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Acta Physica Polonica A

Superconducting Properties of theη-Pairing State in the Penson-Kolb-Hubbard Model

W.R. Czart, S. Robaszkiewicz

Published Nov 1, 2004• 19 citations
Publisher

Abstract

The Penson-Kolb-Hubbard model, i.e. the Hubbard model with the pair-hopping interaction J is studied.We focus on the properties of the superconducting state with the Cooper-pair center-of-mass momentum q = Q (η-phase).The transition into the η-phase, which is favorized by the repulsive J (J < 0) is found to occur only above some critical value |J c |, dependent on band filling, on-site interaction U and band structure, and the system never exhibits standard BCS-like features.This is in obvious contrast with the properties of the isotropic s-wave state, stabilized by the attractive J and attractive U , which exhibit at T = 0 a smooth crossover from the BCS-like limit to that of tightly bound pairs with increasing pairing strength.

DOI
10.12693/aphyspola.106.709

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The Penson-Kolb-Hubbard model, i.e. the Hubbard model with the pair-hopping interaction J is studied.We focus on the properties of the superconducting state with the Cooper-pair center-of-mass momentum q = Q (η-phase).The transition into the η-phase, which is favorized by the repulsive J (J < 0) is found to occur only above some critical value |J c |, dependent on band filling, on-site interaction U and band structure, and the system never exhibits standard BCS-like features.This is in obvious contrast with the properties of the isotropic s-wave state, stabilized by the attractive J and attractive U , which exhibit at T = 0 a smooth crossover from the BCS-like limit to that of tightly bound pairs with increasing pairing strength.
Abstract Penson–Kolb model, i.e. the tight‐binding model with the pair‐hopping (intersite charge exchange) interaction J is considered. In the analysis we focus on the properties of the superconducting state with Cooper‐pair center‐of‐mass momentum q = Q (η‐phase), which can develop in this model for the case of repulsive J(J < 0). The evolutions of the phase diagrams, the critical temperatures and superfluid characteristics with particle concentration and pairing strength are discussed.
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.
In the paper, we study the thermodynamic and electromagnetic properties of the Penson–Kolb (PK) model, i.e., the tight-binding model for fermionic particles with the pair-hopping interaction J. We focus on the case of repulsive J (i.e., J<0), which can stabilize the eta-pairing superconductivity with Cooper-pair center-of-mass momentum q→=Q→, Q→=(π/a,π/a,…). Numerical calculations are performed for several d-dimensional hypercubic lattices: d=2 (the square lattice, SQ), d=3 (the simple cubic lattice) and d=∞ hypercubic lattice (for arbitrary particle concentration 0<n<2 and temperature T). The ground state J versus n phase diagrams and the crossover to the Bose–Einstein condensation regime are analyzed and the evolution of the superfluid characteristics are examined within the (broken symmetry) Hartree–Fock approximation (HFA). The critical fields, the coherence length, the London penetration depth, and the Ginzburg ratio are determined at T=0 and T>0 as a function of n and pairing strength. The analysis of the effects of the Fock term on the ground state phase boundaries and on selected PK model characteristics is performed as well as the influence of the phase fluctuations on the eta-pairing superconductivity is investigated. Within the Kosterlitz–Thouless scenario, the critical temperatures TKT are estimated for d=2 SQ lattice and compared with the critical temperature Tc obtained from HFA. We also determine the temperature Tm at which minimal gap between two quasiparticle bands vanishes in the eta-phase. Our results for repulsive J are contrasted with those found earlier for the PK model with attractive J (i.e., with J>0).
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.
In the paper, we study the thermodynamic and electromagnetic properties of the Penson--Kolb (PK) model, i.e., the tight--binding model for fermionic particles with the pair-hopping interaction JJJ. We focus on the case of repulsive JJJ (i.e., J0J 0J0 as a function of nnn and pairing strength. The analysis of the effects of the Fock term on the ground state phase boundaries and on selected PK model characteristics is performed as well as the influence of the phase fluctuations on the eta-pairing superconductivity is investigated. Within the Kosterlitz--Thouless scenario, the critical temperatures $T_{KT} $ are estimated for d=2d=2d=2 SQ lattice and compared with the critical temperature TcT_cTc​ obtained from HFA. We also determine the temperature TmT_mTm​ at which minimal gap between two quasiparticle bands vanishes in the eta-phase. Our results for repulsive JJJ are contrasted with those found earlier for the PK model with attractive JJJ (i.e., with J>0J>0J>0).
The ground-state phase diagram of the one-dimensional Hubbard chain with pair-hopping interaction is studied. The analysis of the model is performed using the continuum-limit field theory approach and exact diagonalization studies. At half-filling the phase diagram is shown to consist of two superconducting states with Cooper-pair center-of-mass momentum $Q=0 (\mathrm{BCS}\ensuremath{-}{\ensuremath{\eta}}_{0}$ phase) and $Q=\ensuremath{\pi} ({\ensuremath{\eta}}_{\ensuremath{\pi}}$ phase) and four insulating phases corresponding to the Mott antiferromagnet, the Peierls dimerized phase, the charge-density-wave (CDW) insulator, and an unconventional insulating phase characterized by the coexistence of a CDW and a bond-located staggered magnetization. Away from half-filling the phase diagram consists of the superconducting $\mathrm{BCS}\ensuremath{-}{\ensuremath{\eta}}_{0}$ and ${\ensuremath{\eta}}_{\ensuremath{\pi}}$ phases and the metallic Luttinger-liquid phase. The $\mathrm{BCS}\ensuremath{-}{\ensuremath{\eta}}_{0}$ phase exhibits a smooth crossover from a weak-coupling BCS type to a strong-coupling local-pair regime. The ${\ensuremath{\eta}}_{\ensuremath{\pi}}$ phase shows the properties of the doublon (zero-size Cooper-pair) superconductor with Cooper-pair center-of-mass momentum $Q=\ensuremath{\pi}.$ The transition into the ${\ensuremath{\eta}}_{\ensuremath{\pi}}$-paired state corresponds to an abrupt change in the ground-state structure. After the transition the conduction band is completely destroyed and a new ${\ensuremath{\eta}}_{\ensuremath{\pi}}$-pair band, corresponding to the strongly correlated doublon motion, is created.