Spin-symmetric solution of an interacting quantum dot attached to superconducting leads: Andreev states and the 0−π0-\pi transition

Behavior of Andreev gap states in a quantum dot with Coulomb repulsion symmetrically attached to superconducting leads is studied via the perturbation expansion in the interaction strength. We find the exact asymptotic form of the spin-symmetric solution for the Andreev states continuously approaching the Fermi level. We thereby derive a critical interaction at which the Andreev states at zero temperature merge at the Fermi energy, being the upper bound for the $0-\pi$ transition. We show that the spin-symmetric solution becomes degenerate beyond this interaction, in the $\pi$ phase, and the Andreev states do not split unless the degeneracy is lifted. We further demonstrate that the degeneracy of the spin-symmetric state extends also into the $0$ phase in which the solutions with zero and non-zero frequencies of the Andreev states may coexist.Comment: 12 pages, 4 figure

Phase retrapping in aφJosephson junction: onset of the butterfly effect

We investigate experimentally the retrapping of the phase in a φ Josephson junction upon return of the junction to the zero-voltage state. Since the Josephson energy profile U 0 ( ψ ) in φ JJ is a 2 π periodic double-well potential with minima at ψ = ± φ mod 2 π , the question is at which of the two minima − φ or + φ the phase will be trapped upon return from a finite voltage state during quasistatic decrease of the bias current (tilt of the potential). By measuring the relative population of two peaks in escape histograms, we determine the probability of phase trapping in the ± φ wells for different temperatures. Our experimental results agree qualitatively with theoretical predictions. In particular, we observe an onset of the butterfly effect with an oscillating probability of trapping. Unexpectedly, this probability saturates at a value different from 50% at low temperatures

Phase transitions in the spinless Falicov-Kimball model with correlated hopping

The canonical Monte-Carlo is used to study the phase transitions from the low-temperature ordered phase to the high-temperature disordered phase in the two-dimensional Falicov-Kimball model with correlated hopping. As the low-temperature ordered phase we consider the chessboard phase, the axial striped phase and the segregated phase. It is shown that all three phases persist also at finite temperatures (up to the critical temperature $\tau_c$) and that the phase transition at the critical point is of the first order for the chessboard and axial striped phase and of the second order for the segregated phase. In addition, it is found that the critical temperature is reduced with the increasing amplitude of correlated hopping $t'$ in the chessboard phase and it is strongly enhanced by $t'$ in the axial striped and segregated phase.Comment: 17 pages, 6 figure

Thermodynamics of the Generalized Spin-One-Half Falicov-Kimball Model in Two Dimensions

The extrapolation of small-cluster exact-diagonalization calculations and the Monte Carlo method is used to study the spin-one-half Falicov-Kimball model extended by the spin-dependent Coulomb interaction (J) between the localized f and itinerant d electrons as well as the on-site Coulomb interaction $(U_{ff})$ between the localized f electrons. It is shown that in the symmetric case the ground-state phase diagram of the model has an extremely simple structure that consists of only two phases, and namely, the charge-density-wave phase and the spin-density-wave phase. The nonzero temperature studies showed that these phases persist also at finite temperatures. The same calculations that we performed for unsymmetric case showed that charge and spin ordering can be destroyed simultaneously or consecutively

Ground States of the Falicov-Kimball Model Extended by Nonlocal Coulomb Interactions

The small-cluster exact-diagonalizations are used to study the ground states of the Falicov-Kimball model extended by nonlocal Coulomb interactions (the nearest-neighbour interaction $U_{nn}$ and the correlated hopping t'). It is shown that the ground-state phase diagrams found for the conventional Falicov-Kimball model are strongly changed when the nonlocal interactions are added. This is illustrated for two selected values of the on-site Coulomb interaction (U) that represent typical behaviours of the model in the intermediate and strong coupling limit. A number of remarkable results are found. (i) The phase separation takes place for a wide range of $U_{nn}$ and t' in both interaction limits. (ii) New types of inhomogeneous charge ordering are observed for nonzero $U_{nn}$ and t'. (iii) Depending on the values of $U_{nn}$ and t', the model is able to describe both the continuous as well as discontinuous changes of the f-electron occupation number

The Influence of Lattice Defects on the Ground-State Properties of the Falicov-Kimball Model in Two Dimensions

The influence of lattice defects (vacancies) on the ground-state properties of the spinless Falicov-Kimball model is studied by a well-controlled numerical method in two dimensions. It is shown that in the presence of vacancies (distributed randomly) the ground states of the Falicov-Kimball model are phase separated for small f-electron concentrations $n_f$ and exhibit the long-range order for $n_f$ near the half-filled band case $n_f$=1/2. In addition, the dependence of average f-orbital occupancy on the concentration of vacancies is calculated for a wide range of model parameters. The resultant behaviours are used to interpret the experimental data obtained for the mixed-valence system $Sm_{1-x}B_6$

Thermodynamics of the Generalized Spin-One-Half Falicov-Kimball Model in Two Dimensions

The extrapolation of small-cluster exact-diagonalization calculations and the Monte Carlo method is used to study the spin-one-half Falicov-Kimball model extended by the spin-dependent Coulomb interaction (J) between the localized f and itinerant d electrons as well as the on-site Coulomb interaction $(U_{ff})$ between the localized f electrons. It is shown that in the symmetric case the ground-state phase diagram of the model has an extremely simple structure that consists of only two phases, and namely, the charge-density-wave phase and the spin-density-wave phase. The nonzero temperature studies showed that these phases persist also at finite temperatures. The same calculations that we performed for unsymmetric case showed that charge and spin ordering can be destroyed simultaneously or consecutively