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Chin. Phys. B, 2021, Vol. 30(10): 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
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.
Keywords:  edge states      transfer matrix method      long-range hopping  
Received:  31 December 2020      Revised:  09 February 2021      Accepted manuscript online:  25 February 2021
PACS:  73.20.At (Surface states, band structure, electron density of states)  
  61.50.Ah (Theory of crystal structure, crystal symmetry; calculations and modeling)  
  73.22.Dj (Single particle states)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11847061) and the Startup Program of Shanghai University of Engineering Science.
Corresponding Authors:  Huiping Wang     E-mail:

Cite this article: 

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 2021 Chin. Phys. B 30 107301

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