Two-dimensional Hubbard-Holstein bipolaron

Physical Review B - Condensed Matter and Materials Physics

Volumn 69, Issue 24, 2004, Pages

  Macridin, A ^a,c   Sawatzky, G A ^a,b   Jarrell, Mark ^c  

^a UNIVERSITY OF GRONINGEN   (Netherlands)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^c UNIVERSITY OF CINCINNATI   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CHEMICAL BOND; ELECTRON; MATHEMATICAL ANALYSIS; MEASUREMENT; MOLECULAR INTERACTION; MOLECULAR WEIGHT; MONTE CARLO METHOD; PARAMETER; PHASE TRANSITION; PHONON; PHYSICOCHEMICAL MODEL; TECHNIQUE;

EID: 42749106844     PISSN: 01631829     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevB.69.245111     Document Type: Article

References (52)

1. C. Schlenker, Physics of Disordered Materials, edited by D. Adler, H. Fritzche, and S. Ovshinski (Plenum, New York, 1985).
2. S. Tajima, S. Uchida, A. Masaki, H. Takagi, K. Kitazawa, S. Tanaka, and S. Sugai, Phys. Rev. B 35, 696 (1987).
3. J. Scott, J. L. Bredas, J. H Kaufman, P. Pfluger, S. B. Street, and K. Yakhushi, Mol. Cryst. Liq. Cryst. 118, 163 (1983).
4. A. Lanzara, N. L. Saini, M. Brunelli, F. Natali, A. Bianconi, P. G. Radaelli, and S. W. Cheong, Phys. Rev. Lett. 81, 878 (1998); Guo-Meng-Zhao, K. Conder, H. Keller, and K. A. Muller, Nature (London) 381, 676 (1996); K. H. Kim, J. Y. Gu, H. S. Choi, G. W. Park, and T. W. Noh, Phys. Rev. Lett. 77, 1877 (1996); A. J. Millis, P. B. Littlewood, and B. I. Shraiman, ibid. 74, 5144 (1995); A. J. Millis, Nature (London) 392, 147 (1998).
5. A. Lanzara, N. L. Saini, M. Brunelli, F. Natali, A. Bianconi, P. G. Radaelli, and S. W. Cheong, Phys. Rev. Lett. 81, 878 (1998); Guo-Meng-Zhao, K. Conder, H. Keller, and K. A. Muller, Nature (London) 381, 676 (1996); K. H. Kim, J. Y. Gu, H. S. Choi, G. W. Park, and T. W. Noh, Phys. Rev. Lett. 77, 1877 (1996); A. J. Millis, P. B. Littlewood, and B. I. Shraiman, ibid. 74, 5144 (1995); A. J. Millis, Nature (London) 392, 147 (1998).
6. A. Lanzara, N. L. Saini, M. Brunelli, F. Natali, A. Bianconi, P. G. Radaelli, and S. W. Cheong, Phys. Rev. Lett. 81, 878 (1998); Guo-Meng-Zhao, K. Conder, H. Keller, and K. A. Muller, Nature (London) 381, 676 (1996); K. H. Kim, J. Y. Gu, H. S. Choi, G. W. Park, and T. W. Noh, Phys. Rev. Lett. 77, 1877 (1996); A. J. Millis, P. B. Littlewood, and B. I. Shraiman, ibid. 74, 5144 (1995); A. J. Millis, Nature (London) 392, 147 (1998).
7. A. Lanzara, N. L. Saini, M. Brunelli, F. Natali, A. Bianconi, P. G. Radaelli, and S. W. Cheong, Phys. Rev. Lett. 81, 878 (1998); Guo-Meng-Zhao, K. Conder, H. Keller, and K. A. Muller, Nature (London) 381, 676 (1996); K. H. Kim, J. Y. Gu, H. S. Choi, G. W. Park, and T. W. Noh, Phys. Rev. Lett. 77, 1877 (1996); A. J. Millis, P. B. Littlewood, and B. I. Shraiman, ibid. 74, 5144 (1995); A. J. Millis, Nature (London) 392, 147 (1998).
8. A. Lanzara, N. L. Saini, M. Brunelli, F. Natali, A. Bianconi, P. G. Radaelli, and S. W. Cheong, Phys. Rev. Lett. 81, 878 (1998); Guo-Meng-Zhao, K. Conder, H. Keller, and K. A. Muller, Nature (London) 381, 676 (1996); K. H. Kim, J. Y. Gu, H. S. Choi, G. W. Park, and T. W. Noh, Phys. Rev. Lett. 77, 1877 (1996); A. J. Millis, P. B. Littlewood, and B. I. Shraiman, ibid. 74, 5144 (1995); A. J. Millis, Nature (London) 392, 147 (1998).
9. S. Lupi, P. Maselli, M. Capizzi, P. Calvani, P. Giura, and P. Roy, Phys. Rev. Lett. 83, 4852 (1999); E. S. Bozin, G. H. Kwei, H. Takagi, and S. J. L. Billinge, ibid. 84, 5856 (2000); A. Bianconi, N. L. Saini, A. Lanzara, M. Missori, T. Rossetti, H. Oyanagi, H. Yamaguchi, K. Oka, and T. Ito, ibid. 76, 3412 (1996).
10. S. Lupi, P. Maselli, M. Capizzi, P. Calvani, P. Giura, and P. Roy, Phys. Rev. Lett. 83, 4852 (1999); E. S. Bozin, G. H. Kwei, H. Takagi, and S. J. L. Billinge, ibid. 84, 5856 (2000); A. Bianconi, N. L. Saini, A. Lanzara, M. Missori, T. Rossetti, H. Oyanagi, H. Yamaguchi, K. Oka, and T. Ito, ibid. 76, 3412 (1996).
11. S. Lupi, P. Maselli, M. Capizzi, P. Calvani, P. Giura, and P. Roy, Phys. Rev. Lett. 83, 4852 (1999); E. S. Bozin, G. H. Kwei, H. Takagi, and S. J. L. Billinge, ibid. 84, 5856 (2000); A. Bianconi, N. L. Saini, A. Lanzara, M. Missori, T. Rossetti, H. Oyanagi, H. Yamaguchi, K. Oka, and T. Ito, ibid. 76, 3412 (1996).
12. L. D. Landau, Z. Phys. 3, 664 (1933).
13. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957).
14. A. S. Alexandrov and N. F. Mott, Rep. Prog. Phys. 57, 1197 (1994).
15. A. S. Alexandrov, V. V. Kabanov, and D. K. Ray, Phys. Rev. B 49, 9915 (1994).
16. A. B. Migdal, Sov. Phys. JETP 7, 996 (1958); G. M. Eliashberg, ibid. 11, 696 (1960); 12, 1000 (1960).
17. A. B. Migdal, Sov. Phys. JETP 7, 996 (1958); G. M. Eliashberg, ibid. 11, 696 (1960); 12, 1000 (1960).
18. A. B. Migdal, Sov. Phys. JETP 7, 996 (1958); G. M. Eliashberg, ibid. 11, 696 (1960); 12, 1000 (1960).
19. A. S. Alexandrov, Phys. Rev. B 53, 2863 (1995); A. S. Alexandrov and P. P. Edwards, Physica C 331, 97 (2000).
20. A. S. Alexandrov, Phys. Rev. B 53, 2863 (1995); A. S. Alexandrov and P. P. Edwards, Physica C 331, 97 (2000).
21. J. Bonča, T. Katrašnik, and S. A. Trugman, Phys. Rev. Lett. 84, 3153 (2000).
22. A. La Magna and R. Pucci, Phys. Rev. B 55, 14 886 (1997).
23. G. Wellein, H. Roder, and H. Fehske, Phys. Rev. B 53, 9666 (1996); A. Weisse, H. Fehske, G. Wellein, and A. R. Bishop, Phys. Rev. B 62, R747 (2000).
24. G. Wellein, H. Roder, and H. Fehske, Phys. Rev. B 53, 9666 (1996); A. Weisse, H. Fehske, G. Wellein, and A. R. Bishop, Phys. Rev. B 62, R747 (2000).
25. L. Proville and S. Aubry, Physica D 133, 307 (1998); Eur. Phys. J. B 11, 41 (1999).
26. L. Proville and S. Aubry, Physica D 133, 307 (1998); Eur. Phys. J. B 11, 41 (1999).
27. G. De Filippis, V. Cataudella, G. Iadonisi, V. Marigliano Ramaglia, C. A. Perroni, and F. Ventriglia, Phys. Rev. B 64, 155105 (2001).
28. H. de Raedt and A. Lagendijk, Z. Phys. B: Condens. Matter 65, 43 (1986).
29. However the reader should be aware that HH model is presumably not the best candidate to address the physics of cuprate superconductors, at intermediate and large electron-phonon coupling producing bipolarons with extremely large effective mass (Ref, 19). Models with longer range electron-phonon interaction (Ref. 24) are believed to be more realistic for describing cuprates.
30. B. K. Chakraverty, J. Ranninger, and D. Feinberg, Phys. Rev. Lett. 81, 433 (1998).
31. N. Prokof'ev, B. Svistunov, and I. Tupitsyn, JETP Lett. 87, 310 (1998).
32. N. V. Prokof'ev and B. V. Svistunov, Phys. Rev. Lett. 81, 2514 (1998); A. S. Mishchenko, N. V. Prokof'ev, A. Sakamoto, and B. V. Svistunov, Phys. Rev. B 62, 6317 (2000).
33. N. V. Prokof'ev and B. V. Svistunov, Phys. Rev. Lett. 81, 2514 (1998); A. S. Mishchenko, N. V. Prokof'ev, A. Sakamoto, and B. V. Svistunov, Phys. Rev. B 62, 6317 (2000).
34. A. S. Mishchenko, N. V. Prokof'ev, and B. V. Svistunov, Phys. Rev. B 64, 033101 (2001).
35. E. A. Burovski, A. S. Mishchenko, N. V. Prokof'ev, and B. V. Svistunov, Phys. Rev. Lett. 87, 186402 (2001).
36. J. Bonča and S. A. Trugman, Phys. Rev. B 64, 094507 (2001).
37. F due to Pauli exclusion principle which blocks the electron-phonon scattering inside the Fermi sea.
38. I. G. Lang and Yu. A. Firsov, Sov. Phys. JETP 16, 1301 (1963).
39. 0N(0) will be α=2λ.
40. C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1996).
41. P. E. Kornilovitch and E. R. Pike, Phys. Rev. B 55, R8634 (1997); P. E. Kornilovitch, Phys. Rev. Lett. 81, 5382 (1998).
42. P. E. Kornilovitch and E. R. Pike, Phys. Rev. B 55, R8634 (1997); P. E. Kornilovitch, Phys. Rev. Lett. 81, 5382 (1998).
43. Do not confuse the symbol for mass m with the the diagram label in.
44. In fact the separation of singlet and triplet obeys the same idea, the permutation group operations being used.
45. The Holstein polaron properties were calculated with a DQMC code similar to the one presented in Ref. 21 and used for the Fröhlich polaron study.
46. P. W. Anderson, Phys. Rev. Lett. 34, 953 (1975).
47. R. A. Street and N. F. Mott, Phys. Rev. Lett. 35, 1293 (1975).
48. D. Alder and E. J. Yoffa, Phys. Rev. Lett. 36, 1197 (1976).
49. S. Robaszkiewicz, R. Micnas, and K. A. Chao, Phys. Rev. B 23, 1447 (1981); 24, 1579 (1981).
50. S. Robaszkiewicz, R. Micnas, and K. A. Chao, Phys. Rev. B 23, 1447 (1981); 24, 1579 (1981).
51. Notice that the total probability to have the electrons at the distance r from each other is C(r) times the number of sites situated at the relative distance r. Therefore, in Fig. 8, we plotted 4 × C(1) and 4 × C(2) which represent the probability to have the electrons on nearest and next-nearest neighbor sites, respectively.
52. In Figs. 9(b) and 9(c) small jumps in the correlation function at some particular values of r (for example between r=9 and r =10) are observed. This indicates that our projected state has a small amount of d-wave character, as explained in Fig. 10 and the related text paragraph.