Using the tight binding approximation in deriving the quantum critical temperature superconductivity equation

R Abd Elhai,R Abd Elgani,M H M Hilo,M D Abd Allah

doi:10.4236/ns.2013.58114

Abstract

Superconductivity is one of the most important phenomena in solid state physics. Its theoretical framework at low critical temperature Tc is based on Bardeen, Cooper and Schrieffer theory (BCS). But at high Tc above 135, this theory suffers from some setbacks. It cannot explain how the resistivity abruptly drops to zero below Tc , besides the explanation of the so called pseudo gap, isotope and pressure effect, in addition to the phase transition from insulating to super-conductivity state. The models proposed to cure this drawback are mainly based on Hubbard model which has a mathematical complex framework. In this work a model based on quantum mechanics besides generalized special relativity and plasma physics. It is utilized to get new modified Schr?dinger equation sensitive to temperature. An expression for quantum resistance is also obtained which shows existence of critical temperature beyond which the resistance drops to zero. It gives an expression which shows the relation between the energy gap and Tc . These expressions are mathematically simple and are in conformity with experimental results.

Highlights

Superconductivity (SC) was discovered in 1911 in the Leiden laboratory of Kamerlingh Onnes when a so called “blue boy” noticed that the resistivity of Hg metal vanished abruptly at about 4 K
Ogg Jr. proposed a root to high-temperature superconductivity (HTSC) introducing electron pairs in 1946 and Ginzburg and Landau proposed the phenomenological theory of the superconducting phase transition in 1950 providing a comprehensive understanding of the electromagnetic properties below Tc [2]
Where the energy gap is found to be Δ ~ 1.75kTc [6]. This model predicts that Schrödinger equation can be derived by using a new expression of energy obtained from the plasma equation

Summary

Introduction

Superconductivity (SC) was discovered in 1911 in the Leiden laboratory of Kamerlingh Onnes when a so called “blue boy” (local high school student recruited for the tedious job of monitoring experiments) noticed that the resistivity of Hg metal vanished abruptly at about 4 K. Phenomenological models with predictive power were developed in the 30’s and 40’s of the last century [1], F and H London developed the successful phenomenological approach in 1935 describing the behavior of superconductors in the external magnetic field. Superconductors have been studied intensively for their fundamental interest and for the promise of technological applications which would be possible if a material which superconducts at room temperature was discovered. Until 1986, critical temperatures (Tc’s) at which resistance disappears were always less than about 23 K

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