Topological Properties of Bilayer $\alpha-T_{3}$ Lattice Induced by Polarized Light

Abstract

We investigate the topological properties of photon-dressed energy bands in bilayer $\alpha-T_{3}$ lattices under off-resonant circularly polarized light, focusing on aligned and cyclic stacking configurations. Analytical expressions for quasi-energy bands are derived for aligned stacking, while numerical results address cyclic stacking at Dirac points. Circularly polarized light breaks the time-reversal symmetry, lifting the degeneracies at the intersections $t^{a,c}$, leading to the appearance of a Haldane-type Chern insulator in the absence of a magnetic field . At $\alpha = 1/\sqrt{2}$, orbital magnetic moments of corrugated and flat bands exhibit opposite signs, as do their Berry curvatures. For $0 < \alpha < 1$, light-induced band deformations near Dirac points create gaps in the quasi-energy spectrum, where the chemical potential modulates orbital magnetization. Linear magnetization variations align with Chern numbers, yielding quantized anomalous Hall conductivity across stacking types. Notable particle-hole symmetry breaking within $0 < \alpha < 1$ suggests applications in valley caloritronics and quantum sensing. At $\alpha = 1$, flat and corrugated bands remain undistorted; while the flat band contributes no Berry curvature, it produces a finite negative orbital magnetic moment, contrasting with the positive moment of the corrugated band.