Stanisław Robaszkiewicz

Phase separation in a lattice model of a superconductor with pair hopping

We have studied the extended Hubbard model with pair hopping in the atomic limit for arbitrary electron density and chemical potential. The Hamiltonian considered consists of (i) the effective on-site interaction U and (ii) the intersite charge exchange interactions I, determining the hopping of electron pairs between nearest-neighbour sites. The model can be treated as a simple effective model of a superconductor with very short coherence length in which electrons are localized and only electron pairs have a possibility of transferring. The phase diagrams and thermodynamic properties of this model have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. We have also obtained rigorous results for a linear chain (d = 1) in the ground state. Moreover, at T = 0 some results derived within the random phase approximation (and the spin-wave approximation) for d = 2 and 3 lattices and within the low-density expansions for d = 3 lattices are presented. Our investigation of the general case (as a function of the electron concentration n and as a function of the chemical potential μ) shows that, depending on the values of interaction parameters, the system can exhibit not only the homogeneous phases, superconducting (SS) and nonordered (NO), but also the phase separated states (PS: SS-NO). The system considered exhibits interesting multicritical behaviour including tricritical points.

The magnetic field induced phase separation in a model of a superconductor with local electron pairing

We have studied the extended Hubbard model with pair hopping in the atomic limit for arbitrary electron density and chemical potential and focus on paramagnetic effects of the external magnetic field. The Hamiltonian considered consists of (i) the effective on-site interaction U and (ii) the intersite charge exchange interactions I, determining the hopping of electron pairs between nearest-neighbour sites. The phase diagrams and thermodynamic properties of this model have been determined within the variational approach (VA), which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. Our investigation of the general case shows that the system can exhibit not only the homogeneous phases-superconducting (SS) and non-ordered (NO)-but also the phase separated states (PS: SS-NO). Depending on the values of interaction parameters, the PS state can occur in higher fields than the SS phase (field induced PS). Some ground state results beyond the VA are also presented.

The effects of the next-nearest-neighbour density-density interaction in the atomic limit of the extended Hubbard model

We have studied the extended Hubbard model in the atomic limit. The Hamiltonian analysed consists of the effective on-site interaction U and the intersite density-density interactions W(ij) (both nearest-neighbour and next-nearest-neighbour). The model can be considered as a simple effective model of charge ordered insulators. The phase diagrams and thermodynamic properties of this system have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. Our investigation of the general case taking into account for the first time the effects of longer-ranged density-density interaction (repulsive and attractive) as well as possible phase separations shows that, depending on the values of the interaction parameters and the electron concentration, the system can exhibit not only several homogeneous charge ordered (CO) phases, but also various phase separated states (CO-CO and CO-nonordered). One finds that the model considered exhibits very interesting multicritical behaviours and features, including bicritical, tricritical, and critical end points and isolated critical points.

On the superconductivity in the induced pairing model

Abstract The two component model of coexisting local electron pairs and itinerant fermions coupled via charge exchange mechanism, which mutually induces superconductivity in both subsystems, is discussed. The cases of isotropic s-wave and anisotropic pairing of extended s- and d x 2 − y 2 -wave symmetries are analyzed for a 2D square lattice within the BCS-mean field approximation and the Kosterlitz–Thouless theory. We determined the phase diagrams and superconducting characteristics as a function of the position of the local pair (LP) level and the total electron concentration. The model exhibits several types of interesting crossovers from BCS like behavior to that of LP’s. Some of our results are discussed in connection with a two-component scenario of preformed pairs and unpaired electrons for exotic superconductors.

Superconductivity in a Two-Component Model with Local Electron Pairs

AbstractSuperconductivity in the two-component model of coexisting local electron pairs (hard-core charged bosons) and itinerant fermions coupled via charge exchange mechanism is discussed. The cases of isotropic s-wave and anisotropic pairing of extended s-wave and

Monte Carlo study of phase separation in magnetic insulators

d_{x^2 - y^2 }

Extended Falicov-Kimball model: Exact solution for the ground state

symmetries are analyzed for a 2D square lattice within the BCS-mean-field approximation (MFA) and the Kosterlitz–Thouless theory. The phase diagrams and superconducting characteristics of this induced pairing model as a function of the position of the local pair (LP) level and the total carrier concentration are reviewed. The model exhibits crossovers between the BCS-like behavior and that of LPs. In addition, the Uemura plots are obtained for extended s and