Topological defects and higher Chern number two-band structures on checkerboard lattice

In this paper, we focus on studying the meron defects on checkerboard lattice based on two-band structures. Merons are two-dimensional point defects, whose topological charges give the evaluations of the Chern numbers of the two bands. We first reproduce the results of a previous model from the defect perspective. Then, the model is extended to attain the higher Chern number systems. We show that the model can achieve C = ± 3 structures through analyzing the charges of the merons. The energy spectrum also reveals that three gap-closed states appear on the edges.