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The Effects of Electric and Exchange Magnetic Fields on Spin Energy Dispersion, Electronic Heat Capacity and Magnetic Susceptibility of Monolayer Silicene

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Abstract

The Kane-Mele model and Green’s function technique help us to describe and survey the influences of electric and exchange magnetic fields (EF and EMF) on the dynamics of Dirac fermions in the monolayer silicene by studying the energy dispersion (ED), electronic heat capacity (EHC) and Pauli magnetic susceptibility (MS). Spin band gaps show three phases including topological insulator (TI), valley-spin polarized metal (VSPM) and band insulator (BI) in the presence of external EF. The maximum value for EHC and MS have been observed in the VSPM phase. Also, ED evolution with EMF shows that the Fermi level decreases. Interestingly, two critical temperatures have been found in the VSPM regime of 0.5 and 2 in terms of spin-orbit coupling (SOC) strength in the EHC and MS curves, respectively. In addition, remarkable point in the VSPM regime is the observed phase transition from antiferromagnetic to paramagnetic in MS curves. Competition between thermal and quantum effects is the main reason of these critical points which these findings can control the thermal properties of silicene-based devices.

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References

  1. Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Zhang, Y., Dubons, S.V., Grigorieva, I.V., Firsov, A.A.: Science 306, 666 (2004)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. Castro Neto, A.H., Guinea, F., Peres, N.M.R., et al.: Rev. Mod. Phys. 81, 109 (2009)

    Article  ADS  Google Scholar 

  4. Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Katsnelson, M.I., Grigorieva, I.V., Dubonos, S.V., Firsov, A.A.: Nature 438, 197 (2005)

    Article  ADS  Google Scholar 

  5. Butler, S.Z., Hollen, S.M., Cao, L.Y., et al.: ACS Nano 7, 2898 (2013)

    Article  Google Scholar 

  6. Xu, M.S., Liang, T., Shi, M.M., et al.: Chem. Rev. 113, 3766 (2013)

    Article  Google Scholar 

  7. Cahangirov, S., Topsakal, M., Akturk, E., et al.: Phys. Rev. Lett. 102, 236804 (2009)

    Article  ADS  Google Scholar 

  8. Malko, D., Neiss, C., Vines, F., et al.: Phys. Rev. Lett. 108, 086804 (2012)

    Article  ADS  Google Scholar 

  9. Huang, H.Q., Duan, W.H., Liu, Z.R.: New. J. Phys. 15, 023004 (2013)

    Article  ADS  Google Scholar 

  10. Sahin, H., Cahangirov, S., Topsakal, M., Bekaroglu, E., Akturk, E., Senger, R.T., Ciraci, S.: Phys. Rev. B 80, 155453 (2009)

    Article  ADS  Google Scholar 

  11. Kara, A., Enriquez, H., Seitsonend, A.P., Voone, L.C.L.Y., Vizzini, S., Aufrayg, B., Oughaddoub, H.: Surf. Sci. Rep. 67, 1 (2012)

    Article  ADS  Google Scholar 

  12. Vogt, P., De Padova, P., Quaresima, C., Avila, J., Frantzeskakis, E., Asensio, M.C., Resta, A., Ealet, B., Le Lay, G.: Phys. Rev. Lett. 108(15), 155501 (2012)

    Article  ADS  Google Scholar 

  13. Fleurence, A., Friedlein, R., Ozaki, T., Kawai, H., Wang, Y., Yamada-Takamura, Y.: Phys. Rev. Lett. 108(24), 245501 (2014)

    Article  ADS  Google Scholar 

  14. Wang, X.-Q., Li, H.-D., Wang, J.-T.: Phys. Chem. Chem. Phys. 14, 3031 (2012)

    Article  Google Scholar 

  15. Zhang, C., Yan, S.: J. Phys. Chem. C 116, 4163 (2012)

    Article  Google Scholar 

  16. Liu, C.-C., Feng, W., Yao, Y.: Phys. Rev. Lett. 107, 076802 (2011)

    Article  ADS  Google Scholar 

  17. Chen, L., Feng, B.J., Wu, K.H.: Appl. Phys. Lett. 102, 081602 (2013)

    Article  ADS  Google Scholar 

  18. Drummond, N.D., Zolyomi, V., Fal’ko, V.I.: Phys. Rev. B 85, 075423 (2012)

    Article  ADS  Google Scholar 

  19. Ni, Z., Liu, Q., Tang, K., Zheng, J., Zhou, J., Qin, R., Gao, Z., Yu, D., Lu, J.: Nano Lett. 12, 113 (2012)

    Article  ADS  Google Scholar 

  20. Min, H., Hill, J.E., Sinitsyn, N.A., Sahu, B.R., Kleinman, L., MacDonald, A.H.: Phys. Rev. B 74, 165310 (2006)

    Article  ADS  Google Scholar 

  21. Yao, Y., Ye, F., Qi, X.-L., Zhang, S.-C., Fang, Z.: Phys. Rev. B 75(R), 041401 (2007)

    Article  ADS  Google Scholar 

  22. Konschuh, S., Gmitra, M., Fabian, J.: Phys. Rev. B 82, 245412 (2010)

    Article  ADS  Google Scholar 

  23. Liu, C.C., Jiang, H., Yao, Y.G.: Phys. Rev. B 84, 195430 (2011)

    Article  ADS  Google Scholar 

  24. Tabert, C.J., Nicol, E.J.: Phys. Rev. B 88, 085434 (2013)

    Article  ADS  Google Scholar 

  25. Kogan, E.: Graphene 2, 74 (2013)

    Article  Google Scholar 

  26. Gong, L., Xiu, S.L., Zheng, M.M., Zhao, P., Zhang, Z., Liang, Y.Y., Chen, G., Kawazoe, Y.: J. Mater. Chem. C 2, 8773 (2014)

    Article  Google Scholar 

  27. Zibouche, N., Philipsen, P., Heine, T., Kuc, A.: Phys. Chem. Chem. Phys. 16, 11251 (2014)

    Article  Google Scholar 

  28. Kittle, C.: Introduction to solid state physics, 8th edn. Wiley, New York (2004)

    Google Scholar 

  29. Pathria, R.K.: Statistical mechanics. Oxford press, London (1997)

    MATH  Google Scholar 

  30. Drummond, N.D., Zolyomi, V., Fal’ko, V.I.: Phys. Rev. B 85, 075423 (2012)

    Article  ADS  Google Scholar 

  31. Ni, Z., Liu, Q., Tang, K., Zheng, J., Zhou, J., Qin, R., Gao, Z., Yu, D., Lu, J.: Nano Lett. 12, 113 (2012)

    Article  ADS  Google Scholar 

  32. Ezawa, M.: New J. Phys. 14, 033003 (2012)

    Article  ADS  Google Scholar 

  33. Jellal, A., Redouani, I., Bahlouli, H.: Phys. E. 72, 149 (2015)

    Article  Google Scholar 

  34. Ghosh, S., Calizo, I., Teweldebrhan, D., Pokatilov, E.P., Nika, D.L., Balandin, A.A., Bao, W., Miao, F., Ning Lau, C.: Appl. Phys. Lett. 92, 151911 (2008)

    Article  ADS  Google Scholar 

  35. Balandin, A.A., et al.: Nature mater. 10, 569 (2011)

    Article  ADS  Google Scholar 

  36. Katti, V.S., Kubakaddi, S.S.: Phys. E. 47, 192 (2013)

    Article  Google Scholar 

  37. Yarmohammadi, M.: Solid State Commun. 250, 84 (2017)

    Article  ADS  Google Scholar 

  38. Ominato, Y., Koshino, M.: Phys. Rev. B 87, 115433 (2013)

    Article  ADS  Google Scholar 

  39. Perez, J.A.C.: Phys. E. 44, 2089 (2012)

    Article  Google Scholar 

  40. Aufray, B., Vizzini, A., Oughaddou, H., Lndri, C., Ealet, B., Lay, G.L.: Appl. Phys. Lett. 96, 183102 (2010)

    Article  ADS  Google Scholar 

  41. Kane, C.L., Mele, E.J.: Phys. Rev. Lett. 95, 146802 (2005)

    Article  ADS  Google Scholar 

  42. Kane, C.L., Mele, E.J.: Phys. Rev. Lett. 95, 226801 (2005)

    Article  ADS  Google Scholar 

  43. Yokoyama, T.: Phys. Rev. B 87(R), 241409 (2013)

    Article  ADS  Google Scholar 

  44. Haugen, H., Huertas-Hernando, D., Brataas, A.: Phys. Rev. B 77, 115406 (2008)

    Article  ADS  Google Scholar 

  45. Qiao, Z., Yang, S.A., Feng, W., Tse, W.-K., Ding, J., Yao, Y., Wang, J., Niu, Q.: Phys. Rev. B 82, 161414 (2010)

    Article  ADS  Google Scholar 

  46. Economou, E.N.: Green’s functions in quantum physics, 3rd edn. Springer, Berlin (2006)

    Book  Google Scholar 

  47. Kittle, C.: Introduction to solid state physics, 8th edn. Wiley, New York (2004)

    Google Scholar 

Download references

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Correspondence to Kavoos Mirabbaszadeh.

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Mirabbaszadeh, K., Yarmohammadi, M. The Effects of Electric and Exchange Magnetic Fields on Spin Energy Dispersion, Electronic Heat Capacity and Magnetic Susceptibility of Monolayer Silicene. J Supercond Nov Magn 30, 1859–1866 (2017). https://doi.org/10.1007/s10948-017-3981-0

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  • DOI: https://doi.org/10.1007/s10948-017-3981-0

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