Edge States Enhanced By Long-Range Hopping: An Analytical Study*

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.