Eigenspectra and thermodynamic quantities in graphene under the inside and outside magnetic fields

Abstract.

In this research, firstly, the Dirac-Weyl equation has been solved for the bound states of a graphene quantum dot formed by the inhomogeneous distributions of the magnetic fields inside and outside the graphene quantum dot by using the series method. Then, we have obtained the density of states, electronic density and gate voltage using the obtained fermions energy. Also, we have calculated the wave function as the Hessenberg determinants from calculation of their elements. On the other hand, we have obtained of the thermodynamic quantities of the Dirac-Weyl fermions inside the graphene quantum dot. Finally, we have discussed on the obtained analytically results.

This is a preview of subscription content, access via your institution.

References

  1. 1

    C.A. Downing, M.E. Portnoi, Phys. Rev. A 90, 052116 (2014)

    ADS  Article  Google Scholar 

  2. 2

    T.O. Wehling, A.M. Black-Schaffer, A.V. Balatsky, Adv. Phys. 63, 1 (2014)

    ADS  Article  Google Scholar 

  3. 3

    P. Rodriguez-Lopez, W.K. Tes, D.A.R. Dalvit, J. Phys.: Condens. Matter 27, 214019 (2015)

    ADS  Google Scholar 

  4. 4

    K.S. Novoloselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Science 306, 666 (2004)

    ADS  Article  Google Scholar 

  5. 5

    A.K. Geim, K.S. Novoselov, Nat. Mater. 6, 183 (2007)

    ADS  Article  Google Scholar 

  6. 6

    C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud et al., Science 312, 1191 (2006)

    ADS  Article  Google Scholar 

  7. 7

    A. Rycerz, J. Tworzydlo, C.W.J. Beenakker, Nat. Phys. 3, 172 (2007)

    Article  Google Scholar 

  8. 8

    M.C. Lemme, T.J. Echtermeyer, M. Baus, H. Kurz, IEEE Electron. Device Lett. 28, 282 (2007)

    ADS  Article  Google Scholar 

  9. 9

    B. Huard, J.A. Sulpizio, N. Stander, K. Todd, B. Yang, D. Goldhaber-Gordon, Phys. Rev. Lett. 98, 236803 (2007)

    ADS  Article  Google Scholar 

  10. 10

    K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos et al., Nature 438, 197 (2005)

    ADS  Article  Google Scholar 

  11. 11

    K. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, H. Stormer, Solid State Commun. 146, 351 (2008)

    ADS  Article  Google Scholar 

  12. 12

    K. Bolotin, K. Sikes, J. Hone, H. Stormer, P. Kim, Phys. Rev. Lett. 101, 096802 (2008)

    ADS  Article  Google Scholar 

  13. 13

    M.I. Katsnelson, K.S. Novoselov, A.K. Geim, Nature Phys. 2, 620 (2006)

    ADS  Article  Google Scholar 

  14. 14

    M. Eshghi, H. Mehraban, C. R. Phys. 18, 47 (2017)

    ADS  Article  Google Scholar 

  15. 15

    M. Eshghi, H. Mehraban, J. Math. Phys. 57, 082105 (2016)

    ADS  MathSciNet  Article  Google Scholar 

  16. 16

    A. Dobry, O. Fojon, M. Gadella, L.P. Lara, Appl. Math. Comput. 235, 8 (2014)

    MathSciNet  Google Scholar 

  17. 17

    M.A. Dariescu, C. Dariescu, C. Cretu, O. Buhucianu, Rom. J. Phys. 58, 703 (2013)

    Google Scholar 

  18. 18

    E. Milpas, M. Torres, G. Marguia, J. Phys.: Condens. Matter 23, 245304 (2011)

    ADS  Google Scholar 

  19. 19

    S. Kuru, J. Negro, L.M. Nito, J. Phys.: Condens. Matter 21, 455305 (2009)

    ADS  Google Scholar 

  20. 20

    P. Roy, T.K. Ghosh, K. Bhattacharya, J. Phys.: Condens. Matter 24, 055301 (2012)

    ADS  Google Scholar 

  21. 21

    J. Karwowski, H.A. Witek, Theor. Chem. Acc. 133, 1494 (2014)

    Article  Google Scholar 

  22. 22

    K. Kaygisiz, A. Sahin, Gen. Math. Notes 9, 32 (2012)

    Google Scholar 

  23. 23

    L.J. Yin, K.K. Bai, W.X. Wang, S.Y. Li, Y. Zhang, L. He, Front. Phys. 12, 127208 (2017)

    Article  Google Scholar 

  24. 24

    A.J.M. Giesbers, Ponomarenko, K.S. Novoselov, A.K. Geim, M.I. Katsnelson, J.C. Maan, U. Zeitler, Phys. Rev. B 80, 201403(R) (2009)

    ADS  Article  Google Scholar 

  25. 25

    Y. Zhang, Z. Jiang, J.P. Small et al., Phys. Rev. Lett. 96, 136806 (2006)

    ADS  Article  Google Scholar 

  26. 26

    A. Boumali, Phys. Scr. 90, 045702 (2015)

    ADS  Article  Google Scholar 

  27. 27

    S.K. Jacimovski, V.D. Sajfert, J.P. Setrajcic, D.I. Rakovic, Quantum Matter 4, 559 (2015)

    Article  Google Scholar 

  28. 28

    N.M.R. Peres, F. Guinea, A. Castro Neto, Phys. Rev. B 73, 125411 (2006)

    ADS  Article  Google Scholar 

  29. 29

    L. Vicarelli, M.S. Vitiello, D. Coquillat et al., Nat. Mater. 11, 865 (2012)

    ADS  Article  Google Scholar 

  30. 30

    X. Ma, W. Gu, J. Shen, Y. Tang, Nano. Res. Lett. 7, 677 (2012)

    Article  Google Scholar 

  31. 31

    Y. Iyechika, Sci. Tech. Tren. (Quart. Rev.) 37, 76 (2010)

    Google Scholar 

  32. 32

    E. Cazalas, B.K. Sarker, M.E. Moore et al., Appl. Phys. Lett. 106, 223503 (2015)

    ADS  Article  Google Scholar 

  33. 33

    B. Zhan, C. Li, J. Yang et al., Small 20, 4042 (2014)

    Google Scholar 

  34. 34

    C.J. Paez, L.C. Pereira, J.N.B. Rodrigues, N.M.R. Peres, Phys. Rev. B 92, 045426 (2015)

    ADS  Article  Google Scholar 

  35. 35

    A. Matulis, M. Peters, Phys. Rev. B 75, 125429 (2007)

    ADS  Article  Google Scholar 

  36. 36

    M. Tahir, K. Sabeeh, Phys. Rev. B 77, 195421 (2008)

    ADS  Article  Google Scholar 

  37. 37

    R. Nasir, K. Sabeeh, M. Tahir, Phys. Rev. B 81, 085402 (2010)

    ADS  Article  Google Scholar 

  38. 38

    A.R. Wright, J. Liu, Z. Ma, Z. Zeng, W. Xu, C. Zhang, Microelectron. J. 40, 716 (2009)

    Article  Google Scholar 

  39. 39

    J.S. Ardenghi, P. Bechthold, E. Gonzalez, P. Jasen, A. Juan, arXiv:1310.7154v1 (2013)

  40. 40

    E.W. Barnes, A new development of the theory of the hypergeometric functions, in Proceedings of the London Mathematical Society, Vol. s2-6, Issue 1 (1908) p. 141, https://doi.org/10.1112/plms/s2-6.1.141

  41. 41

    R.K. Patria, Statistical Mechanics, 1st ed. (Pergamon Press, Oxford, 1972)

  42. 42

    N. Byers, C.N. Yang, Phys. Rev. Lett. 7, 46 (1961)

    ADS  Article  Google Scholar 

  43. 43

    S.C. Lee, S.W. Kim, J. Korean Phys. Soc. 60, 436 (2012)

    ADS  Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to M. Eshghi.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Eshghi, M., Mehraban, H. & Ahmadi Azar, I. Eigenspectra and thermodynamic quantities in graphene under the inside and outside magnetic fields. Eur. Phys. J. Plus 132, 477 (2017). https://doi.org/10.1140/epjp/i2017-11728-9

Download citation