Abstract
The expression for the electron–phonon coupling coefficient (gk) is obtained by solving a six order polynomial equation obtained via the quantum dynamical many-body theory of the electron and phonon Green’s function for high-temperature superconductors (HTSs). The developed equation depends on the temperature; electron, phonon, and pairon frequencies; and distribution functions. The YBa2Cu3O7−δ cuprate superconductor has been used for the purpose of analysis and is found to be in agreement with the fact that gk decreases with the increase in temperature above 0 K. The distinct behavior obtained via dispersion for gk in different directions, [100] and [010], marked the anisotropy of electron–phonon coupling in HTSs. The derived expression for gk is further used for the evaluation of the superconducting gap via the Bardeen–Cooper–Schrieffer and the McMillan gap equation and both superconducting gap equations approach the Tc value for YBa2Cu3O7−δ, and the obtained reduced gap ratio [2Δ(0)/kBTc] is found to be in the limit of the reduced gap ratio of HTSs.
Highlights
The observation of high-temperature superconductivity by Bednorz and Müller1 and Wu et al.2 in layered cuprates is assuredly one of the remarkable experimental discoveries of the twentieth century
In order to derive the expression for the electron–phonon coupling coefficient for high-temperature superconductors (HTSs), the contribution of electron–phonon interactions has been considered in the form
Where me is the mass of the electron and vp is the phonon velocity. It can be recognized from the obtained expression for the electron–phonon coupling coefficient [Eq (17)] that it comprises the effects of frequencies and distribution functions and shows very strong temperature dependence
Summary
The observation of high-temperature superconductivity by Bednorz and Müller and Wu et al. in layered cuprates is assuredly one of the remarkable experimental discoveries of the twentieth century. A number of theoretical and experimental results have marked the signature of electron–phonon coupling in high-Tc superconductors.. In 1957, an ultimate microscopic theory for superconductivity was discovered by Bardeen, Cooper, and Schrieffer (BCS theory), which spells out the phenomenon of superconductivity by an effective attraction between electrons through exchange of virtual phonons, resulting in electron–phonon coupling to form Cooper pairs. In the present work, based on many-body theory, the expression for the electron–phonon coupling coefficient has been derived as a function of temperature. Along with temperature, it depends on phonon, electron, and pairon frequencies as well as distribution functions. Aij and bij are the range and softening parameters, respectively, with i and j being the ions and rij ≡ r being the distance apart
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