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

TL;DR

The paper investigates how off-resonant circularly polarized light induces topological phases in bilayer $\alpha{-}T_{3}$ lattices for aligned and cyclic stacking. Using Floquet theory in the high-frequency limit, it derives an effective Hamiltonian with a light-induced mass term that breaks time-reversal symmetry and opens gaps at Dirac points, effectively realizing a Haldane-type Chern insulator without a magnetic field. It computes and analyzes Berry curvature, orbital magnetic moments, orbital magnetization, and anomalous Hall conductivity across the parameter $\alpha$ and stacking configurations, revealing a topological transition near $\alpha=1/\sqrt{2}$ and valley-dependent signatures, including linear $M(\mu)$ in band gaps and quantized $\sigma_{xy}$ plateaus. The results show Floquet engineering as a programmable route to realize and control topological phases in the $\alpha{-}T_{3}$ bilayer, with potential implications for valley caloritronics and quantum sensing.

Abstract

We investigate the topological properties of photon-dressed energy bands in bilayer $α-T_{3}$ 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 $α= 1/\sqrt{2}$, orbital magnetic moments of corrugated and flat bands exhibit opposite signs, as do their Berry curvatures. For $0 < α< 1$, 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 $0 < α< 1$ suggests applications in valley caloritronics and quantum sensing. At $α= 1$, 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.

Figures (10)

• Figure 1: We present the band structures of the $\alpha-T_{3}$ bilayer lattice for two types of stacking: (i) aligned stacking $(A_{l}A_{u}-B_{l}B_{u}-C_{l}C_{u})$ and(ii) cyclic stacking $(A_{l}B_{u}-B_{l}C_{u}-C_{l}A_{u})$. The graph illustrates the calculated bands along the qx axis at the high-symmetry points $(M-K^{\prime }-\varGamma-K-M)$ in the Brillouin zone, as shown in Figure (iii). For the nearest-neighbor hopping, a parameter value of $t = 2.7$ eV and interlayer coupling $t_{\perp}=t^{c}_{\perp}=t^{a}_{\perp} = 0.22$ eV are considered, assuming these values are analogous to those of graphene s37 and $(iv)$ a Schematic diagram of the aligned stacked bilayer exposed to off-resonance circular polarization, and ($v$) a schematic diagram of the cyclic stacked bilayer.
• Figure 2: The influence of the $\alpha$ parameter on the quasi-energy dispersion in the K-valley of an aligned stack (i) and a cyclic stack (ii) is illustrated by the graph presented. The results obtained highlight the effect of this parameter on dispersion for different values of $\alpha$, considering circularly polarized light with an energy of $\Delta = 50 meV$
• Figure 3: We repeat figure \ref{['fig2']} for the K'-valley
• Figure 4: Berry curvature curves $\Omega_{m}^{+1}(\mathbf{k})$ for aligned (i) and cyclic (ii) stacking near the K-valley are plotted for different values of $\alpha$, namely $\alpha=0$, $\alpha=0.4$, $\alpha=0.8$, and $\alpha=1$. We consider irradiation of the $\alpha-T_{3}$ bilayer lattice with circularly polarized light of amplitude $\Delta=50$ meV
• Figure 5: The maximum value of $\Omega(k=0)$ at $k=0$ is plotted as a function of $\alpha$ for (i) the K-valley and (ii) the K'-valley of the aligned stack, as well as for (iii) the K-valley and (iv) the K'-valley of the cyclic stack. Here, we consider $\Delta=50$ meV. In the K (K') valley, $\Omega(k=0)$ for the band change sign discontinuously through $\alpha=1/\sqrt{2}$ while $\Omega(k=0)$ for the conduction (valence) band decreases (increases) monotonically as illustrated in the inset. The change in sign of the Berry curvature through $\alpha =1/ \sqrt{2}$ can be seen as a topological signature