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Acta Physica Polonica A

Superconductivity of the Two-Dimensional Penson-Kolb Model

W.R. Czart, S. Robaszkiewicz

Published Dec 1, 2001• 5 citations
Publisher

Abstract

I nst i tut e o f P hysi cs, A dam Mi cki ewi cz Uni versi ty Um ultowsk a 85, 61-61 4 Pozna¥ ( Recei ved Jul y 2, 2001)T w o-dim ension al ( d = 2 ) Penson À K olb mo del , i .e. t he ti ght-bindin g mo del with the pai r-hopp in g (intersite charge exchange ) interaction, is considered and the e˜ects of phase Ûuctuation s on the s -wave sup erconducti vi t y of this system are discussed w ithin the K osterlit z{T houl ess scenario.T he London penetration depth Ñ at T = 0 ; the K osterlitz-T houle ss critical temp erature T c , and the H artree{ Fock approximation critical temp erature T p are determined as a function of particle concentration and interaction.T he U emura typ e plots ( T c vs: Ñ À 2 ( 0) ) are derived.Beyond w eak coupli ng and for low concentrations they show the existence of universal scaling : T c ¿ 1=Ñ 2 ( 0) , as it w as previousl y found for the attractive H ubbard mo del and for the mo dels with intersite electron pairing.PAC S numb ers: 74.20.{z, 71.28.+ d, 74.25.H

DOI
10.12693/aphyspola.100.885

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I nst i tut e o f P hysi cs, A dam Mi cki ewi cz Uni versi ty Um ultowsk a 85, 61-61 4 Pozna¥ ( Recei ved Jul y 2, 2001)T w o-dim ension al ( d = 2 ) Penson À K olb mo del , i .e. t he ti ght-bindin g mo del with the pai r-hopp in g (intersite charge exchange ) interaction, is considered and the e˜ects of phase Ûuctuation s on the s -wave sup erconducti vi t y of this system are discussed w ithin the K osterlit z{T houl ess scenario.T he London penetration depth Ñ at T = 0 ; the K osterlitz-T houle ss critical temp erature T c , and the H artree{ Fock approximation critical temp erature T p are determined as a function of particle concentration and interaction.T he U emura typ e plots ( T c vs: Ñ À 2 ( 0) ) are derived.Beyond w eak coupli ng and for low concentrations they show the existence of universal scaling : T c ¿ 1=Ñ 2 ( 0) , as it w as previousl y found for the attractive H ubbard mo del and for the mo dels with intersite electron pairing.PAC S numb ers: 74.20.{z, 71.28.+ d, 74.25.H
We study thermodynamic and electromagnetic properties of the Penson-Kolb model, i.e., the tight-binding model with the pair-hopping interaction J, and analyze the effects of phase fluctuations on the s-wave superconductivity in this system. The evolution of the critical fields, the coherence length, the Ginzburg ratio, and the London penetration depth \ensuremath{\lambda} with particle concentration n and pairing strength is determined at T=0T=0T=0 for d-dimensional hypercubic lattices d=2d=2d=2 (SQ) and d=3d=3d=3 (SC). Within the Kosterlitz-Thouless scenario the critical temperatures Tc{T}_{c}Tc​ are calculated for d=2d=2d=2 SQ lattice and compared with the ones from BCS-HFA Tp.{T}_{p}.Tp​. The results show a substantial enhancement of the gap to critical temperature ratio due to the phase fluctuations as well as a separation of the energy scales for the pair formation $(\ensuremath{\sim}{k}_{B}{T}_{p})$ and the phase coherence $(\ensuremath{\sim}{k}_{B}{T}_{c}).$ The Uemura type plots, i.e., the Tc{T}_{c}Tc​ vs ${\ensuremath{\lambda}}^{\ensuremath{-}2}(0)$ plots, are obtained both as a function of n and as a function of pairing strength. The results are compared with those found earlier for the attractive Hubbard model.
W e study the evolution from BC S to Bose limit in a two-dimensional d -w ave superconductor at zero temp erature and low density of charge carriers w ithin the mean-Ùeld theory .W e examine single quasipa rticl e prop erties w hen particle density and attraction strength are v aried.F or su£ciently high interaction strength there is a critical density b elow w hich the system has a gap.T he spectral and thermo dynami c prop erties of the system do not evolve smo othly from the BC S-like to the Bose-like regime.
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.