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We develop a scheme of Gor'kov Green's functions to treat impurity effects onCaroli-de Gennes-Matricon (CdGM) mode in superconductors (SCs) by improving theKopnin-Kravtsov scheme with respect to the coherence factors and applicabilityto various SCs. We can study the impurity effects keeping the discreteness ofthe energy spectrum in contrast to the quasiclassical theory. We can thus applythis scheme to the SCs with the small quasiclassical parameter$k_{\mathrm{F}}\xi_{0}$ (which is the product of the Fermi wavenumber$k_{\mathrm{F}}$ and the coherence length $\xi_{0}$ in pure SC at zerotemperature) and/or superclean regime $\Delta_{\mathrm{mini}} \tau \gg1$($\Delta_{\mathrm{mini}}$ and $\tau$ denote, respectively, the level spacing ofthe CdGM mode called minigap and the relaxation time for CdGM mode and we take$\hbar =1$). We investigate the impurity effects as a white noise for a vortexin an s-wave SC and two types of vortices in a chiral p-wave SC, for variousvalues of the quasiclassical parameters and impurity strengths (from moderatelyclean regime to superclean regime), and confirm the validity of this scheme.

Impurity Effects on Caroli-de Gennes-Matricon Mode in a Vortex Core in Superconductors