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

Affiliation(s)

Department of Physics, Faculty of Science, Sudan University of Science and Technology, Khartoum, Sudan.

Department of Physics, Faculty of Science, Sudan University of Science and Technology, Khartoum, Sudan.

ABSTRACT

Superconductivity is one of the most important phenomena in solid state physics. Its theoretical framework at low critical temperature *T*_{c }is based on Bardeen, Cooper and Schrieffer theory (BCS). But at high *T*_{c }above 135, this theory suffers from some setbacks. It cannot explain how the resistivity abruptly drops to zero below *T*_{c }, 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 *T*_{c }. These expressions are mathematically simple and are in conformity with experimental results.

Cite this paper

Elhai, R. , Hilo, M. , Elgani, R. and Allah, M. (2013) Using the tight binding approximation in deriving the quantum critical temperature superconductivity equation.*Natural Science*, **5**, 941-946. doi: 10.4236/ns.2013.58114.

Elhai, R. , Hilo, M. , Elgani, R. and Allah, M. (2013) Using the tight binding approximation in deriving the quantum critical temperature superconductivity equation.

References

[1] Kittle, C. (1976) Introduction to solid state physics. 5th Edition, John Wiley & Sons, New York.

[2] Alexandrov, A.S. (2003) Theory of superconductivity from weak to strong coupling, IoP Publishing, Norwich.

[3] Tsui, D.C, Stormer, H.L and Gossard, A.C (1982) Two dimensional magneto transport in the extreme quantum limit. Physical Review Letters, 48, 1559. doi:10.1103/PhysRevLett.48.1559

[4] Khwjali, A. (2009) Solid state physics. Azzaph press, Sudan.

[5] Halliday, D. and Resnick, R. (1974) Fundamentals of physics. John Wiley, Sons, Inc., New York.

[6] Burns, G. (1985) Solid state physics. Academic Press, Cambridge, 755 p.

[1] Kittle, C. (1976) Introduction to solid state physics. 5th Edition, John Wiley & Sons, New York.

[2] Alexandrov, A.S. (2003) Theory of superconductivity from weak to strong coupling, IoP Publishing, Norwich.

[3] Tsui, D.C, Stormer, H.L and Gossard, A.C (1982) Two dimensional magneto transport in the extreme quantum limit. Physical Review Letters, 48, 1559. doi:10.1103/PhysRevLett.48.1559

[4] Khwjali, A. (2009) Solid state physics. Azzaph press, Sudan.

[5] Halliday, D. and Resnick, R. (1974) Fundamentals of physics. John Wiley, Sons, Inc., New York.

[6] Burns, G. (1985) Solid state physics. Academic Press, Cambridge, 755 p.