Topological phase transition induced by band structure modulation in a Chern insulator

We study a systematic evolution of the topological properties of a Chern insulator upon smooth variation of a hopping parameter (t₁) of the electrons among a pair of nearest neighbour sites on a honeycomb lattice, while keeping the other two hopping terms (t) fixed. In the absence of a Haldane flux, the tuning oft₁results in gradual shifting of the Dirac cones which eventually merge into one at theMpoint in the Brillouin zone (BZ) att₁= 2twith a gapless semi-Dirac dispersion at low energies. In the presence of a Haldane flux, the system becomes a Chern insulator fort₁< 2t, but turns gapless att₁= 2twith the semi-Dirac dispersion being transformed to an anisotropic Dirac one. The spectrum eventually gaps out and transforms into a trivial insulator fort₁> 2t. The Chern number phase diagram obtained via integrating the Berry curvature over the BZ shows a gradual shrinking of the 'topological' lobes, and vanishes just beyondt₁= 2t, where a small but a finite Berry curvature still exists. Thus, there is a phase transition from a topological phase to a trivial phase across the semi-Dirac point (t₁= 2t). The vanishing of the anomalous Hall conductivity plateau and the merger of the chiral edge states with the bulk bands near theMpoint provide robust support of the observed phase transition.