Edge states enhanced by long-range hopping: An analytical study

doi:10.1088/1674-1056/abe9a5

中国物理B ›› 2021, Vol. 30 ›› Issue (10): 107301-107301.doi: 10.1088/1674-1056/abe9a5

Edge states enhanced by long-range hopping: An analytical study

Huiping Wang(王会平)^1,†, Li Ren(任莉)¹, Liguo Qin(秦立国)¹, and Yueyin Qiu(邱岳寅)²

1 School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China;
2 School of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

收稿日期:2020-12-31 修回日期:2021-02-09 接受日期:2021-02-25 发布日期:2021-09-17
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 the Startup Program of Shanghai University of Engineering Science.

Edge states enhanced by long-range hopping: An analytical study

Huiping Wang(王会平)^1,†, Li Ren(任莉)¹, Liguo Qin(秦立国)¹, and Yueyin Qiu(邱岳寅)²

1 School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China;
2 School of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

Received:2020-12-31 Revised:2021-02-09 Accepted:2021-02-25 Published:2021-09-17
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 the Startup Program of Shanghai University of Engineering Science.

摘要/Abstract

摘要： We analyze the behavior of edge states in long-range (LR) interacting systems. In terms of lattice model Hamiltonian with the LR coupling, we determine analytically the condition of existence of edge states within the transfer matrix method (TMM). The expressions we obtain are general and hold for any choice of the LR hopping. The reason why edge states can appear is the transfer matrix in the bulk different from that in the boundary layers. Our predictions are in good agreement with numerical results by exact diagonalization. Our result is helpful in solving novel edge states in one- and two-dimensional (2D) superconductors with LR hopping and pairing.

关键词: edge states, transfer matrix method, long-range hopping

Abstract: We analyze the behavior of edge states in long-range (LR) interacting systems. In terms of lattice model Hamiltonian with the LR coupling, we determine analytically the condition of existence of edge states within the transfer matrix method (TMM). The expressions we obtain are general and hold for any choice of the LR hopping. The reason why edge states can appear is the transfer matrix in the bulk different from that in the boundary layers. Our predictions are in good agreement with numerical results by exact diagonalization. Our result is helpful in solving novel edge states in one- and two-dimensional (2D) superconductors with LR hopping and pairing.

Key words: edge states, transfer matrix method, long-range hopping

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)

Huiping Wang(王会平), Li Ren(任莉), Liguo Qin(秦立国), and Yueyin Qiu(邱岳寅). Edge states enhanced by long-range hopping: An analytical study[J]. 中国物理B, 2021, 30(10): 107301-107301.

Huiping Wang(王会平), Li Ren(任莉), Liguo Qin(秦立国), and Yueyin Qiu(邱岳寅). Edge states enhanced by long-range hopping: An analytical study[J]. Chin. Phys. B, 2021, 30(10): 107301-107301.

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Edge states enhanced by long-range hopping: An analytical study

Edge states enhanced by long-range hopping: An analytical study

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