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 phasetransition 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.