We theoretically study a non-magnetic impurity effect on the vortex bound states of a multi-quantum vortex. The zero-energy peak of the local density of states is investigated for vortex cores with the winding numbers 2 and 4 within the framework of
the quasiclassical theory of superconductivity. We find that the zero-energy peaks, which appear away from the vortex center in the clean limit, move towards the vortex center with increasing the impurity scattering rate, resolving a contradiction between an experimental result and previous theoretical predictions.
We theoretically investigate a non-magnetic impurity effect on the temperature dependence of the vortex core shrinkage (Kramer-Pesch effect) in a single-band s-wave superconductor. The Born limit and the unitary limit scattering are compared within t
he framework of the quasiclassical theory of superconductivity. We find that the impurity effect inside a vortex core in the unitary limit is weaker than in the Born one when a system is in the moderately clean regime, which results in a stronger core shrinkage in the unitary limit than in the Born one.
We theoretically discuss the magnetic-field-angle dependence of the zero-energy density of states (ZEDOS) in superconductors. Point-node and line-node superconducting gaps on spherical and cylindrical Fermi surfaces are considered. The Doppler-shift
(DS) method and the Kramer-Pesch approximation (KPA) are used to calculate the ZEDOS. Numerical results show that consequences of the DS method are corrected by the KPA.
We study the Josephson effect between a conventional s-wave superconductor and a non-centrosymmetric superconductor with Rashba spin-orbit coupling. Rashba spin-orbit coupling affects the Josephson pair tunneling in a characteristic way. The Josephso
n coupling can be decomposed into two parts, a `spin-singlet-like and a `spin-triplet-like component. The latter component can lead to shift of the Josephson phase by pi relative to the former coupling. This has important implications on interference effects and may explain some recent experimental results for the Al/CePt3Si junction.
