Methods of the Many-Body Theory in Superconductivity

  • Alexandre ZagoskinEmail author
Part of the Graduate Texts in Physics book series (GTP)


Physical origins of superconductivity and peculiarity of the superconducting state. Cooper pairing. Instability of the normal state of a system of fermions. BCS Hamiltonian. Elementary excitations in a superconductor. Nambu-Gor’kov formalism for matrix Green’s functions in a superconductor. Andreev reflection and Josephson effect. Coulomb blockade.


Books and Reviews

  1. 1.
    Beenakker, C.W.J., van Houten, H.: Phys. Rev. Lett. 66, 3056 (1991)Google Scholar
  2. 2.
    Barone, A., Paternó, G.: Physics and Applications of the Josephson Effect. Wiley, New York (1982)CrossRefGoogle Scholar
  3. 3.
    Basov, D.N., Tinusk, T.: Electrodynamics of high-\(T_c\) superconductors. Rev. Mod. Phys. 77, 721 (2005) (Section VIII)Google Scholar
  4. 4.
    Landau, L.D., Lifshitz, E.M.: Quantum Mechanics, Non-relativistic Theory (Landau and Lifshitz Course of Theoretical Physics, v. III.). Pergamon Press, Oxford (1989)Google Scholar
  5. 5.
    Lifshitz, E.M., Pitaevskii, L.P.: Statistical Physics pt.II (Landau and Lifshitz Course of theoretical physics, v. IX.). Pergamon Press, Oxford (1980) (Ch. 5. Theory of Superconducting Fermi Gas)Google Scholar
  6. 6.
    Maiti, S., Chubukov, A.V.: Superconductivity from repulsive interaction, . In: Proceedings of the XVII Training Course in the Physics of Strongly Correlated Systems, Vietri sul Mare (Salerno), Italy (2013)
  7. 7.
    Rammer, J., Smith, H.: Quantum field-theoretical methods in transport theory of metals. Rev. Mod. Phys. 58, 323 (1986)Google Scholar
  8. 8.
    Svidzinskii A.V.: Spatially Inhomogeneous Problems in the Theory of Superconductivity. Nauka, Moscow (1982) (in Russian) (An excellent book, using both functional integration and Green’s functions formalism)Google Scholar
  9. 9.
    Tinkham M.: Introduction to Superconductivity, 2nd edn. McGraw Hill, New York (1996) (A classical treatise on superconductivity. This second edition contains a special chapter (Ch.7) devoted to effects in small (mesoscopic) Josephson junctions)Google Scholar
  10. 10.
    Tsuei, C.C., Kirtley, J.R.: Pairing symmetry in cuprate superconductors. Rev. Mod. Phys. 72, 969 (2000)ADSCrossRefGoogle Scholar
  11. 11.
    Van Harlingen, D.J.: Phase-sensitive tests of the symmetry of the pairing state in the high-temperature superconductors-evidence for \(d_{x^{2}-y^{2}}\) symmetry. Rev. Mod. Phys. 67, 515 (1995)ADSCrossRefGoogle Scholar
  12. 12.
    Vonsovsky, S.V., Izyumov Yu A., Kurmaev, E.Z.: Superconductivity of Transition Metals, Their Alloys and Compounds. Springer, Berlin (1982) (Chapter 2 of this comprehensive book provides both formulation of Nambu-Gor’kov formalism and detailed derivation and analysis of Eliashberg equations. In Chapter 3 the formalism is generalized on case of magnetic metal)Google Scholar
  13. 13.
    Zagoskin, A.M.: Quantum Engineering: Theory and Design of Quantum Coherent Structures. Cambridge University Press, Cambridge (2011). (Chapters 2 and 4 contain a review of theory and experiment on superconducting quantum bits (qubits) and qubit arrays)Google Scholar


  1. 14.
    Bagwell, P.F.: Phys. Rev. B 49, 6481 (1994)CrossRefGoogle Scholar
  2. 15.
    Bardeen, J., Johnson, J.L.: Phys. Rev. B 5, 72 (1972)ADSCrossRefGoogle Scholar
  3. 16.
    Blonder, G.E., Tinkham, M., Klapwijk, T.M.: Phys. Rev. B 25, 4515 (1982)ADSCrossRefGoogle Scholar
  4. 17.
    Cuevas, J.C., Martín-Rodero, A., Levy Yeyati A.: Phys. Rev. B 54, 7366 (1996)Google Scholar
  5. 18.
    Huck, A., van Otterlo, A., Sigrist, M.: Phys. Rev. B 56, 14163 (1997)ADSCrossRefGoogle Scholar
  6. 19.
    Ishii, G.: Prog. Theor. Phys. 44, 1525 (1970)ADSCrossRefGoogle Scholar
  7. 20.
    Joyez, P., Lafarge, P., Filipe, A., Esteve, D., Devoret, M.H.: Phys. Rev. Lett. 72, 2458 (1994)ADSCrossRefGoogle Scholar
  8. 21.
    Kohn, W., Luttinger, J.M.: Phys. Rev. Lett. 15, 524 (1965)ADSCrossRefMathSciNetGoogle Scholar
  9. 22.
    Kulik, I.O.: Sov. Phys. JETP 30, 944 (1970)ADSGoogle Scholar
  10. 23.
    Kulik, I.O., Omelyanchuk, A.N.: Fiz. Nizk. Temp. 3, 945; 4, 296 (Sov. J. Low Temp. Phys. 3, 459; 4, 142) (1977)Google Scholar
  11. 24.
    Matveev, K.A., Gisselfält, M.. Glazman, L.I., Jonson, M., Shekhter, R.I.: Phys. Rev. Lett. 70, 2940 (1993)Google Scholar
  12. 25.
    Takayanagi, H., Akazaki, T., Nitta, J.: Surf. Sci. 361–362, 298 (1996)CrossRefGoogle Scholar
  13. 26.
    Tsuei, C.C., et al.: Science 271, 329 (1996)ADSCrossRefGoogle Scholar
  14. 27.
    Yang, C.N.: Rev. Mod. Phys. 34, 694 (1962)ADSCrossRefGoogle Scholar
  15. 28.
    Zagoskin, A.M.: J. Phys.: Condens. Matter 9, L419 (1997)ADSGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of PhysicsLoughborough UniversityLeicestershireUK

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