Anisotropy and spin-fluctuation effects on the spectral properties of Shiba impurities

Abstract: We theoretically consider a quantum magnetic impurity coupled to a superconductor, and obtain the local density of states at the position of the impurity taking into account the effect of spin-fluctuations and single-ion magnetic anisotropy. We particularly focus on the spectrum of subgap Yu-Shiba-Rusinov (YSR or Shiba) states induced by a quantum impurity with easy- or hard-axis uniaxial anisotropy. Although this is a relevant experimental situation in, e.g., magnetic adatoms on the surface of clean metals, it is customary that theoretical descriptions assume a classical-spin approximation which is not able to account for single-ion anisotropy and other quantum effects. Here, quantum fluctuations of the spin are taken into account in the equations of motion of the electronic Green's function in the weak-coupling limit, and considerably modify the energy of the Shiba states compared to the classical-spin approximation. Our results point towards the importance of incorporating quantum fluctuations and anisotropy effects for the correct interpretation of scanning tunneling microscopy (STM) experiments.