Abstract
We use the numerical renormalization group theory to investigate the Yu-Shiba-Rusinov (YSR) bound state properties of single magnetic molecules placed in an s-wave superconducting substrate. The molecule consist of a large core spin and a single orbital, coupled via an exchange interaction. The critical Coulomb interaction for the singlet/doublet transition decreases in the presence of this exchange interaction for both ferro and anti-ferromagnetic couplings. The number of YSR states also increase to two pairs, however, in the singlet phase, one of the pairs have zero spectral weight. We explore the evolution of the in-gap states using the Anderson model. Away from the particle-hole symmetry point, the results suggest a doublet-singlet-doublet transition as the on-site energy is lowered while keeping the Coulomb interaction fixed. To understand these results, we write down an effective model for the molecule in the limit of large superconducting order parameter. Qualitatively, it explains the various phase transitions and spectral nature of the in-gap states. Finally, we analyze the effects of magnetic anisotropic fields of the core spin on in-gap states. Due to internal degrees of freedom of the spin excited states, a multitude of new states emerges within the gap. Depending on the sign and strength of the uniaxial anisotropic field, the results indicate up to three pairs of YSR states.
Highlights
Nanoscale devices embedded in tunnel junctions provide unique opportunities to study quantum many-body effects of impurity systems
We have considered the properties of YSR states created from a magnetic molecule absorbed on the surface of an s-wave superconductor
The molecule is modeled as a single orbital and a core spin, coupled via an exchange interaction
Summary
Nanoscale devices embedded in tunnel junctions provide unique opportunities to study quantum many-body effects of impurity systems. Results from NRG calculations of large spin moments with magnetic anisotropy show that multiple pairs of YSR states may appear [34] due to internal spin excitation These calculations, do not take into account differences due to the localized and delocalized nature of the d and the ligand orbitals, respectively. Due to the presence of the core spin, multiple YSR states emerge inside the superconducting gap This model naturally reflects the geometry of large spin molecular systems such as Fe8 [35], Mn12 [36], and transition-metal phthalocyanines [32,37]. We have assumed that the spin moment of the transition-metal atom interacts only with electrons in the ligand orbital via exchange and has no interaction with the substrate electrons This is because the energies of the d-orbital states are far below the Fermi level, which tends to suppress the charge fluctuations.
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