Quantum Corrals, Eigenmodes and Quantum Mirages in s-wave Superconductors

We study the electronic structure of magnetic and non-magnetic quantum corrals embedded in s-wave superconductors. We demonstrate that a quantum mirage of an impurity bound state peak can be projected from the occupied into the empty focus of a non-magnetic quantum corral via the excitation of the corral's eigenmodes. We observe an enhanced coupling between magnetic impurities inside the corral, which can be varied through oscillations in the corral's impurity potential. Finally, we discuss the form of eigenmodes in magnetic quantum corrals.Comment: 4 pages, 4 figure

Binding energy of an impurity in polar microspheres

We have examined the binding energy of a polaron bound to a hydrogenic donor impurity located in a spherical quantum dot by means of a variational technique for both finite and infinite potential models. The polaronic effect on the binding energy has been considered taking into account the ion-phonon coupling by using the Lee-Low-Pines variational method. The results we have obtained show that the binding energies are drastically affected by the dot radius, the potential barrier height and the polaronic effects.We have examined the binding energy of a polaron bound to a hydrogenic donor impurity located in a spherical quantum dot by means of a variational technique for both finite and infinite potential models. The polaronic effect on the binding energy has been considered taking into account the ion-phonon coupling by using the Lee-Low-Pines variational method. The results we have obtained show that the binding energies are drastically affected by the dot radius, the potential barrier height and the polaronic effects

Bethe ansatz approach to thermodynamics of superconducting magnetic alloys

We derive thermodynamic Bethe ansatz equations for a model describing an $U\to\infty$ Anderson impurity embedded in a BCS superconductor. The equations are solved analytically in the zero-temperature limit, T=0. It is shown that the impurities depress superconductivity in the Kondo limit, however at T=0 the system remains in the superconducting state for any impurity concentration. In the mixed-valence regime, an impurity contribution to the density of states of the system near the Fermi level overcompensates a Cooper pairs weakening, and superconductivity is enhanced.Comment: 4 pages, RevTex, to appear in PR

Gap States in Dilute Magnetic Alloy Superconductors

We study states in the superconducting gap induced by magnetic impurities using self-consistent quantum Monte Carlo with maximum entropy and formally exact analytic continuation methods. The magnetic impurity susceptibility has different characteristics for T_{0} \alt T_{c0} and T_{0} \agt T_{c0} ($T_{0}$: Kondo temperature, $T_{c0}$: superconducting transition temperature) due to the crossover between a doublet and a singlet ground state. We systematically study the location and the weight of the gap states and the gap parameter as a function of $T_{0}/T_{c0}$ and the concentration of the impurities.Comment: 4 pages in ReVTeX including 4 encapsulated Postscript figure

Quantum Interference between Impurities: Creating Novel Many-Body States in s-wave Superconductors

We demonstrate that quantum interference of electronic waves that are scattered by multiple magnetic impurities in an s-wave superconductor gives rise to novel bound states. We predict that by varying the inter-impurity distance or the relative angle between the impurity spins, the states' quantum numbers, as well as their distinct frequency and spatial dependencies, can be altered. Finally, we show that the superconductor can be driven through multiple local crossovers in which its spin polarization, $$, changes between $=0, 1/2$ and 1.Comment: 4 pages, 4 figure

Spin and orbital effects of Cooper pairs coupled to a single magnetic impurity

The Kondo effect strongly depends on spin and orbital degrees of freedom of unconventional superconductivity. We focus on the Kondo effect in the $p_x + i p_y$-wave and $d_{x^2 - y^2} + i d_{xy}$-wave superconductors to compare the magnetic properties of the spin-triplet and spin-singlet Cooper pairs. The difference appears when both of the paired electrons couple to a local spin directly. For the $p_x + i p_y$-wave, the ground state is always a spin doublet for a $S_{\rm imp} = 1/2$ local spin, and it is always a spin singlet for $S_{\rm imp} = 1$. The latter is due to uniaxial spin anisotropy of the triplet Cooper pair. For the $d_{x^2 - y^2} + i d_{xy}$-wave, the interchange of ground states occurs, which resembles a competition between the Kondo effect and the superconducting energy gap in s-wave superconductors. Thus the internal degrees of freedom of Cooper pairs give a variety to the Kondo effect.Comment: 7 pages, 6 figures, RevTex, to be published in Phys. Rev.

Numerical Renormalization Group Study of Kondo Effect in Unconventional Superconductors

Orbital degrees of freedom of a Cooper pair play an important role in the unconventional superconductivity. To elucidate the orbital effect in the Kondo problem, we investigated a single magnetic impurity coupled to Cooper pairs with a $p_x +i p_y$ ($d_{x^2-y^2}+id_{xy}$) symmetry using the numerical renormalization group method. It is found that the ground state is always a spin doublet. The analytical solution for the strong coupling limit explicitly shows that the orbital dynamics of the Cooper pair generates the spin 1/2 of the ground state.Comment: 4 pages, 2 figures, JPSJ.sty, to be published in J. Phys. Soc. Jpn. 70 (2001) No. 1

Quantum phase transition in a minimal model for the Kondo effect in a Josephson junction

We propose a minimal model for the Josephson current through a quantum dot in a Kondo regime. We start with the model that consists of an Anderson impurity connected to two superconducting (SC) leads with the gaps $\Delta_{\alpha}=|\Delta_{\alpha}| e^{i \theta_{\alpha}}$, where $\alpha = L, R$ for the lead at left and right. We show that, when one of the SC gaps is much larger than the others $|\Delta_L| \gg |\Delta_R|$, the starting model can be mapped exactly onto the single-channel model, which consists of the right lead of $\Delta_R$ and the Anderson impurity with an extra onsite SC gap of $\Delta_d \equiv \Gamma_L e^{i \theta_L}$. Here $\theta_L$ and $\Gamma_L$ are defined with respect to the starting model, and $\Gamma_L$ is the level width due to the coupling with the left lead. Based on this simplified model, we study the ground-state properties for the asymmetric gap, $|\Delta_L| \gg |\Delta_R|$, using the numerical renormalization group (NRG) method. The results show that the phase difference of the SC gaps $\phi \equiv \theta_R -\theta_L$, which induces the Josephson current, disturbs the screening of the local moment to destabilize the singlet ground state typical of the Kondo system. It can also drive the quantum phase transition to a magnetic doublet ground state, and at the critical point the Josephson current shows a discontinuous change. The asymmetry of the two SC gaps causes a re-entrant magnetic phase, in which the in-gap bound state lies close to the Fermi level.Comment: 23 pages, 13 figures, typos are correcte