Dipolon theory of energy gap parameters in high-temperature superconductors at zero temperature

Abstract

Many-body field-theoretic techniques involving dipolon propagator and electron Green’s function have been used to derive the general expressions at zero temperature for the renormalized energy gap parameter Δ(k→,ω), the gap renormalization parameter Z(k→,ω), and energy band renormalization parameter χ(k→,ω) for momentum k→ and frequency ω. The present theory takes into account explicitly the dressed dipolons as mediators of superconductivity, the screened Coulomb repulsion, and nonrigid electron energy bands considering retardation and damping effects and electron-hole asymmetry. For superconducting cuprates it has been shown by symmetry considerations that, in the lowest order approximations, there exists two energy gap parameters, one being antisymmetric (as) with respect to the exchange of the kx and ky components of vector k→ and the other being symmetric (s) with respect to the exchange of kx and ky. The antisymmetric solution is a dx2−y2 wave (i.e., ∝ [cos(kx)−cos(ky)]) which changes sign with respect to the exchange of kx and ky, and the symmetric solution which is highly asymmetric s wave or equivalently, a combination of a symmetric s wave and absolute value of dx2−y2 wave (i.e. ∝ | [cos(kx)−cos(ky)] | ) which does not change sign with respect to the exchange of kx and ky. Our self-consistent calculations of the real and imaginary parts of Δ(k→,ω), Z(k→,ω), and χ(k→,ω) verify the existence of these two (different) solutions and lead to the conclusion that the antisymmetric solution of the gap parameter corresponds to the observed regular (reg) superconducting energy gap whereas the symmetric solution corresponds to the observed pseudo (pse) energy gap. Calculations have been made for Bi2Sr2CaCu2O8+δ as well as Bi2Sr2CaCu2O8. Explicitly, for Bi2Sr2CaCu2O8+δ superconductor our calculated values of the antisymmetric and symmetric energy gap parameters are Δ0as=22±15 meV and Δ1s=30±10 meV with Δ0s=1.5±1.5 meV, where Δas(k→)=Δ0as [cos(kx)−cos(ky)] and Δs(k→)=Δ0s+Δ1s| [cos(kx)−cos(ky)] |, in agreement with the corresponding experimental results Δ0reg=16.5±1.5 meV, Δ1pse≈24 meV, and Δ0pse=−0.5±2.5 meV. For Bi2Sr2CaCu2O8 superconductor our calculated values of the antisymmetric and the symmetric energy gap parameters are Δ0as=24±13 meV and Δ1s=29±15 meV with Δ0s≈0 which also agree with the corresponding experimental results Δ0reg=16.5±1.5 meV and Δ1pse=30−40 meV with Δ0pse=−0.5±2.5 meV. Our calculations also indicate that the bosonic energy relevant to superconductivity in Bi2Sr2CaCu2O8+δ superconductor is about 60 meV arising from O1,2 dipolon excitations and that the broad bands observed in optical experiments are due to O1,1, O1,2, and O3 dipolon excitations. Relative contributions from the various dipolon modes have been analyzed. One finds that the symmetric longitudinal modes of oxygen dipolons contribute dominantly in energy gap parameters. The uncertainties in the calculated values of the various parameters are due to uncertainties in the values of the polarizability particularly of oxygen ions, the shielding parameter, the repulsive Coulomb energy, and due to the calculational errors. The origin of the experimentally deduced T* values has been discussed in terms of the present theory which reveals that T* is greater than Tc and that they have the same physical origin.

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