Dipolon theory of energy gap parameters at finite temperature and transition temperatures Tc and T∗ in high-temperature superconductors

Abstract

First temperature dependent regular and pseudo-energy gap parameters and regular and pseudo-transition temperatures arising from the same physical origin have been calculated in the strong coupling formalism. Temperature dependent many-body field-theoretic techniques have been developed, as an extension of our previous zero-temperature formalism, to derive temperature dependent general expressions 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 making use of dipolon propagator and electron Green’s function taking 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. The theory takes into account all necessary and important correlations. Our self-consistent calculations utilize the previously symmetry predicted two energy gap parameters for superconducting cuprates, one being antisymmetric (“as”) with respect to the exchange of the k x and k y components of vector k → and the other being symmetric (“s”) with respect to the exchange of k x and k y . Our present temperature dependent self-consistent solutions of the real and imaginary parts of the Δ ( k → , ω ) , Z ( k → , ω ) and χ ( k → , ω ) confirm the existence of these two (different) solutions and conclude 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. Explicit temperature dependent self-consistent calculations have been performed here for Bi 2Sr 2CaCu 2O 8+ δ as well as Bi 2Sr 2CaCu 2O 8 giving temperature dependent energy gap parameters and corresponding transition temperatures. The calculated results are consistent with the available experimental data. Our calculated results take into account different appropriate sets of electron–electron Coulomb interaction energy and screening constant with Pauling’s as well as TKS polarizabilities for various ions in these systems. The uncertainties in the calculated values of the energy gap parameters and transition temperatures are mainly due to uncertainties in the polarizabilities of the ions, Coulomb energy and the screening constant. Migdal vertex correction has been estimated. The calculated results have been discussed with respect to the available experiments. In particular, our calculations show that T ∗ is greater than the corresponding T c and they ( T c and T ∗) have the same physical origin, in agreement with experiments. Our results have been discussed and directions for further investigations have been pointed out.