Interlayer Coupling and Floquet-Driven Topological Phases in Bilayer Haldane Lattices

Abstract

We investigate Floquet-driven topological phase transitions in an AB-stacked bilayer Haldane lattice with tunable intralayer hopping anisotropy. By combining interlayer hybridization, Haldane flux, and off-resonant circularly polarized light, we obtain controlled transitions among Dirac, semi-Dirac, and higher-Chern insulating phases. As the hopping anisotropy increases, the two inequivalent Dirac points move toward each other and merge at the Brillouin-zone $\mathbf{M}$ point, where a semi-Dirac dispersion emerges with linear and quadratic momentum dependence along orthogonal directions. In this regime, competition between the intrinsic Haldane mass and the Floquet-induced mass drives a sequence of sharp topological transitions with Chern numbers $C=0,\pm1,\pm2$. We further show that interlayer coupling qualitatively reshapes the Floquet band topology by inducing helicity-dependent and valley-selective band inversions at the K and K$'$ points, thereby stabilizing higher-Chern phases in the valence bands. These changes are accompanied by redistribution of the Berry curvature, bulk gap closings, and the collapse or sign reversal of quantized anomalous Hall plateaus. As the system approaches the semi-Dirac limit, the topological phase space narrows and disappears at the critical merger point, beyond which the system becomes topologically trivial even when it remains gapped. Overall, the bilayer geometry broadens the scope of Floquet topological control by enabling dynamically tunable higher-Chern phases and valley-dependent Hall responses governed by interlayer coupling and light helicity.

Figures (12)

• Figure 1: (a) Schematic of AB-stacked bilayer graphene, where the interlayer hopping $t_\perp$ couples the $B$ sublattice of the upper layer to the $A$ sublattice of the lower layer. In both layers, $A$ and $B$ sites are represented by red and blue circles, respectively. (b) Illustration of the in-plane hopping processes. To clearly distinguish the two layers, the sublattices of the lower sheet are denoted as $\mathrm{A}_l$ (yellow) and $\mathrm{B}_l$ (green), while those of the upper sheet are labeled $\mathrm{A}_u$ and $\mathrm{B}_u$. Nearest-neighbor bonds within the lower layer are shown as dashed lines, and the corresponding next-nearest-neighbor hoppings as dashed arrows. The hopping amplitude along the $\boldsymbol{\delta}_1$ direction (highlighted by the yellow arrow) is $t_1$, while the hoppings along $\boldsymbol{\delta}_{2,3}$ are $t$ (with $\boldsymbol{\delta}_i$ defined in the text). The next-nearest-neighbor processes carry complex amplitudes $t_2 e^{i\phi}$ for clockwise paths and $t_2 e^{-i\phi}$ for anticlockwise paths.
• Figure 2: Band structures along the $k_x a_0$ direction at fixed $k_y a_0 = 2\pi/3$. Panels (a)--(l) correspond to finite next-nearest-neighbor hopping $t_2 = 0.0t$ with $t_1 = t$, $1.5t$, $1.8t$, and $2.2t$, respectively. For comparison, panels (e)--(h) show the dispersions in the absence of $t_2$ for the same sequence of $t_1$ values. The remaining parameters are fixed at $t_\perp = 0.5t$, and $\phi_l = \phi_u = \pi/2$.
• Figure 3: Band structures along the $k_x a_0$ direction at fixed $k_y a_0 = 2\pi/3$. Panels (a)--(l) correspond to finite next-nearest-neighbor hopping $t_2 = 0.1t$ with $t_1 = t$, $1.5t$, $1.8t$, and $2.2t$, respectively. For comparison, panels (e)--(h) show the dispersions in the presence of $t_2$, the same sequence of $t_1$ values. The remaining parameters are fixed at $t_\perp = 0.5t$, and $\phi_l = \phi_u = \pi/2$.
• Figure 4: Berry curvature distributions of the valence band $v_1$ for $t_1 = t$, $t_1 = 1.5t$, $t_1 = 1.8t$, and $t_1 = 2.2t$. The other parameters are fixed as $\phi_l = \phi_u = \pi/2$, and $t_\perp = 0.5t$,.
• Figure 5: Berry curvature distributions of the valence band $v_2$ for $t_1 = t$, $t_1 = 1.5t$, $t_1 = 1.8t$, and $t_1 = 2.2t$. The other parameters are fixed as $\phi_l = \phi_u = \pi/2$, and $t_\perp = 0.5t$,.