Skip to main content
SpringerLink
Log in

Anti-adiabatic State: Ground Electronic State of Superconductors

  • Chapter
  • First Online:
Advances in the Theory of Quantum Systems in Chemistry and Physics

Part of the book series: Progress in Theoretical Chemistry and Physics ((PTCP,volume 22))

Abstract

Based on the non-adiabatic ab initio theory of complex electronic ground states, treating electronic structure as explicitly dependent on nuclear dynamics, i.e. on instantaneous nuclear coordinates Q and momenta P, it has been shown that electron-phonon coupling in superconductors induces temperature-dependent electronic structure instability related to analytic critical point (ACP) fluctuation of bands across the Fermi level (FL). As ACP approaches FL, the adiabatic chemical potential μ ad is substantially reduced to μ antad (μ ad ≫ μ antad < ℏω) and the adiabatic Born-Oppenheimer approximation is violated. Due to the effect of nuclear dynamics, the system is stabilized as an antiadiabatic state of broken symmetry with a gap in its one-particle spectrum. Distorted nuclear structure, which is related to nuclei in the phonon mode r inducing transition to an anti-adiabatic state, has fluxional character. Geometric degeneracy of the antiadiabatic ground state enables formation of mobile bipolarons that can move over lattice in external electric potential as super-carriers without dissipation. Thermodynamic properties in the anti-adiabatic state correspond to thermodynamics of superconductors. It has been shown that Cooper-pair formation is not the primary reason for transition into superconducting state, but it is a consequence of anti-adiabatic state formation and represents correction to electron correlation energy. As illustrative examples, results of application of anti-adiabatic theory in study of superconductors MgB2, YB6, YBa2Cu3O7, Nb3Ge and corresponding (non superconducting) analogues are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    To avoid confusion, it should be stressed that telectron correlation energy as used in this paper stands for improvement of e-e interaction term contribution beyond the Hartree-Fock (HF) level, \({E}_{corr} = {E}_{exact} - {E}_{\mathit{HF}}({E}_{exact} < {E}_{\mathit{HF}})\), as it can be calculated e.g. by (1/r)-perturbation theory in 2nd and higher orders, or by configurations interaction method. In condensed matter physics, electron correlation usually stands for an account for Coulomb e-e interaction at least on Hartree or HF level. On the HF level not only repulsive e-e term is present (like on Hartree level where spin is not considered at all), but also exchange term (fermion Coulomb-hole only for electrons with parallel spins). Correlation energy improves unbalanced treatment of e-e interaction for electrons with parallel and antiparalel spins on HF level.

  2. 2.

    It should be stressed that HF-SCF method with semiempirical INDO Hamiltonian used at band structure calculation [55] overestimates bonding character and consequently band-width, which means that high-energy effects can hardly be studied, but for low-energy physics (like gap opening, kink formation,…) the method is reliable enough at least in a qualitative way.

References

  1. Onnes K (1911) Commun Phys Lab Univ Leiden 124c

    Google Scholar 

  2. Bednorz JG, Muller KA (1986) Z Phys B Condens Matter 64:189

    Article  CAS  Google Scholar 

  3. Hor PH, Meng RL, Wang YQ, Gao L, Hung ZJ, Bechtold J, Forster K, Chu CW (1987) Phys Rev Lett 58:1191

    Google Scholar 

  4. Bardeen J, Cooper LN, Schrieffer JR (1957) Phys Rev 108:1175

    Article  CAS  Google Scholar 

  5. Fröhlich H (1950) Phys Rev 79:845

    Article  Google Scholar 

  6. Fröhlich H (1952) Proc R Soc A215:291

    Google Scholar 

  7. Migdal AB (1958) Zh Eksp Teor Fiz 34:1438; (1958) Sov Phys JETP 7:996

    Google Scholar 

  8. Eliashberg GM (1960) Zh Eksp Teor Fiz 38:996; (1960) 39:1437; (1960) Sov Phys JETP 11:696; (1960) 12:1000

    Google Scholar 

  9. Dagotto E (1994) Rev Mod Phys 66:763

    Article  CAS  Google Scholar 

  10. Anderson PW (1997) The theory of superconductivity in high-Tc cuprates. Princeton University Press, Princeton

    Google Scholar 

  11. Kulic ML (2000) Phys Rep 338:1

    Article  CAS  Google Scholar 

  12. McMillan WJ (1968) Phys Rev B 167:331

    Article  CAS  Google Scholar 

  13. Maier Th, Jarrell M, Pruschke T, Keller J (2000) Phys Rev Lett 85:1524

    Article  CAS  Google Scholar 

  14. Sorella S, Martins GB, Becca F, Gazza C, Capriotti L, Parola A, Dogotto E (2001) Phys Rev Lett 88:117002

    Article  Google Scholar 

  15. White SR, Scalapino D (1998) Phys Rev Lett 80:1272; (1999) Phys Rev B 60:753

    Google Scholar 

  16. Paramekanti A, Randeria M, Trivedi N (2004) Phys Rev B 70:054504

    Article  Google Scholar 

  17. Mourachkin A (2002) High-temperature superconductivity in cuprates. Kluwer Academic, Dordrecht

    Google Scholar 

  18. (a) Fukuoka A, Tokima-Yamamoto A, Itoh M, Usami R, Adachi S, Tamato S (1997) Phys Rev B 55:6612; (b) Frank J (1997) Physica C, 198:282–287

    Google Scholar 

  19. Pringle DJ, Williams GVM, Tallon JL (2000) Phys Rev B 62:12527

    Article  CAS  Google Scholar 

  20. Lanzara A, Bogdanov PV, Zhou XJ, Kellar SA, Feng DL, Lu ED, Yoshida T, Eisaki H, Fujimori A, Kishio K, Shimoyama JI, Noda T, Uchida S, Hussain Z, Shen ZX (2001) Nature 412:510

    Article  CAS  Google Scholar 

  21. Zhou XJ, Yoshida T, Lanzara A, Bogdanov PV, Kellar SA, Shen KM, Yang WL, Ronning F, Sasagawa T, Kakeshita T, Noda T, Eisaki H, Uchida S, Lin CT, Zhou F, Xiong JW, Ti WX, Zhao ZX, Fujimori A, Hassain Z, Shen ZX (2003) Nature 423:398

    Article  CAS  Google Scholar 

  22. Gromko AD, Ferdorov AV, Chuang YD, Koralek JD, Aiura Y, Amaguchi YY, Oka KA, Youchi Ando, Dessau DS (2003) Phys Rev B 68:174520

    Google Scholar 

  23. Cuk T, Baumberger F, Lu DH, Ingle N, Zhou XJ, Eisaki H, Kanenko N, Hussain Z, Devereaux TP, Nagaosa N, Shen Z-X (2004) Phys Rev Lett 93:117003

    Article  CAS  Google Scholar 

  24. Takahashi T, Sato T, Matsui H, Terashima K (2005) New J Phys 7:105

    Article  Google Scholar 

  25. Zhou XJ, Cuk T, Evereaux TPD, Nagaosa N, Shen Z-X (2007) In: Schrieffer JR, Brooks JS (eds) Handbook of high-temperature superconductivity. Springer, New York, p 87

    Chapter  Google Scholar 

  26. Okawa M, Ishizaka K, Uchiyama M, Tadamoto M, Masui T, Wang X-Y, Chen C-T, Watanabe S, Chainani A, Saitoh T, Schin S (2009) Phys Rev B 79:144528

    Article  Google Scholar 

  27. Chung JH, Egami T, McQuinney RJ, Yethiraj M, Arai M, Yokoo T, Petrov Y, Mook HA, Endoch Y, Tajima S, Frost C, Dogan F (2003) Phys Rev B 67:014517

    Article  Google Scholar 

  28. Pintschovius L, Reznik D, Reichardt W, Endoch Y, Hiraka H, Tranquada JM, Uchiama H, Masui T, Tajima S (2004) Phys Rev B 69:214506

    Article  Google Scholar 

  29. (a) Pietronero L (1992) Europhys Lett 17:365; (b) Pietronero L, Strassler S (1992) Europhys Lett 18:627; (c) Pietronero L, Strassler S, Grimaldi C (1995) Phys Rev B 52:10516

    Google Scholar 

  30. Proville L, Aubry S (1999) Eur Phys J B 11:41

    Article  CAS  Google Scholar 

  31. Bonca J, Trugman SA, Batistic I (1999) Phys Rev B 60:1633

    Article  CAS  Google Scholar 

  32. Benedetti P, Zeyher R (1998) Phys Rev B 58:14320

    Article  CAS  Google Scholar 

  33. Fehske H, Loos J, Wellein G (1997) Z Phys B 104:619

    Article  CAS  Google Scholar 

  34. Bishop AR, Salkola M (1995) In: Salje EKH (ed) Polarons and bipolarons in High-tc superconductors and related materials. Cambridge University Press, Cambridge

    Google Scholar 

  35. Alexandrov AS, Kornilovitch PE (2002) J Supercond 15:403

    Article  CAS  Google Scholar 

  36. (a) Alexandrov AS, Runninger J (1981) Phys Rev B 23:1796; (b) Alexandrov AS, Runninger J (1981) Phys Rev B 24:1164; (c) Alexandrov AS (1983) Zh Fiz Chim 57:273; (1983) Rus J Phys Chem 57:167

    Google Scholar 

  37. Scalapino DJ (1969) In: Parks RD (ed) Superconductivity, vol 1. Marcel Dekker, New York, p 449

    Google Scholar 

  38. Allen PB, Dynes RC (1975) Phys Rev B 12

    Google Scholar 

  39. Alexandrov AS (2001) Phys C 363:231

    Article  CAS  Google Scholar 

  40. (a) Grimaldi G, Pietronero L, Strassler S (1995) Phys Rev B 52:10530; (b) Grimaldi G, Pietronero L, Strassler S (1995) Phys Rev Lett 75:1158

    Google Scholar 

  41. (a) Grimaldi G, Cappelluti E, Pietronero L (1998) Europhys Lett 42:667; (b) Grimaldi G, Pietronero L, Scottani M (1999) Europhys J B 10:247; (c) Cappelluti E, Grimaldi G, Pietronero L (2001) Phys Rev B 64:125104; (d) Botti M, Cappelluti E, Grimaldi G, Pietronero L (2002) Phys Rev B 66:054532; (e) Cappelluti E, Ciuchi S, Grimaldi G, Pietronero L (2003) Phys Rev B 68:174509

    Google Scholar 

  42. (a) Alexandrov AS (2003) Theory of superconductivity: from weak to strong coupling. IoP Publishing, Bristol/Philadelphia; (b) Alexandrov AS (2005) arXiv:cond-mat/0508769v4

    Google Scholar 

  43. Alexandrov AS, Edwards PP (2000) Phys C 331:97

    Article  CAS  Google Scholar 

  44. Alexandrov AS (1992) Phys Rev B 23:2838

    Article  Google Scholar 

  45. Hague JP, Kornilovich PE, Samson JH, Alexandrov AS (2007) J Phys Condens Matter 19:255214

    Article  Google Scholar 

  46. Nagamatsu J, Nakagava N, Muranaka T, Zenitani Y, Akimitsu J (2001) Nature 410:63

    Article  CAS  Google Scholar 

  47. An JM, Picket WE (2001) Phys Rev Lett 86:4366

    Article  CAS  Google Scholar 

  48. Yilderim T, Gulseren O, Lynn JW, Brown CM, Udovic TJ, Huang Q, Rogado N, Regan KA, Hayward MA, Slusky JS, He T, Hass MK, Khalifah P, Inumaru K, Cava RJ (2001) Phys Rev Lett 87:037001

    Article  Google Scholar 

  49. Kortus J, Mazin II, Belashchenko KD, Antropov VP, Boyer LL (2001) Phys Rev Lett 86:4656

    Article  CAS  Google Scholar 

  50. Baňacký P (2005) Int J Quantum Chem 101:131

    Article  Google Scholar 

  51. Boeri L, Cappelluti E, Pietronero L (2005) Phys Rev B 71:012501

    Article  Google Scholar 

  52. (a) Baňacký P (2008) J Phys Chem Solids 69:2728; (b) Baňacký P (2008) J Phys Chem Solids 69:2696

    Google Scholar 

  53. Svrček M, Baňacký P, Zajac A (1992) Int J Quantum Chem 43:393; (1992) 43:415; (1992) 43:425; (1992) 43:551

    Google Scholar 

  54. Baňacký P (2010) Phonons and electron correlations in high-temperature and other novel superconductors, vol 2010. Hindawi Publ. Corp, New York. Advances in Condensed Matter Physics, special issue, Article ID 752943. http://www.hindawi.com/journals/acmp/2010/752943.html

  55. Noga J, Baňacký P, Biskupič S, Boča R, Pelikan P, Zajac A (1999) J Comp Chem 20:253

    Article  CAS  Google Scholar 

  56. Pople JA, Beveridge DL (1970) Approximate molecular orbital theory. McGraw-Hill Inc, New York

    Google Scholar 

  57. Boča R (1988) Int J Quant Chem 31:941; (1988) 34:385

    Google Scholar 

  58. Zajac A, Pelikán P, Noga J, Baňacký P, Biskupič S, Svrček M (2000) J Phys Chem B 104:1708

    Article  CAS  Google Scholar 

  59. Zajac A, Pelikán P, Minar J, Noga J, Straka M, Baňacký P, Biskupič S (2000) J Solid State Chem 150:286

    Article  CAS  Google Scholar 

  60. Pelikán P, Kosuth M, Biskupič S, Noga J, Straka M, Zajac A, Baňacký P (2001) Int J Quantum Chem 84:157

    Article  Google Scholar 

  61. Baňacký P (2007) Phys C 460:1115

    Google Scholar 

  62. Lomnytska YF, Kuzma YB (2006) J Alloyes Comp 413:114

    Article  CAS  Google Scholar 

  63. Kutzelnigg W (1997) Mol Phys 90:909

    Article  CAS  Google Scholar 

  64. Svrček M, Baňacký P, Biskupič S, Noga J, Pelikan P, Zajac A (1999) Chem Phys Lett 299:151

    Article  Google Scholar 

  65. Baňacký P (2009) In: Courtland KN (ed) Superconducting cuprates. Nova Science Pbl., New York, Chap 6, pp 187:212

    Google Scholar 

  66. Lu DH, Feng DL, Armitage NP, Shen KM, Damascelli A, Kim C, Ronning F, Shen ZX, Bonn DA, Liang R, Hardy WN, Rykov AI, Tajima S (2001) Phys Rev Lett 86:4370

    Article  CAS  Google Scholar 

  67. Martinez-Samper P, Rodrigo JG, Rubio-Bollinger G, Suderow M, Vieira S, Lee S, Tajima S (2003) Phys C 385:233

    Article  CAS  Google Scholar 

  68. Szabo P, Samuely P, Kacmarek J, Klein T, Marcus J, Fruchart D, Miraglia S, Mareinit C, Jensen AGM (2001) Phys Rev Lett 87:137005

    Article  CAS  Google Scholar 

  69. Marz M, Goll G, Goldacker W, Lortz L (2010) Phys Rev B 82

    Google Scholar 

  70. Matthias BT, Gebale TM, Andres K (1968) Science 159:530

    Article  CAS  Google Scholar 

  71. Lortz L, Wang Y, Tutsch U, Abe S, Meingart C, Popovich P, Knafo W, Schitsevalova N, Pademo YB, Junod A (2006) Phys Rev B 73:024512

    Article  Google Scholar 

  72. Xu Y, Zhang L, Cui T, Li Y, Xie Y, Yu W, Ma Y, Zou G (2007) Phys Rev B 76:214103

    Article  Google Scholar 

  73. Schell G, Winter H, Rietchel H, Gompf F (1982) Phys Rev B 25:1589

    Article  CAS  Google Scholar 

  74. Baňacký P, Svrček M (1993) Int J Quantum Chem 46:475

    Article  Google Scholar 

  75. Smilde HJM, Golubov AA, Ariando RG, Dekkers JM, Haskema S, Blank DHA, Rogalla H, Higenkamp H (2005) Phys Rev Lett 95:257001

    Article  CAS  Google Scholar 

  76. Andersen OK, Lichtenstein AI, Jepsen O, Paulsen F (1995) J Phys Chem Solids 56:1573

    Article  CAS  Google Scholar 

  77. Kouba R, Ambrosch-Draxl C, Zangger B (1999) Phys Rev B 60:9321

    Article  CAS  Google Scholar 

  78. Haghighi H, Kaiser JH, Raynar S, West RN, Liu JZ, Shelton R, Howell RH, Solal F, Fluss ML (1991) Phys Rev Lett 67:382

    Article  CAS  Google Scholar 

  79. Singh D, Pickett WE, van Stetten EC, Berko S (1990) Phys Rev B 42:2696

    Article  CAS  Google Scholar 

Download references

Acknowledgments

The author acknowledges support of the grants VEGA 1/0013/08; 1/0005/11 and Philip E. Hoggan for editing the English.

Author information

Authors and Affiliations

  1. Faculty of Natural Sciences, Institute of Chemistry, Chemical Physics division, Comenius University, Mlynská dolina CH2, 84215, Bratislava, Slovakia

    Pavol Baňacký

Authors
  1. Pavol Baňacký
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. , LASMEA, Clermont University, avenue des Landais 24, Aubiere Cedex, 63177, France

    Philip E. Hoggan

  2. Dept. Quantum Chemistry, Uppsala University, Uppsala, Sweden

    Erkki J. Brändas

  3. Labo. Chimie Physique, CNRS, rue Pierre et Marie Curie 11, Paris, 75005, France

    Jean Maruani

  4. Dept. Chemistry, Michigan State University, Chemistry Building, East Lansing, 48824, Michigan, USA

    Piotr Piecuch

  5. Inst. Matemáticas y Física, Fundamental (IMAFF), CSIC Madrid, C/ Serrano 123, Madrid, 28006, Spain

    Gerardo Delgado-Barrio

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Science+Business Media B.V.

About this chapter

Cite this chapter

Baňacký, P. (2012). Anti-adiabatic State: Ground Electronic State of Superconductors. In: Hoggan, P., Brändas, E., Maruani, J., Piecuch, P., Delgado-Barrio, G. (eds) Advances in the Theory of Quantum Systems in Chemistry and Physics. Progress in Theoretical Chemistry and Physics, vol 22. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2076-3_27

Download citation

Publish with us

Policies and ethics

Search

Navigation