Year 2017, Volume 38 , Issue 3, Pages 435 - 443 2017-09-30

Fosforenin Sürekli Modeli Üzerine Dördüncü Mertebeden Dalga Vektörünün Etkisi
Effects of Quartic Wave-Vectors on Continuum Model of Phosphorene

Aybey MOGULKOC [1]


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.

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.

  • [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.
Subjects Basic Sciences
Journal Section Articles
Authors

Author: Aybey MOGULKOC

Dates

Publication Date : September 30, 2017

Bibtex @research article { csj340476, journal = {Cumhuriyet Science Journal}, issn = {2587-2680}, eissn = {2587-246X}, address = {csj@cumhuriyet.edu.tr}, publisher = {Cumhuriyet University}, year = {2017}, volume = {38}, pages = {435 - 443}, doi = {10.17776/csj.340476}, title = {Effects of Quartic Wave-Vectors on Continuum Model of Phosphorene}, key = {cite}, author = {MOGULKOC, Aybey} }
APA MOGULKOC, A . (2017). Effects of Quartic Wave-Vectors on Continuum Model of Phosphorene. Cumhuriyet Science Journal , 38 (3) , 435-443 . DOI: 10.17776/csj.340476
MLA MOGULKOC, A . "Effects of Quartic Wave-Vectors on Continuum Model of Phosphorene". Cumhuriyet Science Journal 38 (2017 ): 435-443 <https://dergipark.org.tr/en/pub/csj/issue/31252/340476>
Chicago MOGULKOC, A . "Effects of Quartic Wave-Vectors on Continuum Model of Phosphorene". Cumhuriyet Science Journal 38 (2017 ): 435-443
RIS TY - JOUR T1 - Effects of Quartic Wave-Vectors on Continuum Model of Phosphorene AU - Aybey MOGULKOC Y1 - 2017 PY - 2017 N1 - doi: 10.17776/csj.340476 DO - 10.17776/csj.340476 T2 - Cumhuriyet Science Journal JF - Journal JO - JOR SP - 435 EP - 443 VL - 38 IS - 3 SN - 2587-2680-2587-246X M3 - doi: 10.17776/csj.340476 UR - https://doi.org/10.17776/csj.340476 Y2 - 2017 ER -
EndNote %0 Cumhuriyet Science Journal Effects of Quartic Wave-Vectors on Continuum Model of Phosphorene %A Aybey MOGULKOC %T Effects of Quartic Wave-Vectors on Continuum Model of Phosphorene %D 2017 %J Cumhuriyet Science Journal %P 2587-2680-2587-246X %V 38 %N 3 %R doi: 10.17776/csj.340476 %U 10.17776/csj.340476
ISNAD MOGULKOC, Aybey . "Effects of Quartic Wave-Vectors on Continuum Model of Phosphorene". Cumhuriyet Science Journal 38 / 3 (September 2017): 435-443 . https://doi.org/10.17776/csj.340476
AMA MOGULKOC A . Effects of Quartic Wave-Vectors on Continuum Model of Phosphorene. CSJ. 2017; 38(3): 435-443.
Vancouver MOGULKOC A . Effects of Quartic Wave-Vectors on Continuum Model of Phosphorene. Cumhuriyet Science Journal. 2017; 38(3): 443-435.