Low Dimensionality as a Factor Stimulating Formation of the Cooper-Like Pairs Characteristic for Superconductors

ABSTRACT

The electron gas examined in a very thin potential tube exhibits some special kind of the excited pairs making them similar to the Cooper pairs. The coupling energy of the pair can be calculated as an amount of energy required to transform the excitation energy of a coupled pair into the one-electron excitation energy. For an extremely thin potential tube the coupling energy of the pair tends to infinity. The gas energy is unstable with respect to the pair excitation which provides a kind of gap near the Fermi level. A decisive part of the gap energy is due to the electron-electron interaction. The gap is attained on condition the length of a thin potential box exceeds some critical value. In the next step, a coherence length in the gas is obtained. This length, combined with a critical magnetic field representing a transition from a superconducting to a normal state, allows us to calculate the penetration depth of the magnetic field for the singlet and triplet excitations. The penetration depth together with the critical magnetic field and energy gap can provide us with a critical current, as well as critical temperature for the superconducting state.

The electron gas examined in a very thin potential tube exhibits some special kind of the excited pairs making them similar to the Cooper pairs. The coupling energy of the pair can be calculated as an amount of energy required to transform the excitation energy of a coupled pair into the one-electron excitation energy. For an extremely thin potential tube the coupling energy of the pair tends to infinity. The gas energy is unstable with respect to the pair excitation which provides a kind of gap near the Fermi level. A decisive part of the gap energy is due to the electron-electron interaction. The gap is attained on condition the length of a thin potential box exceeds some critical value. In the next step, a coherence length in the gas is obtained. This length, combined with a critical magnetic field representing a transition from a superconducting to a normal state, allows us to calculate the penetration depth of the magnetic field for the singlet and triplet excitations. The penetration depth together with the critical magnetic field and energy gap can provide us with a critical current, as well as critical temperature for the superconducting state.

Cite this paper

nullS. Olszewski and T. Roliński, "Low Dimensionality as a Factor Stimulating Formation of the Cooper-Like Pairs Characteristic for Superconductors,"*Journal of Modern Physics*, Vol. 1 No. 5, 2010, pp. 328-339. doi: 10.4236/jmp.2010.15047.

nullS. Olszewski and T. Roliński, "Low Dimensionality as a Factor Stimulating Formation of the Cooper-Like Pairs Characteristic for Superconductors,"

References

[1] N. P. Butch, M. C. de Andrade and M. B. Maple, “Resource Letter Scy-3: Superconductivity,” American Journal of Physics, Vol. 76, No. 2, 2008, pp. 106-118.

[2] Y. P. Huang and D. W. Wang, “Quantum-Phase Diagrams of Fermionic Dipolar Gases in a Planar Array of One-Dimensional Tables,” Physical Review A, Vol. 80, No. 053610, 2009, p. 10.

[3] N. Belmechri, G. Abramovici and M. Herititier, “Phase Diagram and Critical Fields of Organic Quasi-1d Superconductors in an Applied Magnetic Field,” Physica B, Vol. 404, No. 19, 2009, pp. 3131-3133.

[4] K. Kajiwara, M. Tsuchiizu, Y. Suzumura and C. Bourbonnais, “Mechanism of the Singlet to Triplet Superconductivity Crossover in Quasi-One-Dimensional Organic Conductors,” Journal of the Physical Society of Japan, Vol. 78, No. 104702, 2009, p. 11.

[5] D. Jerome, A. Mazaud, M. Ribault and K. Bechgaard, “Superconductivity in a Synthetic Organic Conductor ,” Journal de Physique Lettres (Paris), Vol. 41, No. 4, 1980, pp. L95-L98.

[6] K. Bechgaard, C. J. Jacobsen, K. Mortensen, H. J. Pedersen and N. Thorup, “The Properies of Five Highly Conducting Salts: , , , , and , Derived from Tetramethyltetraselenafulvalene (TMTSF),” Solid State Communications, Vol. 33, No. 11, 1980, pp. 1119-1125.

[7] D. Jerome, “One Dimensional Organic Superconductors: beyond the Fermii Liquid Description,” Journal de Physique IV (Paris), Vol. 10, No. PR3, 2000, pp. 69-84.

[8] D. Jerome, “ Organic Superconductors and Related Physics,” Molecular Crystals and Liquid Crystals, Vol. 380, No. 1, 2002, pp. 3-13.

[9] N. Dupuis, C. Bourbonnais and J. C. Nickel, “Superconductivity and Antiferromagnetism in Quasi-One-Dimensional Organic Conductors,” Journal of Low Temperature Physics, Vol. 32, No. 4-5, 2006, pp. 380-391.

[10] W. A. Little, “Possibility of Synthesizing an Organic Superconductor,” Physical Review, Vol. 134, No. 6A, 1964, pp. A1416-A1424.

[11] Y. Fuseya and M. Ogata, “Increase of Superconducting Correlation due to Dimensionality Change in Quasi-One- Dimensional Conductors,” Journal of the Physical Society of Japan, Vol. 76, No. 093071, 2007, p. 4.

[12] I. J. Lee, S. E. Brown and M. J. Naughton, “Unconventional Superconductivity in a Quasi-One-Dimensional System ,” Journal of the Physical Society of Japan, Vol. 75, No. 051011, 2006, p. 9.

[13] J. Friedel, “Quasi-Low-Dimensionality in a Weak Coupling Limit,” Physica C, Vol. 153-155, 1988, pp. 1610- 1616.

[14] C. Bourbonnais and L. G. Caron, “New Mechanism of Phase Transitions in Quasi-One-Dimensional Conductors,” Europhysics Letters, Vol. 5, No. 3, 1988, pp. 209- 215.

[15] H. Eyring, J. Walter and G. E. Kimball, “Quantum Chemistry,” Wiley, New York, 1957.

[16] C. C. J. Roothaan, “New Developments in Molecular Orbital Theory,” Reviews of Modern Physics, Vol. 23, No. 2, 1951, pp. 69-89.

[17] S. Olszewski, “Hartree-Fock Approximation for the One- Dimensional Electron Gas,” Zeitschrift für Physik B, Vol. 45, No. 4, 1982, pp. 297-306.

[18] C. Kittel, “Quantum Theory of Solids,” 2nd Edition, Wiley, New York, 1987.

[19] M. Cyrot and R. Pavuna, “Introduction to Superconductivity and High- Materials,” World Scientific, Singapore, 1992.

[20] N. H. March, W. H. Young and S. Sampanthar, “Many- Body Problem in Quantum Mechanics,” University Press, Cambridge, 1967.

[21] E. A. Lynton, “Superconductivity,” Methuen, London, 1962.

[22] E. Perfetto and J. Gonzalez, “Electronic Correlations of Small Diameter Carbon Nanotubes,” Journal of Physics: Condensed Matter, Vol. 18, No. 33, 2006, pp. s2105- s2114.

[23] J. M. Ziman, “Principles of the Theory of Solids,” University Press, Cambridge, 1972.

[24] M. R. Schafroth, “Theoretical Aspects of Superconductivity,” In: F. Seitz and D. Turnbull, Eds., Solid State Physics, New York, 1960, pp. 293-498.

[25] C. Kittel, “Introduction to Solid State Physics,” 7th Edition, Wiley, New York, 1996.

[26] D. Ivanenko and A. Sokolov, “Classical Field Theory,”(in Russian), GITTL, Moscow, 1949.

[1] N. P. Butch, M. C. de Andrade and M. B. Maple, “Resource Letter Scy-3: Superconductivity,” American Journal of Physics, Vol. 76, No. 2, 2008, pp. 106-118.

[2] Y. P. Huang and D. W. Wang, “Quantum-Phase Diagrams of Fermionic Dipolar Gases in a Planar Array of One-Dimensional Tables,” Physical Review A, Vol. 80, No. 053610, 2009, p. 10.

[3] N. Belmechri, G. Abramovici and M. Herititier, “Phase Diagram and Critical Fields of Organic Quasi-1d Superconductors in an Applied Magnetic Field,” Physica B, Vol. 404, No. 19, 2009, pp. 3131-3133.

[4] K. Kajiwara, M. Tsuchiizu, Y. Suzumura and C. Bourbonnais, “Mechanism of the Singlet to Triplet Superconductivity Crossover in Quasi-One-Dimensional Organic Conductors,” Journal of the Physical Society of Japan, Vol. 78, No. 104702, 2009, p. 11.

[5] D. Jerome, A. Mazaud, M. Ribault and K. Bechgaard, “Superconductivity in a Synthetic Organic Conductor ,” Journal de Physique Lettres (Paris), Vol. 41, No. 4, 1980, pp. L95-L98.

[6] K. Bechgaard, C. J. Jacobsen, K. Mortensen, H. J. Pedersen and N. Thorup, “The Properies of Five Highly Conducting Salts: , , , , and , Derived from Tetramethyltetraselenafulvalene (TMTSF),” Solid State Communications, Vol. 33, No. 11, 1980, pp. 1119-1125.

[7] D. Jerome, “One Dimensional Organic Superconductors: beyond the Fermii Liquid Description,” Journal de Physique IV (Paris), Vol. 10, No. PR3, 2000, pp. 69-84.

[8] D. Jerome, “ Organic Superconductors and Related Physics,” Molecular Crystals and Liquid Crystals, Vol. 380, No. 1, 2002, pp. 3-13.

[9] N. Dupuis, C. Bourbonnais and J. C. Nickel, “Superconductivity and Antiferromagnetism in Quasi-One-Dimensional Organic Conductors,” Journal of Low Temperature Physics, Vol. 32, No. 4-5, 2006, pp. 380-391.

[10] W. A. Little, “Possibility of Synthesizing an Organic Superconductor,” Physical Review, Vol. 134, No. 6A, 1964, pp. A1416-A1424.

[11] Y. Fuseya and M. Ogata, “Increase of Superconducting Correlation due to Dimensionality Change in Quasi-One- Dimensional Conductors,” Journal of the Physical Society of Japan, Vol. 76, No. 093071, 2007, p. 4.

[12] I. J. Lee, S. E. Brown and M. J. Naughton, “Unconventional Superconductivity in a Quasi-One-Dimensional System ,” Journal of the Physical Society of Japan, Vol. 75, No. 051011, 2006, p. 9.

[13] J. Friedel, “Quasi-Low-Dimensionality in a Weak Coupling Limit,” Physica C, Vol. 153-155, 1988, pp. 1610- 1616.

[14] C. Bourbonnais and L. G. Caron, “New Mechanism of Phase Transitions in Quasi-One-Dimensional Conductors,” Europhysics Letters, Vol. 5, No. 3, 1988, pp. 209- 215.

[15] H. Eyring, J. Walter and G. E. Kimball, “Quantum Chemistry,” Wiley, New York, 1957.

[16] C. C. J. Roothaan, “New Developments in Molecular Orbital Theory,” Reviews of Modern Physics, Vol. 23, No. 2, 1951, pp. 69-89.

[17] S. Olszewski, “Hartree-Fock Approximation for the One- Dimensional Electron Gas,” Zeitschrift für Physik B, Vol. 45, No. 4, 1982, pp. 297-306.

[18] C. Kittel, “Quantum Theory of Solids,” 2nd Edition, Wiley, New York, 1987.

[19] M. Cyrot and R. Pavuna, “Introduction to Superconductivity and High- Materials,” World Scientific, Singapore, 1992.

[20] N. H. March, W. H. Young and S. Sampanthar, “Many- Body Problem in Quantum Mechanics,” University Press, Cambridge, 1967.

[21] E. A. Lynton, “Superconductivity,” Methuen, London, 1962.

[22] E. Perfetto and J. Gonzalez, “Electronic Correlations of Small Diameter Carbon Nanotubes,” Journal of Physics: Condensed Matter, Vol. 18, No. 33, 2006, pp. s2105- s2114.

[23] J. M. Ziman, “Principles of the Theory of Solids,” University Press, Cambridge, 1972.

[24] M. R. Schafroth, “Theoretical Aspects of Superconductivity,” In: F. Seitz and D. Turnbull, Eds., Solid State Physics, New York, 1960, pp. 293-498.

[25] C. Kittel, “Introduction to Solid State Physics,” 7th Edition, Wiley, New York, 1996.

[26] D. Ivanenko and A. Sokolov, “Classical Field Theory,”(in Russian), GITTL, Moscow, 1949.