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Effect of Gap Parameter on Electronic Heat Capacity and Magnetic Susceptibility of Graphene in the Presence of Holstein Phonons

  • Hamed Rezania
  • Mohsen Yarmohammadi
Original Paper
  • 71 Downloads

Abstract

Thermodynamic properties of gapped graphene-like structures by considering the effects of interaction between electrons and Holstein phonons have been studied. Particularly, we study the heat capacity and paramagnetic susceptibility of structures as a function of temperature within the Green’s function method with the help of Holstein model. The paramagnetic susceptibility and heat capacity can be derived by using density of states based on the Kubo formula. We have found the energy dependence of density of states for various values of gap in the presence of Holstein phonons. Finally, the temperature behaviors of specific heat and spin susceptibility of gapped graphene structure due to electron-phonon coupling have been investigated. Our results show the electron-phonon interaction leads to the appearance of a double van Hov singularity for each value of gap parameter. Also, electron-phonon coupling affects the value of heat capacity and magnetic susceptibility at low temperatures.

Keywords

Heat capacity Paramagnetic susceptibility Green’s function 

References

  1. 1.
    Novoselov, K.S., et al.: Science 306, 666 (2004)ADSCrossRefGoogle Scholar
  2. 2.
    Castro Neto, A.H., Guinea, F., Peres, N.M.R., Novoselov, K.S., Geim, A.K.: Rev. Mod. Phys. 81, 109 (2009)ADSCrossRefGoogle Scholar
  3. 3.
    Slater, J.C., Koster, G.F.: Phys. Rev. 94, 1498 (1954)ADSCrossRefGoogle Scholar
  4. 4.
    Saito, R., Dresselhaus, G., Dresselhaus, M.S.: Physical Properties of Carbon Nanotubes, p. 105. Imperial College Press, London (1998)CrossRefGoogle Scholar
  5. 5.
    Kaxiras, E.: Atomic and Electronic Structure of Solids, p. 107. Cambridge University Press, UK (2003)CrossRefGoogle Scholar
  6. 6.
    Aktruck, A., Goldman, N.: J. Appl. Phys. 103, 053702 (2008)ADSCrossRefGoogle Scholar
  7. 7.
    Basko, D.M., Aleiner, I.L.: Phys. Rev. B 77(R), 041409 (2008)ADSCrossRefGoogle Scholar
  8. 8.
    Park, C.-H., Giustino, F., Cohen, M.L., Louie, S.G.: Nano Lett. 8, 4229 (2008)ADSCrossRefGoogle Scholar
  9. 9.
    Su, W.P., Schrieffer, J.R., Heeger, A.J.: Phys. Rev. Lett. 42, 1698 (1979)ADSCrossRefGoogle Scholar
  10. 10.
    Holstein, T.: Ann. Phys. (N.Y) 8, 325 (1959)ADSCrossRefGoogle Scholar
  11. 11.
    Capone, M., Ciuchi, S.: Phys. Rev. Lett. 91, 186405 (2003)ADSCrossRefGoogle Scholar
  12. 12.
    Stauber, T., Peres, N.M.R., Phis, J.: Phys. Rev. B 76, 205423 (2007)ADSCrossRefGoogle Scholar
  13. 13.
    Piscanec, S., et al: Phys. Rev. Lett 93, 185503 (2004)ADSCrossRefGoogle Scholar
  14. 14.
    Piscanec, S., et al: Phys. Rev. B 75, 035427 (2007)ADSCrossRefGoogle Scholar
  15. 15.
    Hudgens, S., Kastner, M., Fritzsche, H.: Phys. Rev. Lett 33, 1552 (1974)ADSCrossRefGoogle Scholar
  16. 16.
    Safran, S.A., DiSalvo, F.J.: Phys. Rev. B 20, 4889 (1979)ADSCrossRefGoogle Scholar
  17. 17.
    McClure, J.W.: Phys. Rev. B 104, 666 (1956)ADSCrossRefGoogle Scholar
  18. 18.
    McClure, J.W.: Phys. Rev. B 119, 606 (1960)ADSCrossRefGoogle Scholar
  19. 19.
    Koshino, M., Ando, T.: Phys. Rev. B 76, 085425 (2007)ADSCrossRefGoogle Scholar
  20. 20.
    Liu, J., Ma, Z., Wright, A.R., Zhang, C.: J. Appl. Phys 103, 103711 (2008)ADSCrossRefGoogle Scholar
  21. 21.
    Peres, N.M.R., Guinea, F., Castro Neto, A.H.: Phys. Rev. B 73, 125411 (2006)ADSCrossRefGoogle Scholar
  22. 22.
    Yi, K.S., Kim, D., Park, K.S.: Phys. Rev. B 76, 115410 (2007)ADSCrossRefGoogle Scholar
  23. 23.
    Osella, S., Minoia, A., Beljonne, D.: J. Phys. Chem. C 120, 6651 (2016)CrossRefGoogle Scholar
  24. 24.
    Rassulinejad-Mousavi, S.M., Mao, Y., Zhang, Y.: J. Appl. Phys 119, 244304 (2016)ADSCrossRefGoogle Scholar
  25. 25.
    Rassulinejad-Mousavi, S.M., Seyf, H.R., Abbasbandy, S.: J. Porous Media 16, 241 (2013)CrossRefGoogle Scholar
  26. 26.
    Rassulinejad-Mousavi, S.M., Abbasbandy, S.: J Fluid Eng-T ASME 133, 101207 (2011)CrossRefGoogle Scholar
  27. 27.
    Rassulinejad-Mousavi, S.M., Abbasbandy, S., Alsulami, H.H.: EPJ Plus 129, 1 (2014)Google Scholar
  28. 28.
    Seyf, H.R., Rassulinejad-Mousavi, S.M.: J Fluid Eng-T ASME 133, 091203 (2011)CrossRefGoogle Scholar
  29. 29.
    Stauber, T., Peres, N.M.: J. Phys.: Condens. Matter 20, 055002 (2008)ADSGoogle Scholar
  30. 30.
    Calandra, M., Mauri, F.: Phys. Rev. B 76, 205411 (2007)ADSCrossRefGoogle Scholar
  31. 31.
    Tse, W.-K., Sarma, D.: Phys. Rev. Lett 99, 236802 (2007)ADSCrossRefGoogle Scholar
  32. 32.
    Migdal, A.B.: Zh. Eksp. Teor. Fiz 34, 1438 (1958)Google Scholar
  33. 33.
    Mahan, G.D.: Many Particle Physics. Plenumn Press, New York (1993)Google Scholar
  34. 34.
    Grosso, G., Parravicini, G.P.: Solid State Physics. Academic Press, Singapore (2000)Google Scholar
  35. 35.
    Bruus, H., Flensberg, K.: Many Body Quantum Theory in Condensed Matter Physics. Oxford University Press, Denmark (2004)Google Scholar
  36. 36.
    Nolthing, W., Ramakanth, A.: Qunatum Theory of Magnetism. Springer, New York (2009)CrossRefGoogle Scholar
  37. 37.
    Kittel, C.: Introduction to Solid State Physics, 8th edn. Wiley, New York (2004)zbMATHGoogle Scholar
  38. 38.
    Hone, J., Batlogg, B., Benes, Z., Johnson, A.T., Fischer, J.E.: Science 289, 1730 (2000)ADSCrossRefGoogle Scholar
  39. 39.
    Mousavi, H., Khodadadi, J.: Phys. E. 50, 11 (2013)CrossRefGoogle Scholar
  40. 40.
    Mousavi, H.: J. Magn. Magn. Mater. 323, 1537 (2011)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of PhysicsRazi UniversityKermanshahIran
  2. 2.Young Researchers and Elite Club, Kermanshah BranchIslamic Azad UniversityKermanshahIran

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