Odd-frequency Cooper pair around a magnetic impurity

The Yu-Shiba-Rusinov (YSR) state appears as a bound of quasiparticle at magnetic atom embedded in superconductor. We discuss why the YSR has energy below superconducting gap and pair potential changes sign atom. Although superconductor been considered breaker since 1960s, we propose an alternative physical picture to explain these reasons. analytical expression Green's function indicates that converts spin-singlet $s$-wave Cooper into odd-frequency pairs rather than breaking it pairing correlations coexist with states gap. relationships among free-energy density, amplitudes correlation functions, change impurity are discussed utilizing self-consistent solution Eilenberger equation. conclude happens only when dominant impurity. In presence local $\ensuremath{\pi}$-phase shift potential, can decrease density there because their response field is paramagnetic.