Boundary criticality of Chern insulator in two-dimensional Su-Schrieffer-Heeger model with next-nearest-neighbor hopping

We investigate the properties of Chern insulator in a two-dimensional (2D) Su-Schrieffer-Heeger (SSH) model with next-nearest-neighbor (NNN) hopping. We find that the Weyl points, serving as phase-transition points, precisely coincide with high-symmetry points. In the phase diagram, there are two nontrivial phases with different nonzero Chern numbers, one trivial phase with zero Chern number, and two different types of phase-transition boundaries formed by the Weyl points. The system with a nonzero Chern number is topologically nontrivial, with localized edge states at the top and bottom. Interestingly, the eigenmodes on the phase-transition boundaries of two different nontrivial phases are localized at the bottom of the system, in contrast with the extended eigenmodes observed on the trivial and nontrivial phase-transition boundaries. Our work provides insights into exploring the correlation between edge state and phase transition boundary in Chern insulator based on the 2D SSH model with NNN hopping.