Optically Controlled Topological Phases in the Deformed $\alpha -T_3$ Lattice

Haldane’s tight-binding model, which describes a Chern insulator in a two-dimensional hexagonal lattice, exhibits quantum Hall conductivity without an external magnetic field. Here, we explore an $\alpha -T_3$ lattice subjected to circularly polarized off-resonance light. This lattice, composed of two sublattices (A and B) and a central site © per unit cell, undergoes deformation by varying the hopping parameter ${\gamma }_1$ while keeping ${\gamma }_2$= ${\gamma }_3$= $\gamma$. Analytical expressions for quasi-energies in the first Brillouin zone reveal significant effects of symmetry breaking. Circularly polarized light lifts the degeneracy of Dirac points, shifting the cones from M. This deformation evolves with ${\gamma }_1$, breaking symmetry at ${\gamma }_1=2\gamma$, as observed in Berry curvature diagrams. In the standard case (${\gamma }_1=\gamma$), particle-hole and inversion symmetries are preserved for $\alpha =0$ and $$. The system transitions from a semi-metal to a Chern insulator, with band-specific Chern numbers: $C_2=1$, $C_1=0$, and $C_0=-1$ for $$ shifting to $C_2=2$, $C_1=0$, and $C_0=-2$ when $$For ${\gamma }_1>2\gamma$, the system enters a trivial insulating phase. These transitions, confirmed via Wannier charge centers, are accompanied by a diminishing Hall conductivity. Our findings highlight tunable topological phases in $\alpha -T_3$ lattices, driven by light and structural deformation, with promising implications for quantum materials.