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Generalized Drude scattering rate from the memory function formalism: an independent verification of the Sharapov-Carbotte result

  • Pankaj BhallaEmail author
  • Navinder Singh
Regular Article

Abstract

An explicit perturbative computation of the Mori’s memory function was performed by Götze and Wölfle (GW) to calculate generalized Drude scattering (GDS) rate for the case of electron-impurity and electron-phonon scattering in metals by assuming constant electronic density of states at the Fermi energy. In the present investigation, we go beyond this assumption and extend the GW formalism to the case in which there is a gap around the Fermi surface in electron density of states. The resulting GDS is compared with a recent one by Sharapov and Carbotte (SC) obtained through a different route. We find good agreement between the two at finite frequencies. However, we find discrepancies in the dc scattering rate. These are due to a crucial assumption made in SC namely ω ≫ | Σ(ϵ + ω) − Σ (ϵ) |. No such high frequency assumption is made in the memory function based technique.

Keywords

Solid State and Materials 

References

  1. 1.
    D.N. Basov, T. Timusk, Rev. Mod. Phys. 77, 721 (2005)CrossRefADSGoogle Scholar
  2. 2.
    D.N. Basov, R.D. Averitt, D. van der Marel, M. Dressel, K. Haule, Rev. Mod. Phys. 83, 471 (2011)CrossRefADSGoogle Scholar
  3. 3.
    T. Timusk, Solid State Commun. 127, 337 (2003)CrossRefADSGoogle Scholar
  4. 4.
    A.V. Puchkov, D.N. Basov, T. Timusk, J. Phys.: Condens. Matter 8, 10049 (1996)ADSGoogle Scholar
  5. 5.
    J.M. Ziman, Electrons and Phonons (Clarendon Oxford, 1960)Google Scholar
  6. 6.
    D. Pines, P. Nozieres, The Theory of Quantum Liquids (Benjamin, New York, 1966)Google Scholar
  7. 7.
    N.W. Ashcroft, N.D. Mermin, Solid State Physics (Saunders College, 1976)Google Scholar
  8. 8.
    Y.M. Dai, B. Xu, P. Cheng, H.Q. Luo, H.H. Wen, X.G. Qiu, R.P.S.M. Lobo, Phys. Rev. B 85, 092504 (2012)CrossRefADSGoogle Scholar
  9. 9.
    Y.S. Lee, K. Segawa, Z.Q. Li, W.J. Padilla, M. Dumm, S.V. Dordevic, C.C. Homes, Y. Ando, D.N. Basov, Phys. Rev. B 72, 054529 (2005)CrossRefADSGoogle Scholar
  10. 10.
    T. Holstein, Ann. Phys. 29, 410 (1964)CrossRefADSMathSciNetGoogle Scholar
  11. 11.
    P.B. Allen, Phys. Rev. B 3, 305 (1971)CrossRefADSGoogle Scholar
  12. 12.
    B. Mitrović, M.A. Fiorucci, Phys. Rev. B 31, 2694 (1985)CrossRefADSGoogle Scholar
  13. 13.
    S.G. Sharapov, J.P. Carbotte, Phys. Rev. B 72, 134506 (2005)CrossRefADSGoogle Scholar
  14. 14.
    H. Mori, Prog. Theor. Phys. 33, 423 (1965)CrossRefADSzbMATHGoogle Scholar
  15. 15.
    W. Götze, P. Wölfle, J. Low Temp. Phys. 5, 575 (1971)CrossRefADSGoogle Scholar
  16. 16.
    W. Götze, P. Wölfle, Phys. Rev. B 6, 1226 (1972)CrossRefADSGoogle Scholar
  17. 17.
    R. Zwanzig, Phys. Rev. 124, 983 (1961)CrossRefADSzbMATHGoogle Scholar
  18. 18.
    R. Zwanzig, in Lectures in Theoretical Physics, edited by W.E. Brittin, B.W. Downs, J. Downs (Interscience, New York, 1961), Vol. 3, p. 135Google Scholar
  19. 19.
    N. Plakida, J. Phys. Soc. Jpn 65, 12 (1996)CrossRefGoogle Scholar
  20. 20.
    N.M. Plakida, Z. Phys. B 103, 383 (1997)CrossRefADSGoogle Scholar
  21. 21.
    A.A. Vladimirov, D. Ihle, N.M. Plakida, Phys. Rev B 85, 224536 (2012)CrossRefADSGoogle Scholar
  22. 22.
    D. Forster, Hydrodynamic Fluctuations, Broken Symmetry And Correlation Functions (Advanced Books Classics, 1995)Google Scholar
  23. 23.
    P. Fulde, Correlated electrons in Quantum Matter (World Scientific, 2012)Google Scholar
  24. 24.
    A. Lucas, J. High Energy Phys. 2015, 1 (2015)CrossRefGoogle Scholar
  25. 25.
    A. Lucas, S. Sachdev, Phys. Rev. B 91, 195122 (2015)CrossRefADSGoogle Scholar
  26. 26.
    A.A. Patel, S. Sachdev, Phys. Rev. B 90, 165146 (2014)CrossRefADSGoogle Scholar
  27. 27.
    N. Das, N. Singh, arXiv:1509.03418 (2015)
  28. 28.
    L.P. Kadanoff, P.C. Martin, Ann. Phys. 24, 419 (1963)CrossRefADSMathSciNetzbMATHGoogle Scholar
  29. 29.
    D.N. Zubarev, Usp. Fiz. Nauk 71, 71 (1960)CrossRefMathSciNetGoogle Scholar
  30. 30.
    G.D. Mahan, Many-Particle Physics, 2nd edn. (Plenum, New York, London, 1990)Google Scholar
  31. 31.
    B. Arfi, Phys. Rev. B, 45, 2352 (1992)CrossRefADSGoogle Scholar
  32. 32.
    R. Kubo, J. Phys. Soc. Jpn 12, 570 (1957)CrossRefADSMathSciNetGoogle Scholar
  33. 33.
    J. Hwang, Phys. Rev. B 83, 014507 (2011)CrossRefADSGoogle Scholar
  34. 34.
    J. Hwang, J.P. Carbotte, Phys. Rev. B, 86, 094502 (2012)CrossRefADSGoogle Scholar
  35. 35.
    P. Bhalla, N. Singh, Eur. Phys. J. B 87, 213 (2014)CrossRefADSGoogle Scholar
  36. 36.
    T. Holstein, Phys. Rev. 96, 535 (1954)CrossRefADSGoogle Scholar
  37. 37.
    R.R. Joyce, P.L. Richards, Phys. Rev. Lett. 24, 1007 (1970)CrossRefADSGoogle Scholar
  38. 38.
    G. Grüner, Rev. Mod. Phys. 60, 1129 (1988)CrossRefADSGoogle Scholar
  39. 39.
    G. Grüner, Rev. Mod. Phys. 60, 1 (1994)CrossRefGoogle Scholar
  40. 40.
    G. Grüner, Density Waves in Solids (Addison-Wesley Publishing Company, 1994)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Physical Research LaboratoryAhmedabadIndia
  2. 2.Indian Institute of TechnologyGandhinagarIndia

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