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Effects of Quartic Wave-Vectors on Continuum Model of Phosphorene

Year 2017, , 435 - 443, 30.09.2017

Aybey Mogulkoc

https://doi.org/10.17776/csj.340476

Abstract

Phosphorene is the
monolayer structures of black phosphorous. Its low-energy physics can be
described by continuum model in the scheme of k∙p theory. Validity of energy
range for this model can be improved by extra terms as trigonal warp effect in
graphene. We construct a new continuum model by expanding the tight-binding
Hamiltonian of phosphorene up to the order of k4 . The new quartic
model increases the energy range where the eigenvalues of continuum and
tight-binding Hamiltonian are matched. Moreover, we examine the Landau levels
of phosphorene by the influence of quartic terms. While quartic terms have
insignificant effects on the lower Landau levels of phosphorene, they have
non-negligible contributions to the higher levels. In this study, we propose a
new continuum model which brings better description to the dynamics of
phosphorene charge carriers.

Keywords

Phosphorene continuum model Landau levels

References

  • [1]. Novoselov, K. S., Geim, A. K., Morozov, S. V., Jiang, D., Zhang, Y., Dubonos, S. V., Grigorieva, I. V., Firsov, A. A. 2004. Science 306: 666-669.
  • [2]. Katsnelson, Mikhail I. Graphene: carbon in two dimensions, 1st ed., Cambridge University Press, 2012.
  • [3]. Joshua, B. S., Hagaman, D., Hai-Feng, J. 2016. Nanotechnology 27: 215602.
  • [4]. Favron, A., Gaufr`es, E., Fossard, F., Phaneuf-LHeureux, A. L., Tang, N. Y. W., L´evesque, P. L., Loiseau, A., Leonelli, R., Francoeur, S., Martel, R., 2015. Nat. Mater. 14: 826–832.
  • [5]. Brent, Jack R., Savjani, Nicky, Lewis, Edward A., Haigh, Sarah J., Lewis, David J., O’Brien, Paul 2014. Chem. Commun. 50: 13338-13341.
  • [6]. Liu, Han, Neal, Adam T., Zhu, Zhen, Luo, Zhe, Xu, Xianfan, Tomnek, D., Ye, Peide D. 2014. ACS Nano 8: 4033-4041.
  • [7]. Li, L., Yu, Y., Ye, G. J., Ge, Q., Ou, X., Wu, H., Feng, D., Chen, X. H., Zhang, Y. 2014. Nat. Nanotech. 9: 372.
  • [8]. Koenig, S. P., Doganov, R. A., Schmidt, H., Castro Neto, A. H., O¨ zyilmaz, B. 2014. Appl. Phys. Lett. 104: 103106.
  • [9]. Tran, V., Soklaski, R., Liang, Y., Yang, L. 2014. Phys. Rev. B 89: 235319.
  • [10]. Qiao, Jingsi, Kong, Xianghua, Hu, Zhi-Xin, Yang, Feng, Ji, Wei 2014. Nat. Commun. 5: 4475.
  • [11]. Xia, F., Wang, H., Jia, Y. 2014. Nat. Commun. 5: 4458.
  • [12]. Wang, X., Jones, A. M., Seyler, K. L., Tran, V., Jia, Y., Zhao, H., Wang, H., Yang, L., Xu, X., Xia, F. 2015. Nat. Nanotech. 10: 517.
  • [13]. Rudenko, A. N., Yuan, Shengjun, Katsnelson, M. I. 2015. Phys. Rev. B 92: 085419.
  • [14]. Rudenko, A. N., Katsnelson, M. I. 2014. Phys. Rev. B 89: 201408.
  • [15]. Jain, Ankit, McGaughey, Alan J. H. 2015. Scientific Reports 5: 8501.
  • [16]. Semenoff, Gordon W. 1984. Phys. Rev. Lett. 53: 2449-2452.
  • [17]. Katsnelson, M.I., Novoselov, K.S., Geim, A.K. 2006. Nature Physics 2: 620–625.
  • [18]. Ajiki, H., Ando, T. 1996. J. Phys. Soc. Jpn. 65: 505-514.
  • [19]. Rakyta, P., Korm´anyos, A., Cserti, J. 2010. Phys. Rev. B 82: 113405.
  • [20]. Azizi, J., Phirouznia, A., Hasanirokh, K. 2015. Physica E 68: 28–32.
  • [21]. Pereira, J. M., Katsnelson, M. I. 2015. Phys. Rev. B 92: 075437.
  • [22]. Zhou, X. Y. Zhang, R., Sun, J. P., Zou, Y. L., Zhang, D., Lou, W. K., Cheng, F., Zhou, G. H., Zhai, F., Chang, Kai 2015. Scientific Reports 5: 12295.
  • [23]. Ezawa, M. 2014. New J. Phys. 16: 115004.
  • [24]. Ziletti, A., Huang, S. M., Coker, D. F., Lin, H. 2015. Phys. Rev. B 92: 085423.
  • [25]. Mogulkoc, A., Modarresi, M., Rudenko, A. N. 2017. Phys. Rev. B 96: 085434.
  • [26]. Long, G., Maryenko, D., Pezzini, S., Xu, S., Wu, Z., Han, T., Lin, J., Wang, Y., An, L., Cai, Y., Zeitler, U., Wang, N. 2017. arXiv preprint arXiv:1703.05177.

Fosforenin Sürekli Modeli Üzerine Dördüncü Mertebeden Dalga Vektörünün Etkisi

Year 2017, , 435 - 443, 30.09.2017

Aybey Mogulkoc

https://doi.org/10.17776/csj.340476

Abstract

Fosforen siyah
fosforun tek tabakalı yapısıdır. Düşük enerji fiziği k∙p teorisi çerçevesinde
sürekli model ile tasvir edilebilir. Sürekli modelin geçerli olduğu enerji
aralığı grafendeki üçgensel eğrilikte olduğu gibi ek terimler ile artırılabilir.
Burada fosforenin sıkı-bağ Hamiltonyeni k4 mertebesine kadar seri
açılarak yeni bir sürekli model oluşturulmuştur. Dördüncü mertebeden yeni model
sürekli ve sıkı-bağ Hamiltonyenlerinin özdeğerlerinin örtüştüğü enerji
aralığını artırmıştır. Dahası dördüncü mertebeden terimin katkısı göz önünde
bulundurularak fosforenin Landau seviyeleri incelenmiştir. Dördüncü mertebeden
terimin düşük Landau seviyeleri üzerinde göz ardı edilebilir etkiye sahipken,
yüksek Landau seviyelerine ihmal edilemeyen katkılar getirir. Bu çalışmada
fosforenin yük taşıyıcılarının dinamiğini daha iyi tasvir eden yeni bir sürekli
model önerilmiştir.

Keywords

Fosforen sürekli model Landau seviyeleri

References

  • [1]. Novoselov, K. S., Geim, A. K., Morozov, S. V., Jiang, D., Zhang, Y., Dubonos, S. V., Grigorieva, I. V., Firsov, A. A. 2004. Science 306: 666-669.
  • [2]. Katsnelson, Mikhail I. Graphene: carbon in two dimensions, 1st ed., Cambridge University Press, 2012.
  • [3]. Joshua, B. S., Hagaman, D., Hai-Feng, J. 2016. Nanotechnology 27: 215602.
  • [4]. Favron, A., Gaufr`es, E., Fossard, F., Phaneuf-LHeureux, A. L., Tang, N. Y. W., L´evesque, P. L., Loiseau, A., Leonelli, R., Francoeur, S., Martel, R., 2015. Nat. Mater. 14: 826–832.
  • [5]. Brent, Jack R., Savjani, Nicky, Lewis, Edward A., Haigh, Sarah J., Lewis, David J., O’Brien, Paul 2014. Chem. Commun. 50: 13338-13341.
  • [6]. Liu, Han, Neal, Adam T., Zhu, Zhen, Luo, Zhe, Xu, Xianfan, Tomnek, D., Ye, Peide D. 2014. ACS Nano 8: 4033-4041.
  • [7]. Li, L., Yu, Y., Ye, G. J., Ge, Q., Ou, X., Wu, H., Feng, D., Chen, X. H., Zhang, Y. 2014. Nat. Nanotech. 9: 372.
  • [8]. Koenig, S. P., Doganov, R. A., Schmidt, H., Castro Neto, A. H., O¨ zyilmaz, B. 2014. Appl. Phys. Lett. 104: 103106.
  • [9]. Tran, V., Soklaski, R., Liang, Y., Yang, L. 2014. Phys. Rev. B 89: 235319.
  • [10]. Qiao, Jingsi, Kong, Xianghua, Hu, Zhi-Xin, Yang, Feng, Ji, Wei 2014. Nat. Commun. 5: 4475.
  • [11]. Xia, F., Wang, H., Jia, Y. 2014. Nat. Commun. 5: 4458.
  • [12]. Wang, X., Jones, A. M., Seyler, K. L., Tran, V., Jia, Y., Zhao, H., Wang, H., Yang, L., Xu, X., Xia, F. 2015. Nat. Nanotech. 10: 517.
  • [13]. Rudenko, A. N., Yuan, Shengjun, Katsnelson, M. I. 2015. Phys. Rev. B 92: 085419.
  • [14]. Rudenko, A. N., Katsnelson, M. I. 2014. Phys. Rev. B 89: 201408.
  • [15]. Jain, Ankit, McGaughey, Alan J. H. 2015. Scientific Reports 5: 8501.
  • [16]. Semenoff, Gordon W. 1984. Phys. Rev. Lett. 53: 2449-2452.
  • [17]. Katsnelson, M.I., Novoselov, K.S., Geim, A.K. 2006. Nature Physics 2: 620–625.
  • [18]. Ajiki, H., Ando, T. 1996. J. Phys. Soc. Jpn. 65: 505-514.
  • [19]. Rakyta, P., Korm´anyos, A., Cserti, J. 2010. Phys. Rev. B 82: 113405.
  • [20]. Azizi, J., Phirouznia, A., Hasanirokh, K. 2015. Physica E 68: 28–32.
  • [21]. Pereira, J. M., Katsnelson, M. I. 2015. Phys. Rev. B 92: 075437.
  • [22]. Zhou, X. Y. Zhang, R., Sun, J. P., Zou, Y. L., Zhang, D., Lou, W. K., Cheng, F., Zhou, G. H., Zhai, F., Chang, Kai 2015. Scientific Reports 5: 12295.
  • [23]. Ezawa, M. 2014. New J. Phys. 16: 115004.
  • [24]. Ziletti, A., Huang, S. M., Coker, D. F., Lin, H. 2015. Phys. Rev. B 92: 085423.
  • [25]. Mogulkoc, A., Modarresi, M., Rudenko, A. N. 2017. Phys. Rev. B 96: 085434.
  • [26]. Long, G., Maryenko, D., Pezzini, S., Xu, S., Wu, Z., Han, T., Lin, J., Wang, Y., An, L., Cai, Y., Zeitler, U., Wang, N. 2017. arXiv preprint arXiv:1703.05177.
There are 26 citations in total.

Details

Journal Section Articles
Authors

Aybey Mogulkoc

Publication Date September 30, 2017
Submission Date June 6, 2017
Acceptance Date July 19, 2017
Published in Issue Year 2017

Cite

APA Mogulkoc, A. (2017). Effects of Quartic Wave-Vectors on Continuum Model of Phosphorene. Cumhuriyet Science Journal, 38(3), 435-443. https://doi.org/10.17776/csj.340476