Coexistence of a double- Q spin-density wave and a multi- Q pair-density wave in cuprate oxide superconductors

Physical Review B - Condensed Matter and Materials Physics

Volumn 73, Issue 9, 2006, Pages

  Ohkawa, Fusayoshi J ^a  

^a HOKKAIDO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33644963572     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.73.092506     Document Type: Article

References (55)

1. J. G. Bednortz and K. A. Müller, Z. Phys. B: Condens. Matter ZPCMDN 0722-3277 10.1007/BF01303701 64, 189 (1986).
2. J. E. Hoffman, Science SCIEAS 0036-8075 10.1126/science.1066974 295, 466 (2002).
3. M. Vershinin, M. Shashank, S. Ono, Y. Abe, Y. Ando, and A. Yazdani, Science SCIEAS 0036-8075 10.1126/science.1093384 303, 1995 (2004).
4. T. Hanaguri, Nature (London) NATUAS 0028-0836 10.1038/nature02861 430, 1001 (2004).
5. C. Howald, H. Eisaki, N. Kaneko, M. Greven, and A. Kapitulnik, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.67.014533 67, 014533 (2003).
6. N. Momono, A. Hashimoto, Y. Kobatake, M. Oda, and M. Ido, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.74.2400 74, 2400 (2005).
7. K. McElroy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94. 197005 94, 197005 (2005).
8. H. Yasuoka, T. Imai, and T. Shimizu, Strong Correlation and Superconductivity, Vol. 89 of Springer Series in Solid State Science (Springer-Verlag, Berlin, 1989), p. 254.
9. H. Ding, Nature (London) NATUAS 0028-0836 10.1038/382051a0 382, 51 (1996).
10. J. M. Harris, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.54.R15665 54, R15665 (1996).
11. A. G. Loeser, Science SCIEAS 0036-8075 273, 325 (1996).
12. A. Ino, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.65.094504 65, 094504 (2002).
13. Ch. Renner, B. Revaz, J.-Y. Genoud, K. Kadowaki, and Ø. Fischer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.149 80, 149 (1998).
14. M. Oda, K. Hoya, R. Kubota, C. Manabe, N. Momono, T. Nakano, and M. Ido, Physica C PHYCE6 0921-4534 10.1016/S0921-4534(97)00505-4 281, 135 (1997).
15. T. Nakano, N. Momono, M. Oda, and M. Ido, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.67.2622 67, 2622 (1998).
16. T. Ekino, Y. Sezaki, and H. Fujii, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.60.6916 60, 6916 (1999).
17. N. D. Mermin and H. Wagner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.17.1133 17, 1133 (1966).
18. F. J. Ohkawa, cond-mat/0508344 (unpublished).
19. J. Zaanen and O. Gunnarsson, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.40.7391 40, R7391 (1989).
20. U. Löw, V. J. Emery, K. Fabricius, and S. A. Kivelson, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.72.1918 72, 1918 (1994).
21. O. Zachar, S. A. Kivelson, and V. J. Emery, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.57.1422 57, 1422 (1998).
22. S. R. White and D. J. Scalapino, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.1272 80, 1272 (1998).
23. S. A. Kiverson, E. Fradkin, and V. J. Emery, Nature (London) NATUAS 0028-0836 10.1038/31177 393, 550 (1998).
24. V. J. Emery, S. A. Kiverson, and J. M. Tranquada, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.96.16.8814 96, 8814 (1999).
25. M. Vojta and S. Sachdev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.3916 83, 3916 (1999).
26. H. Zaanen, Nature (London) NATUAS 0028-0836 10.1038/35008176 404, 714 (2000).
27. F. J. Ohkawa, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.67.535 67, 535 (1998);
28. F. J. Ohkawa, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.66.014408 66, 014408 (2002).
29. H. C. Fu, J. C. Davis, and D.-H. Lee, cond-mat/0403001 (unpublished).
30. S. Sachdev, Science SCIEAS 0036-8075 10.1126/science.288.5465.475 288, 475 (2000).
31. M. Vojta, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.66.104505 66, 104505 (2002).
32. D. Podolsky, E. Demler, K. Damle, and B. I. Halperin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.67.094514 67, 094514 (2003).
33. H.-D. Chen, O. Vafek, A. Yazdani, and S.-C. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.187002 93, 187002 (2004).
34. H.-D. Chen, cond-mat/040232 (unpublished).
35. H.-D. Chen, J. P. Hu, S. Capponi, E. Arrigoni, and S. C. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.137004 89, 137004 (2002).
36. Z. Tesanović, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.217004 93, 217004 (2004).
37. P. W. Anderson, cond-mat/0406038 (unpublished).
38. F. J. Ohkawa, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.58.4156 58, 4156 (1989).
39. J. Hubbard, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 276, 238 (1963);
40. J. Hubbard, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 281, 401 (1964).
41. M. C. Gutzwiller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 10.159 10, 159 (1963);
42. M. C. Gutzwiller, Phys. Rev. PRVAAH 0096-8250 10.1103/PhysRev.134.A923 134, A923 (1964);
43. M. C. Gutzwiller, Phys. Rev. PRVAAH 0096-8250 10.1103/PhysRev.137.A1726 137, A1726 (1965).
44. F. J. Ohkawa, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.44.6812 44, 6812 (1991).
45. F. J. Ohkawa, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.60.3218 60, 3218 (1991);
46. F. J. Ohkawa, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.61.1615 61, 1615 (1992).
47. A. Georges and G. Kotliar, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.45.6479 45, 6479 (1992).
48. F. J. Ohkawa, J. Phys. Soc. Jpn. JUPSAU 0031-9015 74, 3340 (2005).
49. J. E. Hirsch, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.54. 1317 54, 1317 (1985).
50. F. J. Ohkawa, Jpn. J. Appl. Phys., Suppl. JJPYA5 0021-4922 26, L652 (1987);
51. F. J. Ohkawa, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.56.2267 56, 2267 (1987).
52. F. J. Ohkawa, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.59.8930 59, 8930 (1990).
53. A superconducting state with Δl ≠0 for l≠0 is nothing but a generalized Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state induced by SDW fields. Electron pairs of k+(l+ 1 2) Q and -k+(l+ 1 2) Q, whose total momenta are (2l+1)Q, are also possible. However, they are ignored in this paper; they should be considered in case of CDW.
54. J. W. Loram, K. A. Mirza, J. R. Cooper, and W. Y. Liang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71.1740 71, 1740 (1993).
55. H. Alloul, P. Mendels, H. Casalta, J. F. Marucco, and J. Arabski, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.67.3140 67, 3140 (1991).