| CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
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Edge modes in finite-size systems with different edge terminals |
| Huiping Wang(王会平)†, Li Ren(任莉), Xiuli Zhang(张修丽), and Liguo Qin(秦立国) |
| School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China |
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Abstract We investigate the behavior of edge modes in the presence of different edge terminations and long-range (LR) hopping. Here, we mainly focus on such model crystals with two different types of structures (type I: “$\cdots $-$P$-$Q$-$P$-$Q$-$\cdots $” and type II: “$\cdots=P$-$Q=P$-$Q=\cdots$”), where $P$ and $Q$ represent crystal lines (CLs), while the symbols “$-$” and “$=$” denote the distance between the nearest neighbor (NN) CLs. Based on the lattice model Hamiltonian with LR hopping, the existence of edge modes is determined analytically by using the transfer matrix method (TMM) when different edge terminals are taken into consideration. Our findings are consistent with the numerical results obtained by the exact diagonalization method. We also notice that edge modes can exhibit different behaviors under different edge terminals. Our result is helpful in solving novel edge modes in honeycomb crystalline graphene and transition metal dichalcogenides with different edge terminals.
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Received: 27 March 2024
Revised: 13 July 2024
Accepted manuscript online: 01 August 2024
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PACS:
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73.20.At
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(Surface states, band structure, electron density of states)
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61.50.Ah
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(Theory of crystal structure, crystal symmetry; calculations and modeling)
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73.22.Dj
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(Single particle states)
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02.10.Yn
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(Matrix theory)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11847061) and Domestic Visiting Program for Young and Middle-aged Teachers in Shanghai Universities. |
Corresponding Authors:
Huiping Wang
E-mail: hp_wang@fudan.edu.cn;
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Cite this article:
Huiping Wang(王会平), Li Ren(任莉), Xiuli Zhang(张修丽), and Liguo Qin(秦立国) Edge modes in finite-size systems with different edge terminals 2024 Chin. Phys. B 33 107302
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[1] Von Klitzing K 1986 Rev. Mod. Phys. 58 519
[2] Altland A and Zirnbauer M R 1997 Phys. Rev. B 55 1142
[3] Thouless D J, Kohmoto M, Nightingale M P and den Nijs M 1982 Phys. Rev. Lett. 49 405
[4] Kane C L and Mele E J 2005 Phys. Rev. Lett. 95 226801
[5] Bernevig B A, Hughes T L and Zhang S C 2006 Science 314 1757
[6] Slager R J, Mesaros A, Juričić V and Zaanen J 2013 Nat. Phys. 9 98
[7] Fu L 2011 Phys. Rev. Lett. 106 106802
[8] Pan H and Zhang Y W 2012 J. Mater. Chem. 22 7280
[9] Palacios J, Fernádez-Rossier J, Brey L and Fertig H 2010 Semicond. Sci. Technol. 25 033003
[10] Nakada K, Fujita M, Dresselhaus G and Dresselhaus M S 1996 Phys. Rev. B 54 17954
[11] Fujita M, Wakabayashi K, Nakada K and Kusakabe K 1996 J. Phys. Soc. Jpn. 65 1920
[12] Kunstmann J, Ödoğan C, Quandt A and Fehske H 2011 Phys. Rev. B 83 045414
[13] Kohmoto M and Hasegawa Y 2007 Phys. Rev. B 76 205402
[14] Deng J, Yin Y, Niu H, Ding X, Sun J andMedhekar N V 2017 Sci. Rep. 7 7855
[15] Freeney S E, vanden Broeke J J, Harsveld vander Veen AJ J, Swart I and Morais Smith C 2020 Phys. Rev. Lett. 124 236404
[16] Li Y, Zhou Z, Zhang S and Chen Z 2008 J. Am. Chem. Soc. 130 16739
[17] Jia X, Hofmann M, Meunier V, Sumpter B G, Campos-Delgado J, Romo-Herrera J M, Son H, Hsieh Y P, Reina A, Kong J, Terrones M and Dresselhaus M S 2009 Science 323 1701
[18] Enoki T, Kobayashi Y and Fukui K I 2007 Int. Rev. Phys. Chem. 26 609
[19] Viyuela O, Fu L and Martin-Delgado M A 2019 ACS Nano 13 1635
[20] Ezawa M and Nagaosa N 2013 Phys. Rev. B 88 121401
[21] García-Fuente A, Carrascal D, Ross G and Ferrer J 2023 Phys. Rev. B 107 115403
[22] Sadeghizadeh M, Soltani M and Amini M 2023 Sci. Rep. 13 12844
[23] Salehitaleghani S, Maerkl T, Kowalczyk P J, LeSter M, Wang X, Bian G, Chiang T C and Brown S A 2023 2D Mater. 10 015020
[24] GaoY and Brocks G 2023 Physica E 148 115655
[25] Viyuela O, Fu L and Martin-Delgado M A 2018 Phys. Rev. Lett. 120 017001
[26] DeGottardi W, Thakurathi M, Vishveshwara S and Sen D 2013 Phys. Rev. B 88 165111
[27] Di Liberto M, Malpetti D, Japaridze G I and Morais Smith C 2014 Phys. Rev. A 90 023634
[28] Lepori L, Giuliano D and Paganelli S 2018 Phys. Rev. B 97 041109
[29] Maghrebi M F, Gong Z X and Gorshkov A V 2017 Phys. Rev. Lett. 119 023001
[30] Santos L F, Borgonovi F and Celardo G L 2016 Phys. Rev. Lett. 116 250402
[31] Xu K, Zhang X, Luo K, Yu R, Li D and Zhang H 2021 Phys. Rev. B 103 125411
[32] Wang H P, Ren L, Qin L G and Qiu Y 2020 J. Phys. Soc. Jpn. 89 074705
[33] Wang H P, Ren L, Qin L G and Qiu Y 2021 Chin. Phys. B 10 107301
[34] Lee D H and Joannopoulos J D 1981 Phys. Rev. B 23 4988
[35] Zhao Y Y, Li W and Tao R B 2012 Physica B 407 724
[36] Wang H P and Tao R B 2015 Chin. Phys. B 24 117301
[37] Wang H P, Gao T and Tao R B 2015 Sci. Rep. 5 8679 |
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