GAP ENERGY, ISOTOPE EFFECT AND COHERENCE LENGTH IN HIGH T_c-OXIDES

Abstract

The model recently developed by Getino et al. to study the gap energy in the van Hove scenario in high-Tc oxides is extended to study the isotope effect and the coherence length in these materials. We propose a more realistic model by: (1) adding a constant term to the singular logarithmic contribution, within the weak coupling BCS theory and a phonon mediated interaction; (2) assuming the Fermi level lies close to a van Hove singularity for optimal doping. The equations obtained from this approach, are applicable to low as well as high temperature superconductors successfully the superconducting temperature transition Tc, the gap energy ∆, the isotope effect α and the coherence length ξ. For high-Tc oxides, it is found that when the effective mass of carriers tends to be large, α and ξ tend to be small where Tc and ∆ became larges. We shown that when the effective mass of carriers is enclosed between 5 me and 15 me, the values obtained for these parameters are in agreement with experimental data.

THEORY OF THE ISOTOPE EFFECT AND SUPERCONDUCTING TRANSITION TEMPERATURE IN HIGH-Tc OXIDES

“…For the new superconductors and in absence of magnetic excitations, we find the expression of α obtained in a previous work. 23 In this case, we remark that this coefficient decreases from 0.34 to 0.32 when the Debye energy varies from 0.025 eV to 0.065 eV (Fig. 2).…”

“…23 In this case, if we replace the coupling constant λ p = n 1 V p by λ p − µ * where µ * the pseudopotential given by 27…”

“…In this scenario, various approaches have attempted to explain the anomalous behavior of the isotope effect in high-T c superconductors. [18][19][20][21][22][23][24] Other works have tried to explain the small value of this coefficient. 25,26 In all these works, it has been considered only the phonon interaction.…”

Isotope effect due to the super-exchange interaction and van Hove singularity in high-Tc superconductors

“…[8][9][10][11][12][13][14] Many properties of these new compounds have been explained with the singularity in the density of states and electron-phonon interaction. [15][16][17][18][19] This DOS is logarithmic n 1 ln(D/e) near the van Hove singularity and constant n 0 near the band edge. 20 In the absence of doping, the CuO 2 plane has strong antiferromagnetic correlation, and the insulating antiferromagnetic state is converted into a metallic paramagnetic one with doping.…”

“…These values are very small than those obtained by using the electron-phonon interaction. [15][16][17][18][19] When the coupling constant k m increases the superconducting transition temperature T c increases while the isotope coefficient a decreases. In the weak coupling limit, we obtain large T c (39 -135 K) and small isotope coefficient a (0.0277 -0.004).…”