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Acta Physica Polonica A

Electron Phase Separations Involving Superconductivity in the Extended Hubbard Models with Pair Hopping Interaction

Konrad Jerzy Kapcia

Published Feb 1, 2015• 11 citations
Publisher

Abstract

In this work the extended Hubbard models with pair hopping interaction (at the atomic limit) are investigated within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-eld approximation (exact in d → +∞).We analyze mutual stability of the superconducting phase and charge or (ferro/antiferro-)magnetic orderings as well as homogeneous mixed phases.Our preliminary results for U = 0 show that the superconducting phase can coexist with the charge or (ferro/antiferro-)magnetic phases only in states with electron phase separation.

DOI
10.12693/aphyspola.127.204

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In this work the extended Hubbard models with pair hopping interaction (at the atomic limit) are investigated within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-eld approximation (exact in d → +∞).We analyze mutual stability of the superconducting phase and charge or (ferro/antiferro-)magnetic orderings as well as homogeneous mixed phases.Our preliminary results for U = 0 show that the superconducting phase can coexist with the charge or (ferro/antiferro-)magnetic phases only in states with electron phase separation.
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.
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.
We present the analysis of paramagnetic eects of magnetic eld (B) (Zeeman term) in the zero-bandwidth limit of the extended Hubbard model for arbitrary chemical potential µ and electron density n.The eective Hamiltonian considered consists of the on-site interaction U and the intersite charge exchange term I, determining the hopping of electron pairs between nearest-neighbour sites.The model has been analyzed within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-eld approximation (rigorous in the limit of innite dimensions d → +∞).In this report we focus on metastable phases as well as phase separated states involving superconducting and nonordered phases and determine their ranges of occurrence for U/I0 = 1.05 (I0 = zI) in the presence of magnetic eld B = 0. Our investigations of the general case for arbitrary U/I0 show that, depending on the values of interaction parameters (for xed n), the phase separating state can occur in higher elds than the homogeneous superconducting phase (eld-induced phase separated).Moreover, a rst-order superconductingnonordered transition occurs between metastable phases and these metastable phases can exist inside the regions of the phase separated state stability.Such behaviour is associated with the presence of tricritical line on the phase diagrams of the system.
We present studies of the atomic limit of the extended Hubbard model with pair hopping for arbitrary electron density and arbitrary chemical potential. The Hamiltonian consists of (i) the effective on-site interaction U and (ii) the intersite charge exchange term I , determining the hopping of electron pairs between nearest-neighbour sites. In the analysis of the phase diagrams and thermodynamic properties of this model we treat the intersite interactions within the mean-field approximation. In this report we focus on metastable phases and determine their ranges of occurrence. Our investigations in the absence of the external magnetic field show that the system analysed exhibits tricritical behaviour. Two metastable phases (superconducting and nonordered) can exist inside the regions of the phase separated state stability and a first-order transition occurs between these metastable phases.
The phase diagrams and superconducting properties of the extended Hubbard model with pair hopping interaction, i.e., the Penson-Kolb-Hubbard model are studied. The analysis of the model is performed for d-dimensional hypercubic lattices, including d=1d=1d=1 and $d=\ensuremath{\infty},$ by means of the (broken symmetry) Hartree-Fock approximations and, for $d=\ensuremath{\infty},$ by the slave-boson mean-field method. For d=1,d=1,d=1, at half filling the phase diagram is shown to consist of nine different phases including two superconducting states with center-of-mass momentum q=0q=0q=0 and q=Qq=Qq=Q $(\ensuremath{\eta}$ pairing), site and bond-located antiferromagnetic and charge-density wave states as well as three mixed phases with coexisting site and bond orderings. The stability range of the bond-type orderings shrinks with increasing lattice dimensionality d and for $d=\ensuremath{\infty}$ the corresponding diagram consists of four phases only, involving exclusively site-located orderings. Comparing the pair hopping model with the attractive Hubbard model we found in both cases gradual evolution from the BCS-like limit to the tightly bound pairs regime and a monotonic increase of the gap in the excitation spectrum with increasing coupling. However, the dynamics of electron pairs in both models is qualitatively different, which results in different dependences of condensation energies and critical temperatures on interaction parameters as well as in different electrodynamic properties, especially in a strong coupling regime.
We study the extended Hubbard model with on-site density-density U and intersite pair hopping J interactions, i.e. the Penson-Kolb-Hubbard model.This report focuses mainly on the properties of the model at T ≥ 0 in the case of repulsive J (J < 0) which may stabilize superconductivity with η-pairing.The analysis is performed within the (broken symmetry) Hartree-Fock approximation for arbitrary interaction parameters (J < 0 and U ) and electron concentration (0 < n < 2) on the d = 2 square lattice.The phase diagrams of the model at T = 0 and at finite temperatures are examined taking into account magnetic and charge-ordered phases and superconducting states with η-and s-wave pairing.