Harmonic disturbance on the topological phases of a Chern insulator

We demonstrate the effect of a harmonic oscillator perturbing potential on the topological phases of a Chern insulator formed from a square lattice with two quantum states per site. For a region with a non-trivial topological phase characterized by a non-zero Chern number, the perturbation introduced an energy gap closing and divided the non-trivial region into three, which possessed a topologically trivial region and two non-trivial regions. The perturbation induced singularities on the Berry curvature which led to the division of the original topologically non-trivial region.