Chern insulators and topological flat bands in cavity-embedded kagome systems

TL;DR

This paper demonstrates that embedding a kagome lattice in a circularly polarized cavity field induces topological band structures via light–matter coupling, realizing Chern insulators and topological flat bands. Using a muffin-tin potential and a Coulomb-gauge cavity QED framework, the authors analyze bulk bands across coupling regimes and confirm bulk–edge correspondence with a low-energy AD-frame tight-binding model. They show that TRS breaking by the cavity opens mass gaps, yielding Chern numbers such as $C=1$ in the first gap and $C=-1$ after USC-induced phase transitions, with a nearly flat band carrying nonzero Chern number at weak coupling. The findings reveal USC-enabled topological phase transitions between distinct Chern insulators in the kagome system and propose experimental pathways, including THz realizations and quantum Hall transport, to observe cavity-induced edge modes and chirality switching.

Abstract

We investigate topological band structures of a kagome system coupled to a circularly polarized cavity mode, using a model based on a muffin-tin potential and quantum light-matter interaction. We show that Chern insulating phases emerge in the cavity-embedded kagome system due to the light-matter interaction that breaks time-reversal symmetry. We also find that a nearly flat band can be topologically nontrivial with a nonzero Chern number. By varying the light-matter interaction, we also reveal that topological phase transitions occur between different Chern insulating phases in the ultrastrong coupling regime. The phase transitions change the sign of the Chern number, switching the direction of the edge current. We demonstrate the existence of topological edge modes in the cavity-embedded kagome Chern insulators by constructing a low-energy effective tight-binding model.

Figures (6)

• Figure 1: (a) and (b) Periodic potential for kagome and honeycomb lattices, respectively. In (a), the center of the small circles corresponds to that of the triangular unit cells in the kagome lattice. In (b), the small circles are absent because the potential terms with radius $\rho_{\mathrm{T}}$ vanish. (c) and (d) Energy bands for $\alpha=1$ and $\alpha =0$, respectively.
• Figure 2: (a) Chern numbers of the kagome system with the circularly polarized cavity field. Each band is topologically characterized by the Chern numbers $(C_1, C_2, C_3)$. (b) Low-energy band structure at $g /\omega_{\mathrm{c}}=0.2$, and the band gap due to the cavity field at the K and $\Gamma$ points, respectively. (c)-(f) Low-energy band structures at $g /\omega_{\mathrm{c}}=1.65, 1.8, 2.02$ and $2.2$, respectively. (c) and (e) show the topological phase transitions at $g /\omega_{\mathrm{c}}=1.65$ and $2.02$, where the energy gap closes between the second and third bands at the $\Gamma$ point, and the first and second bands at the $\mathrm{K}$ point, respectively.
• Figure 3: Low-energy band structure in the honeycomb system at the coupling strength $g /\omega_{\mathrm{c}}=0.5$.
• Figure 4: (a)-(c) Comparison of bulk band structures from the exact analysis and the tight-binding model at $g /\omega_{\mathrm{c}}=0.2, 1.8$, and $2.9$, which are topologically characterized by $(C_1, C_2, C_3)=(1,0,-1), (1,-2,1)$, and $(-1,0,1)$, respectively. We adjust the lowest energy eigenvalue obtained from the tight-binding model at the K point to match that obtained from the exact analysis because the energy shift does not change the band topology. (d)-(f) Topological edge states for $g /\omega_{\mathrm{c}}=0.2, 1.8$, and $2.9$, respectively, with the periodic boundary condition in the $x$-direction and open boundary condition in the $y$-direction. Red (green) solid lines indicate gapless edge modes localized at the top (bottom) edge.
• Figure 5: Chern numbers of the tight-binding model for the kagome system.