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Acta Physica Polonica A

Phase Separations in the Narrow-Bandwidth Limit of the Penson-Kolb-Hubbard Model at Zero Temperature

Konrad Jerzy Kapcia, W.R. Czart

Published Mar 1, 2018• 6 citations
Publisher

Abstract

In this work we study the ground state of the Penson-Kolb-Hubard model in the limit of narrow-bandwidth.We present phase diagrams of the model for fixed chemical potential and concentration (involving various phase separations).The results are derived within the Hartree-Fock approximation (HFA) in the narrow-bandwidth regime and compared with the exact ones in the atomic limit and the high-dimension regime.Our investigation reveals that the HFA can reconstruct the exact diagram at the ground state when the bandwidth approaches to zero.

DOI
10.12693/aphyspola.133.401

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In this work we study the ground state of the Penson-Kolb-Hubard model in the limit of narrow-bandwidth.We present phase diagrams of the model for fixed chemical potential and concentration (involving various phase separations).The results are derived within the Hartree-Fock approximation (HFA) in the narrow-bandwidth regime and compared with the exact ones in the atomic limit and the high-dimension regime.Our investigation reveals that the HFA can reconstruct the exact diagram at the ground state when the bandwidth approaches to zero.
The extended Hubbard model with the pair-hopping interaction, i.e. the Penson-Kolb-Hubbard model, is one of the conceptually simplest phenomenological models for studying correlations and for description of superconductivity in very narrow-band systems with short-range, almost unretarded pairing.We present ground state phase diagrams of the model derived within the broken-symmetry Hartree-Fock approximation in the narrow-bandwidth regime and compare these results with the exact ones in the atomic limit for the limit of high dimensions.The investigation of the diagrams of the model show that results obtained within both approaches are consistent, although for the case of the finite single-electron hopping phases with magnetic long-range order also occur.
In this paper we determine the phase diagrams (for T=0T=0T=0 as well as T>0T>0T>0) of the Penson-Kolb-Hubbard model for two dimensional square lattice within Hartree-Fock mean-field theory focusing on investigation of superconducting phases and possibility of the occurrence of the phase separation. We obtain that the phase separation, which is a state of coexistence of two different superconducting phases (with sss-wave and ηηη-wave symmetries), occurs in define range of the electron concentration. In addition, increasing temperature can change the symmetry of the superconducting order parameter (from ηηη-wave into sss-wave). The system considered exhibits also an interesting multicritical behaviour including bicritical points.
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.
We investigate in the Hartree approximation the temperature and filling dependence of the superconducting $\ensuremath{\pi}$ phase for the Penson-Kolb-Hubbard model. Due to the presence of the pair-hopping term, the phase survives for repulsive values of the on-site Coulomb interaction, exhibiting an interesting filling and temperature dependence. The structure of the self-consistent equations peculiar to the $\ensuremath{\pi}$ phase of the model allows us to explicitly solve them for the chemical potential. The phase diagrams are shown and discussed in dimension 2 and 3. We also show that, when a next-nearest-neighbors hopping term is included, the critical temperature of the superconducting region increases, and the corresponding range of filling values is shifted away from half-filling. Comparisons with known exact results are also discussed.
The variation of the superconducting order parameter (extended s wave) with hole concentration is studied for a narrow-band system, described by an extended Hubbard model, using the renormalized Hamiltonian approach (RHA) and X-operator technique in the strong-correlation limit and by the Hartree-Fock approximation for the weak correlation case. A comparison of the results obtained by using the RHA and the X-operator technique are made for different densities of states. Analytical results for the superconducting order parameter and its relation to the delocalization energies in the normal and superconducting states are obtained at zero chemical potential.
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.