Skip to main content
Log in

Optical Sum Rule in Finite Bands

  • Published:
Journal of Low Temperature Physics Aims and scope Submit manuscript

In a single finite electronic band the total optical spectral weight or optical sum carries information on the interactions involved between the charge carriers as well as on their band structure. It varies with temperature as well as with impurity scattering. The single band optical sum also bears some relationship to the charge carrier kinetic energy and, thus, can potentially provide useful information, particularly on its change as the charge carriers go from normal to superconducting state. Here we review the considerable advances that have recently been made in the context of high Tc oxides, both theoretical and experimental.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. C. Campuzano, M. R. Norman, and M. Randeria, in The Physics of Superconductivity; Conventional and High-T c Superconductors, K.-H. Bennemann and J. B. Ketterson (eds.), Springer, Berlin (2003), Vol. II, p. 167.

  2. Damascelli A., Hussain Z., Shen Z.X. (2003). Rev. Mod. Phys. 75, 473

    Article  ADS  Google Scholar 

  3. Matsui H., Terashima K., Sato T., Takahashi T., Fujita M., Yamada K. (2005). Phys. Rev. Lett. 95:017003

    Article  ADS  Google Scholar 

  4. D. A. Bonn and W. N. Hardy, in Physical Properties of High Temperature Superconductors, D. M. Ginsberg (ed.), World Scientific, Singapore (1996), Vol. 5, p. 7.

  5. C. C. Tsuei and J. R. Kirtley, in The Physics of Superconductivity; Conventional and High-T c Superconductors, K.-H. Bennemann and J. B. Ketterson (eds.), Springer, Berlin (2003), Vol. I, p. 648.

  6. Nuss M.C., Mankiewich P.M., O’Malley M.L., Westerwick E.H., Littlewood P.B. (1991). Phys. Rev. Lett. 66:3305

    Article  ADS  Google Scholar 

  7. Bonn D.A., Dosanjh P., Liang R., Hardy W.N. (1992). Phys. Rev. Lett. 68:2390

    Article  ADS  Google Scholar 

  8. Romero D.B., Porter C.D., Tanner D.B., Forro L., Mandrus D., Mihaly L., Carr G.L., Williams G.P. (1992). Phys. Rev. Lett. 68:1590

    Article  ADS  Google Scholar 

  9. Nicol E.J., Carbotte J.P. (1991). Phys. Rev. B 44:7741

    Article  ADS  Google Scholar 

  10. Lee S.-F., Morgan D.C., Ormeno R.J., Broun D.M., Doyle R.A., Waldram J.R., Kadowaki K. (1996) Phys. Rev. Lett. 77, 735

    Article  ADS  Google Scholar 

  11. Broun S.M., Morgan D.C., Ormeno R.J., Lee S.F., Tyler A.W., Mackenzie A.P., Waldram J.R. (1997). Phys. Rev. B 56:R11443

    Article  ADS  Google Scholar 

  12. Hirsch J.E. (1989). Phys. Lett. A 134, 451

    Article  ADS  Google Scholar 

  13. J. E. Hirsch, Physica C 199, 305 (1992); Physica C 201, 347 (1992).

  14. Hirsch J.E., Marsiglio F. (1989). Phys. Rev. B 39:11515

    Article  ADS  Google Scholar 

  15. J. E. Hirsch and F. Marsiglio, Physics C 331, 150 (2000); Phys. Rev. B 62, 15131 (2000).

  16. P. W. Anderson, Science 279, 1196 (1998), in The Theory of Superconductivity in the High T c Cuprates, S. B. Treiman (ed.), Princeton University Press, Princeton (1997).

  17. Chakravarty S. (1998). Eur. Phys. J. B 5, 337

    Article  ADS  Google Scholar 

  18. Kubo R. (1957). J. Phys. Soc. Japan 12, 570

    Article  MathSciNet  ADS  Google Scholar 

  19. Basov D.N., Woods S.I., Katz A.S., Singley E.J., Dynes R.C., Xu M., Hinks D.G., Homes C.C., Strongin M. (1999) Science 283, 49

    Article  ADS  Google Scholar 

  20. L. B. Ioffe and A. J. Millis, Science 285, 1241 (1999); Phys. Rev. B 61, 9077 (2000).

  21. W. Kim and J. P. Carbotte, Phys. Rev B 61, 11886R (2000); 62, 8661 (2000); 63, 140505R (2001); 63, 054526 (2001); 64, 104501 (2001).

  22. Kumar N., Jayannavar A.M. (1992). Phys. Rev. B 45:5001

    Article  ADS  Google Scholar 

  23. P. W. Anderson and Z. Zou, Phys. Rev. Lett. 60, 132 (1988); 60, 2557 (1988).

  24. A. J. Leggett, Braz. J. Phys. 22, 129 (1992); M. Turlabov and A.J. Leggett, Phys. Rev. B 62, 064518 (2001).

  25. Z. Tesanovic, Phys. Rev. B 36, 2364 (1987); 38, 2489 (1988).

    Google Scholar 

  26. Halbritter J. (1998). J. Supercond. 11, 231

    Article  Google Scholar 

  27. W. A. Atkinson and J. P. Carbotte, Phys. Rev. B 52, 10601 (1995); 55, 3230 (1997); 55, 12748 (1997).

  28. Wu W.C., Atkinson W.A., Carbotte J.P. (1997). J. Supercond. 11, 305

    Google Scholar 

  29. Xiang T., Wheatley J.M. (1996). Phys. Rev. Lett. 77:4632

    Article  ADS  Google Scholar 

  30. Hirschfeld P.J., Quinlan S.M., Scalapino D.J. (1997). Phys. Rev. B 55:12742

    Article  ADS  Google Scholar 

  31. Kim E.H. (1997). Phys. Rev. B 58:2452

    Article  ADS  Google Scholar 

  32. Graf M.J., Palumbo M., Rainer D., Sauls J.A. (1995). Phys. Rev. B 52:10588

    Article  ADS  Google Scholar 

  33. Schachinger E., Carbotte J.P. (2001). Phys. Rev. B 64:094501

    Article  ADS  Google Scholar 

  34. D. van der Marel, H. J. A. Molegraaf, C. Presura, and L. Santoso, in Concepts in Electron Correlations, A. Hewson and V. Zlatic (eds.), Kluwer (2003) p. 7.

  35. Deutscher G., Santander-Syro A.F., Bontemps N. (2005). Phys. Rev. B 72:092504

    Article  ADS  Google Scholar 

  36. F. Carbone, A. B. Kuzmenko, H. J. A. Molegraaf, E. van Heumen, V. Lukovac, F. Marsiglio, D. van der Marel, K. Haule, G. Kotliar, H. Berger, S. Courjault, P. H. Kes, M. Li, cond-mat/0605209 (unpublished).

  37. Ferrell R.A., Glover R.E. (1958). Phys. Rev. 109:1398

    Article  MATH  ADS  Google Scholar 

  38. Tinkham M., Ferrell R.B. (1959). Phys. Rev. Lett. 2, 331

    Article  ADS  Google Scholar 

  39. F. Marsiglio, F. Carbone, A. Kuzmenk, and D. van der Marel, cond-mat/0606688 (unpublished).

  40. Knigavko A., Carbotte J.P., Marsiglio F. (2004). Phys. Rev. B. 70:224501

    Article  ADS  Google Scholar 

  41. F. Marsiglio, J. E. Hirsch, Phys. Rev. B 41, 6435 (1990); Physica C 165, 71 (1990).

    Google Scholar 

  42. Quijada M.A., Tanner D.B., Kelley R.J., Onellion M., Berger H., Margaritondo G. (1999). Phys. Rev. B 60:14917

    Article  ADS  Google Scholar 

  43. L. Benfatto, F. Marsiglio, and J. P. Carbotte, cond-mat/0603661 (unpublished).

  44. A. E. Karakozov and E. G. Maksimov, cond-mat/0511185 (unpublished).

  45. P. Monthoux and D. Pines, Phys. Rev. B 47, 6069 (1993); 49, 4261 (1994).

  46. P. Monthoux, A. V. Balatsky, and D. Pines, Phys. Rev. Lett. 67, 3448 (1991); Phys. Rev. B 46, 14803 (1992).

    Google Scholar 

  47. Millis A.J., Monien H., Pines D. (1990). Phys. Rev. B 42, 167

    Article  ADS  Google Scholar 

  48. D. Branch and J. P. Carbotte, Can. J. Phys. 77, 531 (1999); J. Supercond. 12, 667 (1999); 13, 535 (2000).

  49. Abanov A., Chubukov A.V., Schmalian J. (2003). Adv. Phys. 52, 119

    Article  ADS  Google Scholar 

  50. Schachinger E., Carbotte J.P. (2005). Phys. Rev. B 72:014535

    Article  ADS  Google Scholar 

  51. V. Chubukov, D. Pines, and J. Schmalian, in The Physics of Superconductivity; Conventional and High-T c Superconductors, K.-H. Bennemann and J. B. Ketterson (eds.), Springer, Berlin (2003), Vol. I, p. 495.

  52. Toschi A., Capone M., Ortolani M., Calvani P., Lupi S., Castellani C. (2005). Phys. Rev. Lett. 95:097002

    Article  ADS  Google Scholar 

  53. Georges A., Kotliar G., Rozenberg M.J., Krauth W. (1996). Rev. Mod. Phys. 68, 13

    Article  MathSciNet  ADS  Google Scholar 

  54. Ortolani M., Calvani P., Lupi S. (2005). Phys. Rev. Lett. 94:067002

    Article  ADS  Google Scholar 

  55. A. Lucarelli, S. Lupi, M. Ortolani, P. Calvani, P. Maselli, M. Capizzi, P. Giura, H. Eisaki, N. Kikugawa, T. Fujita, M. Fujita, and K. Yamada, Phys. Rev. Lett. 90, 037002 (2003).

    Google Scholar 

  56. Santander-Syro A.F., Lobo R.P.S.M., Bontemps N., Konstantinovic Z., Raffy H. (2002). Phys. Rev. Lett. 88:097005

    Article  ADS  Google Scholar 

  57. Santander-Syro A.F., Lobo R.P.S.M., Bontemps N., Konstantinovic Z., Li Z.Z., Raffy H. (2003). Europhys. Lett. 62, 568

    Article  ADS  Google Scholar 

  58. Santander-Syro A.F., Lobo R.P.S.M., Bontemps N., Lopera W., Giratá D., Konstantinovic Z., Li Z.Z., Raffy H. (2004). Phys. Rev. 70:134504

    Article  Google Scholar 

  59. Molegraaf H.J.A., Presura C., van der Marel D., Kes P.H., Li M. (2002). Science 295, 22

    Article  Google Scholar 

  60. Maier Th.A., Jarrell M., Macridin A., Slezak C. (2004). Phys. Rev. Lett. 92:027005

    Article  ADS  Google Scholar 

  61. K. Haule and G. Kotliar, cond-mat/0601478 (unpublished).

  62. Grimaldi G., Cappelutti E., Pietrobero L. (1998). Europhys. Lett. 42, 667

    Article  ADS  Google Scholar 

  63. Cappelluti E., Grimaldi C., Pietronero L. (2001). Phys. Rev. B 64:125104

    Article  ADS  Google Scholar 

  64. Capeppelluti E., Pietronero L. (2003). Phys. Rev. B 68:224511

    Article  ADS  Google Scholar 

  65. Doğan F., Marsiglio F. (2003). Phys. Rev. B 68:165102

    Article  ADS  Google Scholar 

  66. Knigavko A., Carbotte J.P. (2005). Phys. Rev. B 72:035125

    Article  ADS  Google Scholar 

  67. Knigavko A., Carbotte J.P. (2006). Phys. Rev. B 73:125114

    Article  ADS  Google Scholar 

  68. Knigavko A., Carbotte J.P., Marsiglio F. (2005). Europhys. Lett. 71, 776

    Article  ADS  Google Scholar 

  69. Marsiglio F., Schossmann M., Carbotte J.P. (1988). Phys. Rev. B 32:4965

    Article  ADS  Google Scholar 

  70. Carbotte J.P., Schachinger E., Hwang J. (2005). Phys. Rev. B 71:054506

    Article  ADS  Google Scholar 

  71. Schachinger E., Carbotte J.P. (2000). Phys. Rev. B 62:9054

    Article  ADS  Google Scholar 

  72. J. Hwang, J. Yang, T. Timusk, S. G. Sharapov, J. P. Carbotte, D. A. Bonn, R. Liang, and W. N. Hardy, Phys. Rev. B 73, 014508 (2006).

    Google Scholar 

  73. A. V. Boris, N. N. Kovaleva, D. V. Dolgov, T. Holden, C. T. Lin, B. Keimer, and C. Bernhard, Science 304, 708 (2004).

    Google Scholar 

  74. A. B. Kuzmenko, H. J. A. Molegraaf, F. Carbone, and D. van der Marel, Phys. Rev. B 72, 144503 (2005).

    Google Scholar 

  75. Santander-Syro A.F., Bontemps N. (2004) Science 304, 708

    Article  Google Scholar 

  76. Carbotte J.P., Schachinger E., Basov D.N. (1999). Nature (London) 401, 354

    Article  ADS  Google Scholar 

  77. Schachinger E., Carbotte J.P., Basov D.N. (2001). Europhys. Lett. 54, 380

    Article  ADS  Google Scholar 

  78. E. Schachinger and J. P. Carbotte, in Models and Methods of High-TC Superconductivity: some Frontal Aspects, J. K. Srivastava and S. M. Rao (eds.), Nova Science, NY (2003), Vol. II, p. 73.

  79. P. Bourges, in The Gap Symmetry and Fluctuations in High Temperature Superconductors, J. Bok, G. Deutscher, D. Pavuna, and S.A. Wolf (eds.), Plenum Press, London (1998), p. 349.

  80. Schachinger E., Carbotte J.P. (2002). Phys. Rev. B 65:064514

    Article  ADS  Google Scholar 

  81. Hosseini A., Harris R., Kamal S., Dosanjh P., Preston J., Liang R., Hardy W.N., Bonn D.A. (1999). Phys. Rev. B 60:1349

    Article  ADS  Google Scholar 

  82. D. A. Bonn, R. Liang, T. M. Risemann, D. J. Baar, D. C. Morgan, K. Zhang, P. Dosanjh, T. L. Duty, A. MacFarlane, G. D. Morris, J. H. Brewer, W. H. Hardy, C. Kallin, and A. J. Berlinsky, Phys. Rev. B 47, 11314 (1993).

    Google Scholar 

  83. E. Schachinger and J. P. Carbotte, Phys. Rev. B 57, 13773 (1998); 57, 7970 (1998).

  84. Schachinger E., Carbotte J.P., Marsiglio F. (1997). Phys. Rev. B 56:2738

    Article  ADS  Google Scholar 

  85. R. S. Markiewicz, S. Sahrakorpi, M. Lindroos, H. Lin, and A. Bansil, cond-mat/0503064 (unpublished) and references therein.

  86. F. Marsiglio, Phys. Rev. B 73 064507 (2006); Erratum to be published.

    Google Scholar 

  87. M. R. Norman and C. Pépin, Phys. Rev. B 66, 100506(R) (2002).

  88. M. R. Norman and C. Pépin, Rep. Progr. Phys. 66, 1547 (2003).

  89. M. R. Norman and H. Ding, Phys. Rev. B 57, R11089 (1998).

  90. Hlubina R., Rice T.M. (1995). Phys. Rev. B 51:9253

    Article  ADS  Google Scholar 

  91. Valla T., Fedorov A.V., Johnson P.D., Li Q., Gu G.D., Koshizuka N. (2000). Phys. Rev. Lett. 85, 828

    Article  ADS  Google Scholar 

  92. Sandeman K.G., Schofield A.J. (2001). Phys. Rev. B 63:094510

    Article  ADS  Google Scholar 

  93. Stojkovic B.P., Pines D. (1996). Phys. Rev. Lett. 76, 811

    Article  ADS  Google Scholar 

  94. Varma C.M., Littlewood P.B., Schmitt-Rink S., Abrahams A., Ruckenstein A.E. (1989). Phys. Rev. Lett. 63:1996

    Article  ADS  Google Scholar 

  95. Varma C.M. (1997). Phys. Rev. B 55:14554

    Article  ADS  Google Scholar 

  96. Puchkov A.V., Basov D.N., Timusk T. (1996). J. Phys.: Condens. Matter 8:10049

    Article  ADS  Google Scholar 

  97. This was pointed out in footnote 15 of Ref. 35.

  98. N. Bontemps, R. P. S. M. Lobo, A. F. Santander-Syro, A. Zimmers, cond-mat/0603024 (unpublished).

  99. Tallon J.L., Loram J.W. (2001). Physica C 349, 53

    Article  ADS  Google Scholar 

  100. Toschi A., Capone M., Castellani C. (2005). Phys. Rev. B 72:235118

    Article  ADS  Google Scholar 

  101. B. Kyung, A. Georges, and A.-M. S. Tremblay, cond-mat/0508645 (unpublished).

  102. Emery V.J., Kivelson S.A. (1995). Nature (London) 374, 434

    Article  ADS  Google Scholar 

  103. Randeria M., Trivedi N., Moreo A., Scalettar R.T. (1992). Phys. Rev. Lett. 69:2001

    Article  ADS  Google Scholar 

  104. Franz M., Millis A.J. (1998). Phys. Rev. B 58:14572

    Article  ADS  Google Scholar 

  105. Kwon N.-J., Dorsey A.T. (1999). Phys. Rev. B 59:6438

    Article  ADS  Google Scholar 

  106. Herbut I.F. (2002). Phys. Rev. Lett. 88:047006

    Article  ADS  Google Scholar 

  107. T. Eckl, D. J. Scalapino, E. Arrigoni, and W. Hanke, Phys. Rev. B 66, 140510(R) (2002).

  108. Eckl T., Hanke W., Arrigoni E. (2003). Phys. Rev. B 68:014505

    Article  ADS  Google Scholar 

  109. Kopeć T.K. (2003). Phys. Rev. B 67:014520

    Article  ADS  Google Scholar 

  110. Chakravarty S., Laughlin R.B., Morr D.K., Nayak C. (2001). Phys. Rev. B 63:094503

    Article  ADS  Google Scholar 

  111. B. Dòra, A. Virosztek, and K. Maki, Phys. Rev. B 65, 155119 (2002); K. Maki, B. Dòra, M. Kartsovnik, A. Virosztek, B. Korin-Hamzic, and M. Basletic, Phys. Rev. Lett. 90, 256402 (2003).

    Google Scholar 

  112. Chakravarty S., Kee H.-Y., Nayak C. (2001). Int. J. Mod. Phys. B 15:2901

    Article  ADS  Google Scholar 

  113. Zhu J.-X., Kim W., Ting C.S., Carbotte J.P. (2001). Phys. Rev. Lett. 87:197001

    Article  ADS  Google Scholar 

  114. Yang X., Nayak C. (2002). Phys. Rev. B 65:064523

    Article  ADS  Google Scholar 

  115. Wang Q.H., Han J.H., Lee D.H. (2001). Phys. Rev. Lett. 87:077004

    Article  ADS  Google Scholar 

  116. Chakravarty S., Nayak C., Tewari S. (2003). Phys. Rev. B 68:100504

    Article  ADS  Google Scholar 

  117. Chakravarty S., Nayak C., Tewari S., Yang X. (2002). Phys. Rev. Lett. 89:277003

    Article  ADS  Google Scholar 

  118. Tewari S., Kee H.-Y., Nayak C., Chakravarty S. (2001). Phys. Rev. B 64:224516

    Article  ADS  Google Scholar 

  119. Capelutti E., Zehyer R. (1999). Phys. Rev. B 59:6475

    Article  ADS  Google Scholar 

  120. Benfatto L., Caprara S., DiCastro C. (2000). Eur. Phys. J. B 17, 95

    Article  ADS  Google Scholar 

  121. Benfatto L., Sharapov S., Beck H. (2004). Eur. Phys. J. B 34, 469

    Article  ADS  Google Scholar 

  122. Aristov D.N., Zeyher R. (2004). Phys. Rev. B 70:212511

    Article  ADS  Google Scholar 

  123. Valenzuela B., Nicol E.J., Carbotte J.P. (2005). Phys. Rev. B 71:134503

    Article  ADS  Google Scholar 

  124. Kim W., Carbotte J.P. (2002). Phys. Rev. B 66:033104

    Article  ADS  Google Scholar 

  125. Kim W., Zhu J.X., Carbotte J.P., Ting C.S. (2002). Phys. Rev. B 65:064502

    Article  ADS  Google Scholar 

  126. Benfatto L., Sharapov S., Andrenacci N., Beck H. (2005). Phys. Rev. B 71:104511

    Article  ADS  Google Scholar 

  127. Benfatto L., Sharapov S. (2006). Low Temp. Phys. 32, 533

    Article  ADS  Google Scholar 

  128. Halperin B.I., Rice T.M. (1968). Solid State Phys. 21, 115

    Article  Google Scholar 

  129. Affleck I., Marston J.B. (1988). Phys. Rev. B 37:3774

    Article  ADS  Google Scholar 

  130. Aristov D.N., Zeyher R. (2005). Phys. Rev. B 72, 115118

    Article  ADS  Google Scholar 

  131. Gerami R., Nayak C. (2006). Phys. Rev. B 73, 024505

    Article  ADS  Google Scholar 

  132. Homes C.C., Dordevic S.V., Bonn D.A., Liang R., Hardy W.N. (2004). Phys. Rev. B 69, 024514

    Article  ADS  Google Scholar 

  133. Karakozov A.E., Maksimov F.G., Dolgov O.V. (2002). Solid State Commun. 124, 119

    Article  ADS  Google Scholar 

  134. Shaw W., Swihart J.C. (1968). Phys. Rev. Lett 20:1000

    Article  ADS  Google Scholar 

  135. Carbotte J.P., Schachinger E. (2004). Phys. Rev. B 69, 224501

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to E. Schachinger.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Carbotte, J.P., Schachinger, E. Optical Sum Rule in Finite Bands. J Low Temp Phys 144, 61–120 (2006). https://doi.org/10.1007/s10909-006-9228-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10909-006-9228-2

Keywords

Pacs numbers

Navigation