A gauge theory for two-band model of Chern insulators and induced topological defects

In this paper a gauge theory is proposed for the two-band model of Chern insulators. Based on the so-called 't Hooft monopole model, a U(1) Maxwell electromagnetic sub-field is constructed from an SU(2) gauge field, from which arise two types of topological defects, monopoles and merons. We focus on the topological number in the Hall conductance ${sigma }_{{xy}}=tfrac{{e}^{2}}{h}C$, where C is the Chern number. It is discovered that in the monopole case C is indeterminate, while in the meron case C takes different values, due to a varying on-site energy m. As a typical example, we apply this method to the square lattice and compute the winding numbers (topological charges) of the defects; the C-evaluations we obtain reproduce the results of the usual literature. Furthermore, based on the gauge theory we propose a new model to obtain the high Chern numbers ∣C∣ = 2, 4.