total local density of states around the HQV in f-wave superconductors becomes rather low compared to that around a singly quantized vortex. This is because, when flux and spin of the Cooper pairs are parallel, local density of states of quasi-particles shows bound state at zero energy. On the other hand, when flux and spin are anti-parallel, there is no phase singularity in the order parameter.