Bose-Einstein Condensation of Cooper-Pairs in the Conventional Superconductors

Yıl 2021, Cilt: 24 Sayı: 3, 238 - 246, 29.08.2021

Ulrich Köbler

https://doi.org/10.5541/ijot.899820

Cited By: 3

Öz

Observed crossover events between different power functions of absolute temperature occurring below about ~1 K in the temperature dependence of the heat capacity or the thermal conductivity of the conventional superconductors are identified as transitions from Maxwell-Boltzmann to Bose-Einstein (BE) statistics of the Cooper-pairs. Because of the low mass of the Cooper pairs of 2me (with me as mass of the electron) and their high density, the BE-condensation temperature, TBE, of the Cooper-pairs is about five orders of magnitude higher than for the dilute alkali atom condensates. The condensation temperature TBE turns out to be proportional to the superconducting transition temperature TSC. From the observed TBE-values it is possible to calculate the density of the Cooper pairs. Assuming that the Cooper pairs form a dense gas of bosons, the diameter of the Cooper-pair orbitals turns out to be equal to the London penetration depth. As a conclusion, due to the large orbital diamagnetism of the Cooper-pairs pairs, only one layer of Cooper-pairs, next to the inner surface of the sample, is sufficient to shield an applied external magnetic field completely.

Anahtar Kelimeler

Bose-Einstein condensation, conventional superconductors, heat capacity, thermal conductivity

Kaynakça

• [1] K.G. Wilson, J. Kogut, The Renormalization Group Theory and the ε Expansion. Phys. Rep. 12C, 75-199, 1974.
• [2] R. Kleiner, W. Buckel, Superconductivity: an introduction, Weinheim, Wiley-VCH, 2016.
• [3] U. Köbler, Universality in the Temperature Dependence of the Heat Capacity of Magnetic Solids. Int. J. Thermodyn. 23, 147-174, 2020.
• [4] U. Köbler, The unresolved deficiencies of the atomistic theories of solid-state physics. to be published in J. Phys. Soc. Jpn.
• [5] U. Köbler, A. Hoser, Experimental Studies of Boson Fields in Solids, Singapore, World Scientific, 2018.
• [6] B.B. Goodman, E. Mendoza, The critical magnetic fields of aluminum, cadmium, gallium and zinc. The London, Edinburgh and Dublin Philosophical Magazine, LXII, 594-602, 1951.
• [7] J. Bardeen, L.N. Cooper, J.R. Schrieffer, Theory of Superconductivity. Phys. Rev. 108, 1175-1204, 1957.
• [8] W.S. Corak, M.P. Garfunkel, C.B. Satterthwaite, A. Wexler, Atomic Heats of Copper Silver and Gold from 1 0K to 5 0K. Phys. Rev. 98, 1699-1708, 1955.
• [9] J.L. Luo et al., Low-Temperature Specific Heat of Superconducting MgB2. Chin. Phys. Lett. 18, 820-822, 2001.
• [10] U. Köbler, On the Thermal Conductivity of Metals and of Insulators. Int. J. Thermodyn. 20, 210-218, 2017.
• [11] A. Hoser, U. Köbler, Functional crossover in the dispersion relations of magnons and phonons. J. Phys.: Conf. Series 746, 012062, 1-8, 2015. [12] U. Köbler, On the Distinction between Debye Bosons and Acoustic Phonons. Int. J. Thermodyn. 18, 277- 284, 2015. [13] U. Köbler, The Importance of the Debye Bosons (Sound Waves) for the Lattice Dynamics of Solids. Int. J. Thermodyn. 23, 59-79, 2020.
• [14] C.B. Satterthwaite, Thermal Conductivity of Normal and Superconducting Aluminum. Phys. Rev. 125, 873-876, 1962.
• [15] U. Köbler, Boson Fields in Ordered Magnets. Acta. Phys. Pol. A 127, 350-352, 2015.
• [16] U. Köbler, Bosonic and magnonic magnon dispersions. J. Magn. Magn. Mater. 502, 166533, 2020.
• [17] B.J.C. van der Hoeven, Jr., P.H. Keesom, Specific Heat of Lead and Lead Alloys. Phys. Rev. 137, A103- A107, 1965.
• [18] Ch. Enss, S. Hunklinger, Low-Temperature Physics, Berlin, Springer, 2005.
• [19] C.J. Pethick, H. Smith, Bose-Einstein Condensation in Dilute Gases, Cambridge University Press, 2008.
• [20] D.G. Fried, T.C. Killian, L. Willmann, D. Landhuis, S.C. Moss, D. Kleppner, T.J. Greytak, Bose-Einstein Condensation of Atomic Hydrogen. Phys. Rev. Lett. 81, 3811-3814, 1998.
• [21] R. Radebaugh, P.H. Keesom, Low-Temperature Thermodynamic Properties of Vanadium, I. Superconducting and Normal States. Phys. Rev. 149, 209-216, 1966.
• [22] N.E. Phillips, Low-Temperature Heat Capacities of Gallium, Cadmium and Copper. Phys. Rev. 134, A385- A391, 1964.
• [23] N.E. Phillips, Heat Capacity of Aluminum between 0.1 0K and 4.0 0K. Phys. Rev. 114, 676-686, 1959.
• [24] C.A. Bryant, P.H. Keesom, Specific Heat of Indium below 1 oK, Phys. Rev. Lett. 4, 460-462, 1960.
• [25] J.R. Clement, E.H. Quinnell, Atomic Heat of Indium below 20 oK, Phys. Rev. 92, 258-267, 1953.
• [26] U. Köbler, Crossover phenomena in the critical range near magnetic ordering transition. J. Magn. Magn. Mater. 453, 17-29, 2018. [27] Y.S. Touloukian, R.W. Powell, C.Y. Ho, P.G. Klemens, Thermophysical Properties of Matter, vol. 1: Thermal Conducivity of Metallic Elements and Alloys, New York, IFI/Plenum, 1970.
• [28] R.F.S. Hearmon, The elastic constants of crystals and other anisotropic materials. Landolt-Börnstein, vol. III/11, ed. by K.-H. Hellwege and A.M. Hellwege, 1-286, Berlin, Springer, 1979.
• [29] B.J.C. van der Hoeven, Jr., P.H. Keesom, Specific Heat of Niobium between 0.4 and 4.2 oK. Phys. Rev. 134, A1320-A1321, 1964.
• [30] M. v. Laue, F. London, H. London, Zur Theorie der Supraleitung, Z. Physik 96, 359-364, 1935.
• [31] F. London, H. London, Supraleitung und Diamagnetismus. Physica 2, 341-354, 1935.