Impurity Effects on Caroli-de Gennes-Matricon Mode in Vortex Core in Superconductors
We have developed a scheme of Gor’kov Green’s functions to treat the impurity effects on the Caroli–de Gennes–Matricon (CdGM) mode in superconductors (SCs) by improving the Kopnin–Kravtsov scheme with respect to the coherence factors and applicability to various SCs. We can study the impurity effects while keeping the discreteness of the energy spectrum, in contrast to the quasiclassical theory. We can thus apply this scheme to SCs with a small quasiclassical parameter kFξ0 (which is the product of the Fermi wavenumber kF and the coherence length ξ0 in a pure SC at zero temperature) and/or in the superclean regime \(\Delta _{\text{mini}}\tau \gg 1\) (Δmini and τ denote, respectively, the level spacing of the CdGM mode called the minigap and the relaxation time for the CdGM mode and we take ħ = 1). We investigate the impurity effects as a white noise for a vortex in an s-wave SC and two types of vortex in a chiral p-wave SC for various values of the quasiclassical parameter and impurity strength (from the ...