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

Abstract

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.

Superconductivity, Charge Orderings, Magnetism, and Their Phase Separations in the Ground State of Lattice Models of Superconductor with Very Short Coherence Length

“…Names of transition orders used are consistent with our earlier works [7][8][9][10][11][12][13][14][33][34][35][36]. In particular, a transition between a homogeneous phase and the PS state is symbolically named as a "third-order" transition.…”

“…refs. [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and references therein). Moreover, the phase separation (PS) has been evidenced (by various microscopy techniques such as STM, MFM, etc.)…”

“…The effective model considered has a form of single-band extended Hubbard model with pair hopping at the atomic limit (t = 0) [4][5][6][7][8][9][10][11][12][13][14][15][16][17]: …”

“…The analysis of the ground state of model (1) has been performed by means of a variational approach (VA) in the grand canonical ensemble [6][7][8][9][10][11][12][13][14], which treats on-site U term exactly and the intersite interactions within the mean-field approximation (MFA). The MFA is a rigorous treatment of the intersite terms in the limit of infinite dimensions d → +∞ (or large coordination number z); thus, the result obtained in this paper for model (1) are also exact in the limit d → +∞.…”

“…where E ± (n ± ) are values of the energy of two separating phases at n ± corresponding to the lowest homogeneous solution for a given phase, m is the fraction of the system with charge density n + , and mn + + (1 − m)n − = n [8,[31][32][33][34].…”