The Bosons of the Conventional Superconductors

Yıl 2023, Cilt: 26 Sayı: 1, 26 - 35, 14.03.2023

Ulrich Köbler

https://doi.org/10.5541/ijot.1169691

Cited By: 1

Öz

For the conventional superconductors it will be shown that not only the superconducting energy gap, Egap(T=0), and the critical field, Bc(T=0), but also the London penetration depth, λL(T=0), scale in a reasonable approximation with the superconducting transition temperature, TSC, as ~TSC, ~TSC2 and ~T-1/2, respectively. From these scaling relations the conclusion obtained earlier, using a completely different method, is confirmed that the London penetration depth corresponds to the diameter of the Cooper-pairs. As a consequence, only one layer of Cooper pairs is sufficient to shield an external magnetic field completely. The large diamagnetism of the superconductors is caused by the large orbital area of the Cooper-pairs. From the fact that, in the zero-field ground state, the temperature dependence of the superconducting heat capacity is given above and below TSC by power functions of absolute temperature it follows that the only critical point is T=0. The superconducting transitions of the element superconductors, therefore, are all within the critical range at T=0. As a consequence, above and below TSC there is short-range order only. As we know from Renormalization Group (RG) theory, in the critical range the dynamics is the dynamics of a boson field, exclusively. Evidently, the Cooper-pairs have to be considered as the short-range ordered units created by this boson field. It is reasonable to assume that the relevant bosons in the superconducting state are identical with the bosons giving rise to the universal linear-in-T electronic heat capacity above TSC. Plausibility arguments will be given that these bosons must be electric quadrupole radiation generated by the non-spherical charge distributions in the soft zones between the metal atoms. The radiation field emitted by an electric quadrupole can be assumed to be essentially curled or circular. In the ordered state below TSC, the bosons are condensed in resonating spherical modes which encapsulate the two Cooper-pair electrons and shield their charge perfectly.

Anahtar Kelimeler

Cooper-pairs, Ordered boson fields, Stimulated emission

Destekleyen Kurum

Forschungszentrum Jülich, Institute PGI. 52425 Jülich, Germany

Kaynakça

• J. Bardeen, L.N. Cooper, J.R. Schrieffer, “Theory of Superconductivity”, Phys. Rev. vol. 108, pp. 1175-1204, 1957.
• A.M. Kadin, “Spatial Structure of the Cooper Pair” Supercond. And Novel Magnetism, vol. 20, pp. 285-282, 2007.
• N. Andrenacci, M. Capezzali, H. Beck, “Internal structure of fluctuating Cooper pairs”, Eur. Phys. J. B, vol. 53, pp. 417-432, 2006.
• W.V. Pogosov, “Applicability of Bardeen-Cooper-Schrieffer theory to small-sized superconductors: Role of Cooper-pair binding energy”, Solid State Commun. vol. 207, pp. 1-4, 2015.
• T. Örd, K. Rägo, A. Vargunin, G. Litak, “Strong temperature effect on the size of the Cooper-pairs in a two-band superconductor” Eur. Phys. J . B, 91:2, pp. 1-6, 2018.
• N. Ahmad, S.H. Naqib, “Estimation of Cooper pair density and its relation to the critical current density in Y(Ca)BCO high-Tc cuprate superconductors” Results in Physics, vol. 17, pp.103054, 1-6, 2020.
• F.D. Neto, M.A. Neto, O.D. Rodriguez Salmon, “Cooper-pair size and binding energy for unconventional superconducting systems”, Physica C:Supercond. and its Appl. 549 pp. 159-163, 2018.
• T. Böhm et al., ”Microscopic origin of Cooper pairing in the iron-based superconductor Ba1-xKxFe2As2”, Quantum Materials, 3:48, pp. 1-6, 2018.
• U. Köbler, “On the precise value of the magnetic ordering temperature”, J. Magn. Magn. Mater. 546, pp. 168839, 1-6, 2022.
• U. Köbler, “New Explanation of the Excitation Spectra of Conventional Superconductors J. of Low Temp. Phys. https://doi.org/10.1007/s10909-022-02886-7.
• A. Hoser, U. Köbler, “Boson Fields in Ordered Magnets”, Acta Phys. Pol. A, vol. 127, pp. 350-352, 2015.
• J. Goldstone, A. Salam, S. Weinberg, “Broken Symmetries”, Phys. Rev. vol 127, pp. 965-970, 1962.
• U. Köbler, “Universality in the temperature dependence of the heat capacity of magnetic solids”, Int. J. of Thermo. vol. 23, pp.147-174, 2020.
• A. Hoser, U. Köbler, “Linear spin chains in paramagnetic and in ordered bulk magnets”, Physica B, vol. 551, pp.83-88, 2018.
• U. Köbler, “Bosonic and magnonic magnon dispersions”, J. Magn. Magn. Mater. vol. 502, pp. 166533, 1-18, 2020.
• U. Köbler, “Bose-Einstein Condensation of Cooper-Pairs in the Conventional Superconductors” Int. J. of Thermo. 24, pp. 238-246, 2021.
• U. Köbler, ”On the Thermal Conductivity of Metals and of Insulators”, Int. J. of Thermo., vol. 20, pp. 210-218, 2017.
• C. Probst, J. Wittig, “Superconductivity of bcc Barium under Pressure”, Phys. Rev. Lett. Vol. 39, pp.1161-1163, 1977.
• C.J. Pethick, H. Smith: ”Bose-Einstein condensation in dilute gases”, Cambridge Univ. Press, 2008.
• B. Mühlschlegel, “Die thermodynamischen Funktionen des Supraleiters“, Z. Physik, vol. 155, pp. 313-327, 1959.
• U. Köbler, A. Hoser: Experimental Studies of Boson Fields in Solids, World Scientific, Singapore, 2018.
• G.K. White, “Thermal Expansion at Low Temperatures IV. Normal and Superconducting Lead”, Phil. Mag. Vol. 7, pp. 271-278, 1962.
• U. Köbler, “One-Dimensional Boson Fields in the Critical Range of EuS and EuO”, Acta Phys. Pol. A, vol. 128, pp. 398-407, 2015.
• O.W. Dietrich, “Critical magnetic fluctuations in MnF2”, J. Phys. C: Solid State Phys. vol. 2, pp. 2022-2036, 1969.
• B.B. Goodman, E. Mendoza, “The Critical Magnetic Field of Aluminium, Gallium and Zinc”, Philosophical Magazine vol. 42, pp. 594-602, 1951.
• R. Kleiner, W. Buckel: Superconductivity: an introduction, Wiley-VCH, Weinheim, 2016.
• W. Meissner, R. Ochsenfeld, “Ein neuer Effekt bei Eintritt der Supraleitfähigkeit“ Naturwissenschaften, vol. 21, pp. 787-788, 1933.
• F. London, H. London, “Supraleitung und Diamagnetismus”, Physica, vol. 2, pp. 341-354, 1935.
• M. v. Laue, F. u. H. London, “Zur Theorie der Supraleitung”, Z. Physik, vol. 96, pp. 359-364, 1935.
• K.G. Wilson, J. Kogut, “The renormalization group and the ε expansion”, Phys. Rep. vol. 12C, pp. 75-199, 1974.
• U. Köbler, “Crossover phenomena in the critical range near magnetic ordering transition”, J. Magn. Magn. Mater. Vol. 453, pp. 17-29, 2018.
• P. Townsend, J. Sutton, “Investigation by Electron Tunneling of the Superconducting Energy Gaps in Nb, Ta, Sn, and Pb”, Phys. Rev. vol. 128, pp. 591-595, 1962.
• S.M. Anlage, B.W. Langley, G. Deutscher, J. Halbritter, M.R. Beasley, “Measurements of the temperature dependence of the magnetic penetration depth in Yba2Cu3O7-δ superconducting thin films”, Phys. Rev. B, vol. 44, pp. 9764-9767, 1991.
• M. Lang, N. Toyota, T. Sasaki, H. Sato, “Magnetic Penetration Depth of κ-(BEDT-TTF)2Cu(NCS)2: Strong Evidence for Conventional Cooper Pairing” Phys. Rev. Lett. vol. 69, pp. 1443-1446, 1992.
• A.A. Golubov, A. Brinkman, O.V. Dolgov, J. Kortus, O. Jepsen, “Multiband model for penetration depth in MgB2”, Phys. Rev. B vol. 66, pp. 054524, 1-5, 2002.
• R.K. Pathria: Statistical Mechanics, 2nd ed., Butterworth-Heinemann, Oxford, 1996.
• P. Heller, “Experimental investigations of critical phenomena”, Rep. Prog. Phys. vol. 30, pp. 731-826, 1967.
• U. Köbler, V. Bodryakov, “On the melting process of solids”, Int. J. of Thermo. vol. 18, pp. 200-204, 2015.
• A. Hubert, R. Schäfer: Magnetic Domains, Springer, Berlin, 2000.
• E. Fatuzzo, W.J. Merz: Ferroelectricity, North-Holland, Amsterdam, 1967.
• U. Köbler, A. Hoser, C. Thomas: ”Dimensionality crossover upon magnetic saturation of Fe, Ni and Co”, J. Magn. Magn. Mater. vol. 321, pp. 1202-1208, 2009.
• U. Köbler, “Sound waves and phonons in crystalline solids”, J. Chem. Thermo., to be published.
• U. Köbler, “Magnetic ordering by boson fields”, Eur. Phys. J. B., to be published.
• U. Köbler, “Thermal decay of magnons in MnF2”, J. Magn. Magn. Mater. vol. 551, pp. 169129, 1-9, 2022.