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Modern Physics Letters B

SUPERCONDUCTIVITY WITH ‘η PAIRING’: GAP PARAMETER AND SINGLE PARTICLE TUNNELING

Grzegorz Litak A, T. Domański

Published Feb 10, 1994• 1 citation
Publisher

Abstract

We examine the ‘η pairing’ superconductivity using the negative U Hubbard model on the bipartite lattice. The superconducting gap parameter for η pairing is compared with the equilibrium Hartree-Fock-Bogolubov solution for the half-filled system in various temperatures and strengths of interaction. The quasiparticle density of states and the single particle tunneling are investigated.

DOI
10.1142/s0217984994000169

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We examine the ‘η pairing’ superconductivity using the negative U Hubbard model on the bipartite lattice. The superconducting gap parameter for η pairing is compared with the equilibrium Hartree-Fock-Bogolubov solution for the half-filled system in various temperatures and strengths of interaction. The quasiparticle density of states and the single particle tunneling are investigated.
We have studied the influence of singular fluctuations around the mean-field solution as well as higher order contributions to the geometry controlled asymptotic expansion of the propagators on η-pairing superconductivity in the strong coupling negative-U Hubbard model in the presence of unpaired electrons. The modifications of the mean-field results due to the introduction of disorder and allowance for finite U are also calculated. Besides the singularities already present in the O(2) nonlinear σ-model we find a filling-depending singular depression of the repulsive effective pair-hopping interaction which strongly alters the mean-field phase diagram and appears to suppress the η-pairing phase near the band edges.
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 this letter, we propose a modified attractive Hubbard model at half filling that can exhibit superconductivity through η -pairing mechanism in spin-density wave representation and derive a concise relationship between the energy disparity and the single-particle energy spectrum. This relationship, in the two limits of U , clearly shows that the system does not display superconductivity for very low doping concentration. but demonstrates superconductivity when the doping concentration exceeds a certain critical value. This conclusion is in qualitative agreement with the familiar experiments on high- T c superconductivity.
We have developed a method for studying superconductivity in the negative-U Hubbard model. It is based on the Hubbard-alloy-analogy approximation applied to the Gor'kov equation for the model. We find that, unlike the case of the BCS solution, the formation of pairs and their condensation into a super-conducting ground state take place at two different temperatures. We calculate the condensation temperature T(c) for all U and discuss the nature of the normal state which, for large enough U, features a macroscopically large number of pairs. Briefly, we argue that the model has relevance for high-temperature superconductors.
One-particle properties of the normal state of a negative-U Hubbard model are analysed within the framework of the incoherent local-pair (ILP) approach. In the self-consistent Hartree-Fock approximation an analytic expression for the critical value U(c) < 0 of the coupling strength is obtained below which the system becomes unstable towards the formation of incoherent local pairs. The single-particle excitation spectrum for different regimes of the attraction strength U and particle concentration n is investigated, and the U-n phase diagram is discussed.