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When a quantum dot is embedded into a superconducting environment, it leads to the formations of localized Shiba states inside the gap. If the Coulomb interaction is sufficiently small, the Shiba states consist of a pair of singlet states and a doublet, that compete for the ground state and induce a quantum phase transition. In the presence of an external microwave field, the Shiba energy spectrum is significantly modified. Moreover, the transmission of the cavity inherits features that can pinpoint the exact location of the quantum critical point. In terms of methods used, our analytical calculations are supplemented by state of the art numerical renormalization group calculations.When a quantum dot is embedded into a superconducting environment, it leads to the formations of localized Shiba states inside the gap. If the Coulomb interaction is sufficiently small, the Shiba states consist of a pair of singlet states and a doublet, that compete for the ground state and induce a quantum phase transition. In the presence of an external microwave field, the Shiba energy spectrum is significantly modified. Moreover, the transmission of the cavity inherits features that can pinpoint the exact location of the quantum critical point. In terms of methods used, our analytical calculations are supplemented by state of the art numerical renormalization group calculations.

Glasses from xFe2O3 · (100 − x)[P2O5 · TeO2] system, with 0 ≤ x ≤ 50 mol%, were investigated by X-ray diffraction, FT-IR and EPR spectroscopies. The XRD patterns show a vitreous state of studied samples for x ≤ 35 mol% Fe2O3. The FT-IR spectrum of the P2O5 · TeO2 glass matrix reveals a structure formed from PO4, TeO4 and TeO3 units. The addition and the increasing of Fe2O3 content modify progressively the structure of the glass matrix. The local structure in the investigated glasses was revealed by means of EPR using Fe3+ (3d5; 6S5/2) ions as paramagnetic probes. The EPR spectra present two resonance absorption lines characteristic to Fe3+ ions centred at geff ≈ 2.0, for 0.5 ≤ x ≤ 35 mol% and geff ≈ 4.3, for 0.5 ≤ x ≤ 5 mol%. The variation of the EPR parameters, the intensity and line-width of these absorption lines, with iron ions composition has been followed.

We present results for strong-coupling calculations for the density of states in the presence of magnetic impurities in a two-band superconductor. Our calculations were done for the particular case of a ${\mathrm{MgB}}_{2}$ compound where two bands $(\ensuremath{\sigma}$ and $\ensuremath{\pi}$ B-like) intersect the Fermi level. If only the $\ensuremath{\pi}$ band is responsible for superconductivity, then an impurity band will form in the energy gap of the $\ensuremath{\pi}$ band. If the $\ensuremath{\sigma}$ band is involved, then new features may be found in the density of states at frequencies between the superconducting gaps corresponding to $\ensuremath{\pi}$ and $\ensuremath{\sigma}$ bands. The validity of our results can be directly verified by measuring the density of states in the presence of magnetic impurities using tunneling experiments in ${\mathrm{MgB}}_{2}.$ We also present analytical results for the doping dependence of the critical temperature.