A new numerical method for quasi-particle spectroscopy around a pair of vortices in triplet superconductors Original Research Article

Triplet superconductors such as Sr2RuO4 and NaxCoO2·yH2ONaxCoO2·yH2O are now found to be p -wave (px±ipy)(px±ipy) or f -wave ((px±ipy)coscpz)((px±ipy)coscpz) superconductors. In conventional singlet superconductors, vortices are quantized because phase of order parameter must rotate by 2π2π around a vortex. But triplet superconductors have a degree of freedom of spin, which is described by d -vector. The d -vector and phase can rotate by ππ around a vortex, separately. Therefore appearance of HQVs is predicted. Theoretically, it is found that a pair of HQVs is more stable than a singly quantized vortex, for several parameter regions. In this study, in order to investigate quasi-particle bound states around two vortices in s-wave superconductors, we have developed a new numerical method to solve the BdG equation for two vortices state, using Mathieu functions. We confirmed the validity of this method for two vortices state and applied it in case of a pair of vortices. And we solved it.