Table of Contents Author Guidelines Submit a Manuscript
Advances in Condensed Matter Physics
Volume 2010, Article ID 350787, 14 pages
http://dx.doi.org/10.1155/2010/350787
Review Article

Existence of an Intermediate Metallic Phase at the SDW-CDW Crossover Region in the One-Dimensional Holstein-Hubbard Model at Half-Filling

School of Physics, University of Hyderabad, Hyderabad 500 046, India

Received 5 September 2009; Accepted 8 December 2009

Academic Editor: Alexandre Sasha Alexandrov

Copyright © 2010 Ashok Chatterjee. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. G. Bednorz and K. A. Müller, “Possible high Tc superconductivity in the Ba–La–Cu–O system,” Zeitschrift für Physik B, vol. 64, no. 2, pp. 189–193, 1986. View at Publisher · View at Google Scholar · View at Scopus
  2. J. W. Halley, Ed., Theories of High Temperature Superconductivity, Addison Wesley, Harlow, UK, 1988.
  3. T. Jarlborg, “Band structure and electron-phonon coupling in the La1xSrCuO4 superconductors,” Helvetica Physica Acta, vol. 61, p. 421, 1988. View at Google Scholar
  4. R. E. Cohen, W. E. Pickett, H. Krakauer, and D. A. Papaconstan-topoulos, “High Tc superconductors as ionic metals and the role of phonons in high Tc superconductivity,” Phase Transitions, vol. 22, no. 1–4, pp. 167–183, 1990. View at Google Scholar
  5. R. E. Cohen, W. E. Pickett, and H. Krakauer, “Theoretical determination of strong electron-phonon coupling in YBa2Cu3O7,” Physical Review Letters, vol. 64, no. 21, pp. 2575–2578, 1990. View at Publisher · View at Google Scholar · View at Scopus
  6. C. O. Rodriguez, A. I. Liechtenstein, I. I. Mazin, O. Jepsen, O. K. Andersen, and M. Methfessol, “Optical near-zone-center phonons and their interaction with electrons in YBa2Cu3O7: results of the local-density approximation,” Physical Review B, vol. 42, no. 4, pp. 2692–2695, 1990. View at Publisher · View at Google Scholar · View at Scopus
  7. R. Zeyher, “Improtance of long-range electron-phonon coupling in high-Tc superconductors,” Zeitschrift für Physik B, vol. 80, no. 2, pp. 187–192, 1990. View at Publisher · View at Google Scholar · View at Scopus
  8. B. K. Chakraverty, D. Feinberg, Z. Hang, and M. Avignon, “Squeezed bipolaronic states and high temperature superconductivity in BaLaCuO systems,” Solid State Communications, vol. 64, no. 8, pp. 1147–1151, 1987. View at Google Scholar · View at Scopus
  9. D. Emin, “Formation, motion, and high-temperature superconductivity of large bipolarons,” Physical Review Letters, vol. 62, no. 13, pp. 1544–1547, 1989. View at Publisher · View at Google Scholar · View at Scopus
  10. D. Emin and M. S. Hillery, “Formation of a large singlet bipolaron: application to high-temperature bipolaronic superconductivity,” Physical Review B, vol. 39, no. 10, pp. 6575–6593, 1989. View at Publisher · View at Google Scholar · View at Scopus
  11. J. Ranninger, in Proceedings of the Conference on Lattice Effects in High Tc Superconductors, Y. Bar-Yam, T. Egami, J. Mustre de Leon, and A. R. Bishop, Eds., p. 389, 1992.
  12. S. Sil and A. Chatterjee, “Multi-dimensional Fröhlich bipolaron and dimensional scaling,” International Journal of Modern Physics B, vol. 4, no. 11-12, pp. 1879–1888, 1990. View at Google Scholar
  13. S. Sil and A. Chatterjee, “Stability of large optical singlet bipolarons, many-particle effects and high temperature superconductivity,” Modern Physics Letters B, vol. 6, no. 15, pp. 959–966, 1992. View at Publisher · View at Google Scholar
  14. J. R. Hardy and J. W. Hocken, “Possible origins of high-Tc superconductivity,” Physical Review Letters, vol. 60, no. 21, pp. 2191–2193, 1988. View at Publisher · View at Google Scholar · View at Scopus
  15. A. S. Alexandrov and N. F. Mott, “Bipolarons,” Reports on Progress in Physics, vol. 57, no. 12, pp. 1197–1288, 1994. View at Publisher · View at Google Scholar · View at Scopus
  16. R. Micnas, J. Ranninger, and S. Robaszkiewicz, “Superconductivity in narrow-band systems with local nonretarded attractive interactions,” Reviews of Modern Physics, vol. 62, no. 1, pp. 113–171, 1990. View at Publisher · View at Google Scholar · View at Scopus
  17. A. J. Mills, P. B. Littlewood, and B. I. Shraiman, “Double exchange alone does not explain the resistivity of La1xSrxMnO3,” Physical Review Letters, vol. 74, no. 25, pp. 5144–5147, 1995. View at Publisher · View at Google Scholar · View at Scopus
  18. K. H. Kim, J. Y. Gu, H. S. Choi, G. W. Park, and T. W. Noh, “Frequency shifts of the internal phonon modes in La0.7Ca0.3Mno3,” Physical Review Letters, vol. 77, no. 9, pp. 1877–1880, 1996. View at Publisher · View at Google Scholar · View at Scopus
  19. R. P. Sharma, L. E. Rehn, P. M. Baldo, and J. Z. Liu, “Direct evidence of anomalous Cu-O vibrational modes near Tc in ErBa2Cu3O7δ,” Physical Review Letters, vol. 62, no. 24, pp. 2869–2872, 1989. View at Publisher · View at Google Scholar · View at Scopus
  20. R. P. Sharma, L. E. Rehn, P. M. Baldo, and J. Z. Liu, “Shift of phonon anomaly with Tc observed in (Y,Er)Ba2Cu3O7δ- by ion channeling,” Physical Review B, vol. 40, no. 16, pp. 11396–11399, 1989. View at Publisher · View at Google Scholar · View at Scopus
  21. M. Arai, K. Yamada, Y. Hidaka et al., “Anomaly of phonon state of superconducting YBa2Cu3O7 studied by inelastic neutron scattering,” Physical Review Letters, vol. 69, no. 2, pp. 359–362, 1992. View at Publisher · View at Google Scholar · View at Scopus
  22. C. M. Foster, A. J. Heeger, Y. H. Kim, G. Stucky, and N. Herron, “Photogenerated carriers in La2CuO4, YBa2Cu3O7δ and TI2Ba2Ca(1x)GdxCu2O8: polarizability-induced pairing of polarons,” Synthetic Metals, vol. 33, no. 2, pp. 171–183, 1989. View at Google Scholar · View at Scopus
  23. D. Mihailović, C. M. Foster, K. Voss, and A. J. Heeger, “Application of the polaron-transport theory to σ(ω) in TI2Ba2Ca1xGdxCu2O8, YBa2Cu3O7δ, and La2xSrxCuO4,” Physical Review B, vol. 42, no. 13, pp. 7989–7993, 1990. View at Publisher · View at Google Scholar · View at Scopus
  24. S. D. Conradson, I. D. Raistrick, and A. R. Bishop, “Axial oxygen-centered lattice instabilities and high-temperature superconductivity,” Science, vol. 248, no. 4961, pp. 1394–1398, 1990. View at Google Scholar · View at Scopus
  25. J. Mustre de Leon, S. D. Conradson, I. Batistic, and A. R. Bishop, “Evidence for an axial oxygen-centered lattice fluctuation associated with the superconducting transition in YBa2Cu3O7,” Physical Review Letters, vol. 65, no. 13, pp. 1675–1678, 1990. View at Publisher · View at Google Scholar · View at Scopus
  26. H. A. Mook, M. Mostoller, J. A. Harvey, N. W. Hill, B. C. Chakoumakos, and B. C. Sales, “Observation of phonon softening at the superconducting transition in Bi2Sr2CaCu2O8,” Physical Review Letters, vol. 65, no. 21, pp. 2712–2715, 1990. View at Publisher · View at Google Scholar · View at Scopus
  27. H. A. Mook, B. C. Chakoumakos, M. Mostoller, A. T. Boothroyd, and D. M. Paul, “Phonons and superconductivity in Bi2Sr2CaCu2O8,” Physical Review Letters, vol. 69, no. 15, pp. 2272–2275, 1992. View at Publisher · View at Google Scholar · View at Scopus
  28. T. Holstein, “Studies of polaron motion—part I: the molecular-crystal model,” Annals of Physics, vol. 8, no. 3, pp. 325–342, 1959. View at Google Scholar · View at Scopus
  29. T. K. Mitra, A. Chatterjee, and S. Mukhopadhyay, “Polarons,” Physics Reports, vol. 153, no. 2-3, pp. 91–207, 1987. View at Google Scholar · View at Scopus
  30. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, “Theory of superconductivity,” Physical Review, vol. 108, no. 5, pp. 1175–1204, 1957. View at Publisher · View at Google Scholar · View at Scopus
  31. A. Alexandrov and J. Ranninger, “Theory of bipolarons and bipolaronic bands,” Physical Review B, vol. 23, no. 4, pp. 1796–1801, 1981. View at Publisher · View at Google Scholar · View at Scopus
  32. A. N. Das and S. Sil, “Electron-phonon interaction in a strongly correlated Hubbard system,” Physica C, vol. 161, no. 3, pp. 325–330, 1989. View at Google Scholar · View at Scopus
  33. E. Berger, P. Valaśĕk, and W. von der Linden, “Two-dimensional Hubbard-Holstein model,” Physical Review B, vol. 52, no. 7, pp. 4806–4814, 1995. View at Publisher · View at Google Scholar · View at Scopus
  34. S. Sil and B. Bhattacharyya, “Effect of electron-phonon interaction on a one-dimensional correlated electron system,” Physical Review B, vol. 54, no. 20, pp. 14349–14354, 1996. View at Google Scholar · View at Scopus
  35. C.-H. Pao and H.-B. Schüttler, “Superconducting instability in the Holstein-Hubbard model: a numerical renormalization-group study,” Physical Review B, vol. 57, no. 9, pp. 5051–5054, 1998. View at Google Scholar · View at Scopus
  36. A. Weiße, H. Fehske, G. Wellein, and A. R. Bishop, “Optimized phonon approach for the diagonalization of electron-phonon problems,” Physical Review B, vol. 62, no. 2, pp. R747–R750, 2000. View at Google Scholar · View at Scopus
  37. V. Cataudella, G. De Filippis, and G. Iadonisi, “Polaron features of the one-dimensional Holstein molecular crystal model,” Physical Review B, vol. 62, no. 3, pp. 1496–1499, 2000. View at Google Scholar · View at Scopus
  38. W. Koller, A. C. Hewson, and D. M. Edwards, “Polaronic quasiparticles in a strongly correlated electron band,” Physical Review Letters, vol. 95, no. 25, Article ID 256401, 4 pages, 2005. View at Publisher · View at Google Scholar · View at Scopus
  39. G. Sangiovanni, M. Capone, C. Castellani, and M. Grilli, “Electron-phonon interaction close to a mott transition,” Physical Review Letters, vol. 94, no. 2, Article ID 026401, 4 pages, 2005. View at Publisher · View at Google Scholar · View at Scopus
  40. P. Barone, R. Raimondi, M. Capone, and C. Castellani, “Effective electron-phonon coupling and polaronic transition in the presence of strong correlation,” Physical Review B, vol. 73, no. 8, Article ID 085120, 5 pages, 2006. View at Publisher · View at Google Scholar · View at Scopus
  41. Y. Takada, “Superconductivity in the half-filled Hubbard-Holstein model in the antiadiabatic region,” Journal of the Physical Society of Japan, vol. 65, no. 6, pp. 1544–1547, 1996. View at Google Scholar · View at Scopus
  42. E. Jeckelmann, C. Zhang, and S. R. White, “Metal-insulator transition in the one-dimensional Holstein model at half filling,” Physical Review B, vol. 60, no. 11, pp. 7950–7955, 1999. View at Google Scholar · View at Scopus
  43. Q. Wang, H. Zheng, and M. Avignon, “Phase diagram and optical conductivity of the one-dimensional spinless Holstein model,” Physical Review B, vol. 63, no. 1, Article ID 014305, 5 pages, 2001. View at Google Scholar · View at Scopus
  44. Y. Takada and A. Chatterjee, “Possibility of a metallic phase in the charge-density-wave–spin-density-wave crossover region in the one-dimensional Hubbard-Holstein model at half filling,” Physical Review B, vol. 67, no. 8, Article ID 081102, 4 pages, 2003. View at Publisher · View at Google Scholar · View at Scopus
  45. A. Chatterjee and Y. Takada, “The Hubbard-Holstein model with anharmonic phonons in one dimension,” Journal of the Physical Society of Japan, vol. 73, no. 4, pp. 964–969, 2004. View at Publisher · View at Google Scholar · View at Scopus
  46. P. M. Krishna and A. Chatterjee, “Existence of a metallic phase in a 1D Holstein-Hubbard model at half filling,” Physica C, vol. 457, no. 1-2, pp. 55–59, 2007. View at Publisher · View at Google Scholar · View at Scopus
  47. E. H. Lieb and F. Y. Wu, “Absence of mott transition in an exact solution of the short-range, one-band model in one dimension,” Physical Review Letters, vol. 20, no. 25, pp. 1445–1448, 1968. View at Publisher · View at Google Scholar · View at Scopus
  48. I. G. Lang and Yu. A. Firsov, Zh. Éksp. Teor. Fiz., vol. 43, p. 1843, 1962, Soviet Physics—JETP, vol. 16, p. 1301, 1963.
  49. A. N. Das and S. Sil, “A study of the polaronic band width and the small-to-large-polaron transition in a many-polaron system,” Journal of Physics: Condensed Matter, vol. 5, no. 44, pp. 8265–8276, 1993. View at Publisher · View at Google Scholar · View at Scopus
  50. M. Zoli and A. N. Das, “Polaron crossover in molecular solids,” Journal of Physics: Condensed Matter, vol. 16, no. 21, pp. 3597–3607, 2004. View at Publisher · View at Google Scholar · View at Scopus
  51. M. Frick, I. Morgenstern, and W. von der Linden, “High-temperature superconductivity in the apex-oxygen model: a quantum Monte Carlo study,” Zeitschrift für Physik B, vol. 82, no. 3, pp. 339–345, 1991. View at Publisher · View at Google Scholar · View at Scopus
  52. M. Frick, I. Morgenstern, and W. von der Linden, “Anharmonic phonons and strong electronic correlations in high-Tc superconductors: a Quantum Monte Carlo study,” Physica C, vol. 185–189, part 3, pp. 1523–1524, 1991. View at Publisher · View at Google Scholar · View at Scopus
  53. A. Bussmann-Holder and A. R. Bishop, “Anharmonicity-induced multiphonon processes in high-temperature superconductors,” Physical Review B, vol. 44, no. 6, pp. 2853–2856, 1991. View at Publisher · View at Google Scholar · View at Scopus
  54. N. M. Plakida, V. L. Aksenov, and S. L. Drechsler, “Anharmonic model for high-Tc superconductors,” Europhysics Letters, vol. 4, no. 11, pp. 1309–1314, 1987. View at Google Scholar · View at Scopus
  55. N. M. Plakida, “Lattice instability and strong electron-phonon coupling for high-Tc superconductivity,” Physica C, vol. 162–164, part 2, pp. 1341–1342, 1989. View at Google Scholar · View at Scopus
  56. N. M. Plakida and S. E. Krasavin, “A microscopical model of anharmonic lattice dynamics of La2CuO4,” Physica C, vol. 185–189, part 3, pp. 1531–1532, 1991. View at Publisher · View at Google Scholar · View at Scopus
  57. H. de Raedt, T. Schneider, and M. P. Sörensen, “Superconductivity in Hubbard models coupled to non-fermionic degrees of freedom,” Zeitschrift für Physik B, vol. 79, no. 3, pp. 327–332, 1990. View at Publisher · View at Google Scholar · View at Scopus
  58. J. Konior, “Anharmonic polaronic model and high-Tc superconductivity,” Physical Review B, vol. 47, no. 21, pp. 14425–14433, 1993. View at Publisher · View at Google Scholar · View at Scopus
  59. J. K. Freericks and G. D. Mahan, “Strong-coupling expansions for the anharmonic Holstein model and for the Holstein-Hubbard model,” Physical Review B, vol. 54, no. 13, pp. 9372–9384, 1996. View at Google Scholar · View at Scopus
  60. G. D. Mukherjee, C. Bansal, and A. Chatterjee, “Thermal expansion study of ordered and disordered Fe3Al: an effective approach for the determination of vibrational entropy,” Physical Review Letters, vol. 76, no. 11, pp. 1876–1879, 1996. View at Publisher · View at Google Scholar · View at Scopus
  61. G. D. Mukherjee, C. Bansal, and A. Chatterjee, “Thermal expansion analysis of Fe3xMnxAl alloys,” Physical Review B, vol. 58, no. 10, pp. 6172–6179, 1998. View at Google Scholar · View at Scopus
  62. G. D. Mukherjee, A. Chatterjee, and C. Bansal, “Anomalous thermal expansion behavior of the YBaCuO superconductor. Indirect evidence of polaron formation,” Physica C, vol. 232, no. 3-4, pp. 241–245, 1994. View at Google Scholar · View at Scopus
  63. G. D. Mukherjee, C. Bansal, and A. Chatterjee, “Thermal expansion study of Bi-2223 superconductor: an evidence of polaronic mechanism of high Tc superconductivity with strong two-dimensional fluctuations,” Physica C, vol. 333, no. 3, pp. 229–234, 2000. View at Publisher · View at Google Scholar · View at Scopus
  64. C. Kittel, Introduction to Solid State Physics, John Wiley & Sons, New York, NY, USA, 1996.
  65. R. T. Clay and R. P. Hardikar, “Intermediate phase of the one dimensional half-filled Hubbard-Holstein model,” Physical Review Letters, vol. 95, no. 9, Article ID 096401, 4 pages, 2005. View at Publisher · View at Google Scholar · View at Scopus
  66. H. Zheng, “Squeezed polarons in one dimension,” Physics Letters A, vol. 131, no. 2, pp. 115–118, 1988. View at Google Scholar · View at Scopus
  67. C. F. Lo and R. Sollie, “Correlated squeezed polaron states in one dimension,” Physical Review B, vol. 48, no. 14, pp. 10183–10187, 1993. View at Publisher · View at Google Scholar · View at Scopus
  68. A. F. Hebard, M. J. Rosseinsky, R. C. Haddon et al., “Superconductivity at 18?K in potassium-doped C60,” Nature, vol. 350, no. 6319, pp. 600–601, 1991. View at Google Scholar · View at Scopus
  69. O. Gunnarsson, “Superconductivity in fullerides,” Reviews of Modern Physics, vol. 69, no. 2, pp. 575–606, 1997. View at Google Scholar · View at Scopus
  70. Y. Takada, “Explanation of the anomalous isotope effect in superconducting alkali-metal-doped fullerenes,” Journal of the Physical Society of Japan, vol. 65, no. 10, pp. 3134–3137, 1996. View at Google Scholar · View at Scopus
  71. Y. Takada and T. Hotta, “Superconductivity in the alkali-doped fullerides: competition of phonon-mediated attractions with coulomb repulsions in polaron pairing,” International Journal of Modern Physics B, vol. 12, no. 29–31, pp. 3042–3051, 1998. View at Google Scholar · View at Scopus