Edge modes in finite-size systems with different edge terminals

doi:10.1088/1674-1056/ad6a05

中国物理B ›› 2024, Vol. 33 ›› Issue (10): 107302-107302.doi: 10.1088/1674-1056/ad6a05

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

收稿日期:2024-03-27 修回日期:2024-07-13 接受日期:2024-08-01 出版日期:2024-10-03 发布日期:2024-09-13
通讯作者: Huiping Wang E-mail:hp_wang@fudan.edu.cn;
基金资助:
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.

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

Received:2024-03-27 Revised:2024-07-13 Accepted:2024-08-01 Online:2024-10-03 Published:2024-09-13
Contact: Huiping Wang E-mail:hp_wang@fudan.edu.cn;
Supported by:
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.

摘要/Abstract

摘要： 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.

关键词: edge modes, long-range hopping, different edge terminals

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.

Key words: edge modes, long-range hopping, different edge terminals

中图分类号: (Surface states, band structure, electron density of states)

73.20.At

61.50.Ah (Theory of crystal structure, crystal symmetry; calculations and modeling) 73.22.Dj (Single particle states) 02.10.Yn (Matrix theory)

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[J]. 中国物理B, 2024, 33(10): 107302-107302.

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[J]. Chin. Phys. B, 2024, 33(10): 107302-107302.

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Edge modes in finite-size systems with different edge terminals

Edge modes in finite-size systems with different edge terminals

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