Applications of Double Group Theory in 2D Materials
Abstract
Group theory is a fundamental mathematical frame- work valuable for analyzing the band structures in materials science. The hexagonal structures have unique electronic struc- tures, especially in 2D materials in group-IV, where the system is observed as the topological insulator. Meanwhile, in the case of group-V, it is semiconductors. This paper analyzes group- IV and group-V band structures based on group theory and proposes a method to identify the irreducible representation (IR) in symmorphic systems. It is found that all materials in group- IV are topological insulators. The evaluation of Z2 invariant v in group-V found that the phosphorene and bismuthene cases are v = 0 and v = 1, respectively, and belong to trivial and topological insulator materials for phosphorene and bismuthene, respectively.
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V. I. Senashov, IOP Conference Series: Materials Science and Engineering, vol. 1230, no. 1, p. 012018, mar 2022.
K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science, vol. 306, no. 5696, pp. 666–669, 2004.
A. Geim and K. Novoselov, Nat. Mater., vol. 6, p. 183–191, 2007.
P. Vogt, P. De Padova, C. Quaresima, J. Avila, E. Frantzeskakis, M. C. Asensio, A. Resta, B. Ealet, and G. Le Lay, Phys. Rev. Lett., vol. 108, p. 155501, Apr 2012.
L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, H. Xian Chen, and Y. Zhang, Nat. Nanotechnol., vol. 9, p. 372, 2014.
M. N. Brunetti, O. L. Berman, and R. Y. Kezerashvili, Phys. Rev. B, vol. 100, p. 155433, Oct 2019.
Y. Tanaka, M. Saito, and F. Ishii, Jpn J. Appl. Phys., vol. 57, no. 12, p. 125201, 2018.
I. ˇ Zuti´c, J. Fabian, and S. Das Sarma, Rev. Mod. Phys., vol. 76, pp. 323–410, 2004.
Z. Liu, C.-X. Liu, Y.-S. Wu, W.-H. Duan, F. Liu, and J. Wu, Phys. Rev. Lett., vol. 107, p. 136805, 2011.
T. Nagao, J. T. Sadowski, M. Saito, S. Yaginuma, Y. Fujikawa, T. Kogure, T. Ohno, Y. Hasegawa, S. Hasegawa, and T. Sakurai, Phys. Rev. Lett., vol. 93, p. 105501, 2004.
M. Saito, T. Ohno, and T. Miyazaki, Appl. Surf. Sci., vol. 237, no. 1, pp. 80–85, 2004.
J. Kang, J. D. Wood, S. A. Wells, J.-H. Lee, X. Liu, K.-S. Chen, and M. C. Hersam, ACS Nano, vol. 9, no. 4, pp. 3596–3604, 2015.
J. R. Brent, N. Savjani, E. A. Lewis, S. J. Haigh, D. J. Lewis, and P. O’Brien, Chem. Commun., vol. 50, pp. 13 338–13 341, 2014.
A. Castellanos-Gomez, L. Vicarelli, E. Prada, J. O. Island, K. L. Narasimha-Acharya, S. I. Blanter, D. J. Groenendijk, M. Buscema, G. A. Steele, J. V. Alvarez, H. W. Zandbergen, J. J. Palacios, and H. S. J. van der Zant, 2D Materials, vol. 1, no. 2, p. 025001, 2014.
N. A. P. Namari and M. Saito, Jpn. J. Appl. Phys., vol. 58, no. 6, p. 061003, may 2019.
M. Y. H. Widianto, A. Zaharo, N. A. P. Namari, and M. Saito, Jpn. J. Appl. Phys., vol. 60, no. 6, p. 061001, 2021.
M. Wada, S. Murakami, F. Freimuth, and G. Bihlmayer, Phys. Rev. B, vol. 83, p. 121310, 2011.
Y. Lu, W. Xu, M. Zeng, G. Yao, L. Shen, M. Yang, Z. Luo, F. Pan, K. Wu, T. Das, P. He, J. Jiang, J. Martin, Y. P. Feng, H. Lin, and X.-s. Wang, Nano Lett., vol. 15, no. 1, pp. 80–87, 2015.
S. Minami, I. Sugita, R. Tomita, H. Oshima, and M. Saito, Jpn. J. Appl. Phys., vol. 56, no. 10, p. 105102, sep 2017.
A. Zaharo, A. Purqon, T. Winata, and M. Saito, Jpn. J. Appl. Phys., vol. 59, no. 7, p. 071006, jun 2020.
J. Gao, Q. Wu, C. Persson, and Z. Wang, Comp. Phys. Commun., vol. 261, p. 107760, 2021.
A. Matsugatani, S. Ono, Y. Nomura, and H. Watanabe, Comp. Phys.
Commun., vol. 264, p. 107948, 2021.
S. A. Putri, Y. Yamaguchi, T. A. Ariasoca, M. Y. H.Widianto, K. Tagami, and M. Saito, Surf. Sci., vol. 714, p. 121917, 2021.
M. Y. H. Widianto and M. Saito, Jpn. J. Appl. Phys., vol. 61, no. 3, p. 035503, 2022.
T. Yamasaki, A. Kuroda, T. Kato, J. Nara, J. Koga, T. Uda, K. Minami, and T. Ohno, Comput. Phys. Commun., vol. 244, pp. 264–276, 2019.
A. Yanase, Fortran Program For Space Group (TSPACE). Tokyo: (in Japanese) Shokabo, 1995.
L. Fu and C. L. Kane, Phys. Rev. B, vol. 76, p. 045302, Jul 2007.
L. Fu, C. L. Kane, and E. J. Mele, Phys. Rev. Lett., vol. 98, p. 106803, Mar 2007.
Y. Kim, B. J. Wieder, C. L. Kane, and A. M. Rappe, Phys. Rev. Lett., vol. 115, p. 036806, Jul 2015.
M. Z. Hasan and C. L. Kane, Rev. Mod. Phys., vol. 82, pp. 3045-3067, Nov 2010.
C. L. Kane and E. J. Mele, Phys. Rev. Lett., vol. 95, p. 226801, Nov 2005.
DOI: http://dx.doi.org/10.12962/j24775401.v9i2.19206
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