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Superconductivity

Semiconductor Physics

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Abstract

There exists a large diversity of superconductors following different mechanisms to achieve the superconducting phase. Low-temperature superconductivity appears in metals and degenerate semiconductors; it is induced by the formation of electron pairs in a bipolaron state referred to as Cooper pair. The superconductive state is separated from the normal-conductivity state by an energy gap below the Fermi energy. This gap appears at the critical temperature and widens as the temperature decreases. In type I low-temperature superconductors an external magnetic field is expelled from the bulk up to an upper value, which eliminates superconductivity. In type II superconductors an array of flux lines penetrates into the bulk above a lower critical field, creating a mixed normal and superconductive phase up to the upper critical field.

High-temperature superconductivity of type II is observed mostly in layered compounds such as cuprates and iron pnictides, with critical temperatures exceeding 100 K. Superconductivity in these materials is usually carried by hole pairs and requires sufficient doping. The mechanism of pair formation differs from that in metals and involves an interaction with spin fluctuations. The symmetry of the layered superconductive system and of the superconductive gap is lower than in the basically isotropic metals; in cuprates pairs with a lateral d symmetry are found.

K. W. Böer: deceased

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Notes

  1. 1.

    The polaron state introduced in Sect. 1.2 of chapter “Carrier-Transport Equations”.

  2. 2.

    g(EF) was used in Eq. 1 at T = 0 K.

  3. 3.

    Exponents β in Tc ∝ M–β are 0.5 for isotopes of Hg, Cd, and Tl, 0.48 for Pb, 0.47 for Sn; also smaller effect are observed, e.g., β = 0.33 for Mo and 0.2 for Os.

  4. 4.

    λ is related to the density of superconducting carriers ns by \( \lambda =\sqrt{m_{\mathrm{Cp}}/\left({\mu}_0{q}_{\mathrm{Cp}}^2\ {n}_{\mathrm{s}}\right)} \), where mCp = 2mn and qCp = −2e.

  5. 5.

    Doping can also be performed by changing the composition with oxygen. An excess of oxygen extracts electrons from the environment to form O2− ions; these electrons partly come from the CuO2 layers, leaving holes.

  6. 6.

    Metallic conductivity is found above the Néel temperature, which, e.g., for undoped YBa2Cu3O6+x, is quite high (500 K for x = 0, decreasing with doping). Below this temperature antiferromagnetic ordering leads to an energy gap and consequently to insolating behavior.

  7. 7.

    The flux-line melting temperature is about 75 K for a material with Tc = 93 K, and is somewhat lower for Tc = 125 K material.

  8. 8.

    All high-Tc superconductors are strong spin-density wave systems.

  9. 9.

    Confinement of three-dimensional excitons to two dimensions leads to a substantial increase of the exciton binding-energy see Sect. 2.1 of chapter “Excitons”. The superlattice-like (2D) structure of the ceramic superconductors could provide such a confinement.

  10. 10.

    Here excitons, or polarons, become more tightly bound (Frenkel excitons). Earlier observation of heavy-fermion superconductors (Stewart 1984; Joynt and Taillefer 2002) may point toward the assistance of more tightly bound polarons (with mn ≅ 200 m0) in forming superconducting compounds, (e.g., CeCu2Si2 or UPt3).

References

  • Allen PB, Mitrović B (1982) Theory of superconducting Tc. Solid State Phys 37:1

    Google Scholar 

  • Anderson P (1987) The resonating valence bond state in La2CuO4 and superconductivity. Science 235:1196

    Article  ADS  Google Scholar 

  • Appel J (1966) Superconductivity in pseudoferroelectrics. Phys Rev Lett 17:1045

    Google Scholar 

  • Bardeen J, Cooper LN, Schrieffer JR (1957) Theory of superconductivity. Phys Rev 108:1175.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Batlogg B (1991) Physical properties of high-Tc superconductors. Phys Today 44:44

    Article  Google Scholar 

  • Bednorz JG, Müller KA (1986) Possible high-Tc superconductivity in the Ba-La-Cu-O system. Z Phys B 64:189

    Article  ADS  Google Scholar 

  • Bill A, Morawitz H, Kresin VZ (2003) Electronic collective modes and superconductivity in layered conductors. Phys Rev B 68:144519

    Article  ADS  Google Scholar 

  • Blatt JM (1961) Persistent ring currents in an ideal Bose gas. Phys Rev Lett 7:82

    Article  ADS  MATH  Google Scholar 

  • Boebinger GS, Ando A, Passner A, Kimura T, Okuya M, Shimoyama J, Kishio K, Tamasaku K, Ichikawa N, Uchida S (1996) Insulator-to-metal crossover in the normal state of La2−xSrxCuO4 near optimum doping. Phys Rev Lett 77:5417

    Article  ADS  Google Scholar 

  • Buckel W, Kleiner R (2004) Superconductivity: fundamentals and applications. Wiley-VCH, Weinheim

    Book  Google Scholar 

  • Chen G, Goddard WA (1988) The magnon pairing mechanism of superconductivity in cuprate ceramics. Science 239:899

    Article  ADS  Google Scholar 

  • Chu CW (1997) High-temperature superconducting materials: a decade of impressive advancement of Tc. IEEE Trans Appl Supercond 7:80

    Article  ADS  Google Scholar 

  • Chu CW, Hor PH, Meng RL, Gao L, Huang ZJ, Wang YQ (1987) Evidence for superconductivity above 40 K in the La-Ba-Cu-O compound system. Phys Rev Lett 58:405

    Article  ADS  Google Scholar 

  • Cohen ML (1964) Superconductivity in many-valley semiconductors and in semimetals. Phys Rev 134:A511

    Google Scholar 

  • De Gennes PG (1966) Superconductivity in metals and alloys. Benjamin, New York

    MATH  Google Scholar 

  • Fetter AL, Walecka JD (1971) Quantum theory of many-particle systems. McGraw-Hill, New York

    Google Scholar 

  • Gurevich VL, Larkin AI, Firsov YuA (1962) On the possibility of superconductivity in semiconductors. Sov Phys Sol State 4:131

    Google Scholar 

  • Gurvitch M, Fiory AT (1987) Resistivity of La1.825Sr0.175CuO4 and YBa2Cu3O7 to 1100 K: absence of saturation and its implications. Phys Rev Lett 59:1337

    Article  ADS  Google Scholar 

  • Harris JM, Yan YF, Ong NP (1992) Experimental test of the T2 law for the Hall angle from Tc to 500 K in oxygen-reduced YBa2Cu3O6+x crystals. Phys Rev B 46:14293

    Article  ADS  Google Scholar 

  • Harshman DR, Mills AP (1992) Concerning the nature of high-Tc superconductivity: Survey of experimental properties and implications for interlayer coupling. Phys Rev B 45:10684

    Google Scholar 

  • Hein RA , Gibson JW, Mazelsky R, Miller RC, Hulm JK (1964) Superconductivity in germanium telluride. Phys Rev Lett 12:320

    Google Scholar 

  • Hosono H, Ren Z-A (2009) Focus on iron-based superconductors. New J Phys 11:025003

    Article  Google Scholar 

  • Hussey NE (2007) Normal state transport properties. In: Schrieffer JR, Brooks JS (eds) Handbook of high-temperature superconductivity. Theory and experiment. Springer, New York, pp 399–425

    Chapter  Google Scholar 

  • Hwang HY, Batlogg B, Takagi H, Kao HL, Kwo J, Cava RJ, Krajewski JJ, Peck WF Jr (1994) Scaling of the temperature dependent Hall effect in La2−xSrxCuO4. Phys Rev Lett 72:2636

    Article  ADS  Google Scholar 

  • Ishida K, Nakai Y, Hosono H (2009) To what extent iron-pnictide new superconductors have been clarified: a progress report. J Phys Soc Jpn 78:062001

    Article  ADS  Google Scholar 

  • Ishiguro T, Yamaji K, Saito G (1998) Organic superconductors. Springer, Berlin

    Book  Google Scholar 

  • Jérome D (1994) Organic superconductors. Solid State Commun 92:89

    Article  ADS  Google Scholar 

  • Joynt R, Taillefer L (2002) The superconducting phases of UPt3. Rev Mod Phys 74:235

    Article  ADS  Google Scholar 

  • Kirtley JR, Tsuei CC, Ariando A, Verwijs CJM, Harkema S, Hilgenkamp H (2006) Angle-resolved phase-sensitive determination of the in-plane gap symmetry in YBa2Cu3O7−δ. Nat Phys 2:190

    Article  Google Scholar 

  • Koitzsch A, Borisenko SV, Kordyuk AA, Kim TK, Knupfer M, Fink J, Golden MS, Koops W, Berger H, Keimer B, Lin CT, Ono S, Ando Y, Follath R (2004) Origin of the shadow Fermi surface in Bi-based cuprates. Phys Rev B 69:220505

    Article  ADS  Google Scholar 

  • Lee PA, Nagaosa N, Wen XG (2006) Doping a Mott insulator: physics of high-temperature superconductivity. Rev Mod Phys 78:17

    Article  ADS  Google Scholar 

  • Leggett AJ (2006) What DO we know about high Tc? Nat Phys 2:134

    Article  Google Scholar 

  • Little WA (1992) Generalization of BCS superconductivity to non-phonon mediated interactions: the excitonic interaction. In: Maekawa S, Sato M (eds) Physics of high-temperature superconductors. Springer, Heidelberg, pp 113–124

    Chapter  Google Scholar 

  • London F, London H (1935) The electromagnetic equations of the supraconductor. Proc Roy Soc (London) A 149:72

    Google Scholar 

  • Matsushita T (2014) Flux pinning in superconductors. Springer, Berlin

    Book  Google Scholar 

  • Meissner W, Ochsenfeld R (1933) Ein neuer Effekt bei Eintritt der Supraleitfähigkeit. Naturwiss 21:787 (A new effect at the onset of superconductivity, in German)

    Google Scholar 

  • Nakayama Y, Motohashi T, Otzschi K, Shimoyama J, Kishio K (2000) In-plane anisotropy of critical current density in Bi1.6Pb0.6Sr1.8CaCu2.0Oy. Physica C 341:1477

    Article  ADS  Google Scholar 

  • Onsager L (1961) Magnetic flux through a superconducting ring. Phys Rev Lett 7:50

    Article  ADS  Google Scholar 

  • Plakida N (2010) High-temperature cuprate superconductors. Springer, Berlin

    Book  Google Scholar 

  • Platé M, Mottershead JDF, Elfimov IS, Peets DC, Liang R, Bonn DA, Hardy WN, Chiuzbaian S, Falub M, Shi M, Patthey L, Damascelli A (2005) Fermi surface and quasiparticle excitations of overdoped Tl2Ba2CuO6+δ. Phys Rev Lett 95:077001

    Article  ADS  Google Scholar 

  • Renner C, Revaz B, Genoud J-Y, Kadowaki K, Fischer Ø (1998) Pseudogap precursor of the superconducting gap in under- and overdoped Bi2Sr2CaCu2O8+δ. Phys Rev Lett 80:149

    Article  ADS  Google Scholar 

  • Reynolds CA, Serin B, Wright WH, Nesbitt LB (1950) Superconductivity of isotopes of mercury. Phys Rev 78:487

    Article  ADS  Google Scholar 

  • Schooley JF,Hosler WR, Cohen ML (1964) Superconductivity in semiconducting SrTiO3. Phys Rev Let. 12:474

    Google Scholar 

  • Schrieffer JR (1964) Theory of superconductivity. Benjamin, New York

    MATH  Google Scholar 

  • Schrieffer JR (1991) The influence of spin fluctuations on the physical properties of high Tc materials. Physica C 185:17

    Article  ADS  Google Scholar 

  • Schrieffer JR, Wen X-G, Zhang S-C (1988) Spin-bag mechanism of high-temperature superconductivity. Phys Rev Lett 60:944

    Article  ADS  Google Scholar 

  • Schwarz A, Liebmann M, Pi UH, Wiesendanger R (2010) Real space visualization of thermal fluctuations in a triangular flux-line lattice. New J Phys 12:033022

    Article  Google Scholar 

  • Segawa K, Ando Y (2004) Intrinsic Hall response of the CuO2 planes in a chain-plane composite system of YBa2Cu3Oy. Phys Rev B 69:104521

    Article  ADS  Google Scholar 

  • Stewart GR (1984) Heavy-fermion systems. Rev Mod Phys 56:755

    Article  ADS  Google Scholar 

  • Tajima Y, Hikita M, Ishii T, Fuke H, Sugiyama K, Date M, Yamagishi A, Katsui A, Hidaka Y, Iwata T, Tsurumi S (1988) Upper critical field and resistivity of single-crystal EuBa2Cu3Oy: direct measurements under high field up to 50 T. Phys Rev B 37:7956

    Article  ADS  Google Scholar 

  • Tajima S, Kaneko T, Wada T, Tomeno I, Tai K, Mizuo Y, Yamauchi H, Koshizuka K, Ido T, Uchida S (1991) Plasmons in high-Tc superconducting cuprates. Physica C 185:1013

    Article  ADS  Google Scholar 

  • Tallon JL, Bernhard C, Shaked H, Hitterman RL, Jorgensen JD (1995) Generic superconducting phase behavior in high-Tc cuprates: Tc variation with hole concentration in YBa2Cu3O7−δ. Phys Rev B 51:12911

    Article  ADS  Google Scholar 

  • Terai T, Kobayashi T, Ito Y, Kishio K, Shimoyama J (1997) Change in superconducting properties of Bi-2212 single crystal due to fast neutron irradiation followed by thermal annealing. Physica C 282:2285

    Article  ADS  Google Scholar 

  • Theuss H (1993) Flux line pinning by point defects in single crystalline high-Tc. Physica C 208:155

    Article  ADS  Google Scholar 

  • Townsend P, Sutton J (1962) Investigation by electron tunneling of the superconducting energy gaps in Nb, Ta, Sn and Pb. Phys Rev 128:591

    Article  ADS  Google Scholar 

  • Tsuei CC, Kirtley JR, Ren ZF, Wang JH, Raffy H, Li ZZ (1997) Pure dx2−y2 order-parameter symmetry in the tetragonal superconductor Tl2Ba2CuO6+δ. Nature 387:481

    Article  ADS  Google Scholar 

  • van Dover RB, Gyorgy EM, Schneemeyer LF, Mitchell JW, Rao KV, Puzniak R, Waszczak JV (1989) Critical currents near 106 A cm−2 at 77 K in neutron-irradiated single-crystal YBa2Cu3O7. Nature 342:55

    Article  ADS  Google Scholar 

  • Varma CM (1997) Non-fermi-liquid states and pairing instability of a general model of copper oxide metals. Phys Rev B 55:14554

    Article  ADS  Google Scholar 

  • Varma CM, Schmitt-Rink S, Abrahams E (1987) Charge transfer excitations and superconductivity in “ionic” metals. Solid State Commun 62:681

    Article  ADS  Google Scholar 

  • Xu X, Fang J, Cao X, Li K (1995) The critical current density and the pinning mechanism of epitaxial YBa2Cu3O7−δ thin films. Solid State Commun 93:291

    Article  ADS  Google Scholar 

  • Zhang W, Bennemann KH (1995) Theory of magnetic textures in high-Tc superconductors: electron versus hole doping dependence. J Phys Condens Matter 7:1335

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Naples, FL, USA

    Karl W. Böer

  2. Institut für Festkörperphysik, EW5-1, Technische Universität Berlin, Berlin, Germany

    Udo W. Pohl

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Böer, K.W., Pohl, U.W. (2020). Superconductivity. In: Semiconductor Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-06540-3_26-3

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  • DOI: https://doi.org/10.1007/978-3-319-06540-3_26-3

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    Superconductivity
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    DOI: https://doi.org/10.1007/978-3-319-06540-3_26-4

  2. Superconductivity
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    DOI: https://doi.org/10.1007/978-3-319-06540-3_26-3

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    Superconductivity
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    DOI: https://doi.org/10.1007/978-3-319-06540-3_26-1

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