Twist-Induced Quantum Geometry Reconfiguration in Moiré Flat Bands

Abstract

The interplay between band topology, Berry curvature, and moiré flat bands lies at the heart of recent advances in quantum materials. In well-studied moiré systems such as twisted bilayer graphene and transition metal dichalcogenides, the quantum geometry of moiré flat bands typically reflects that of the monolayer, with Berry curvature originating from the band edge at the same valley. Whether this correspondence persists in systems with complex monolayer band structures and broken symmetries remains unclear. Here, we study twisted bilayers of loop-current-ordered kagome lattices (tb-LCK), which have been proposed in the context of vanadium-based kagome materials, using tight-binding models, and uncover a twist-induced reconfiguration of quantum geometry. By tuning the phase of the loop-current order, we identify the suppression of monolayer Berry curvature through twist-driven band reconstruction. We attribute these effects to strong interlayer hybridizations, enabled by the unusually large interlayer tunneling inherent to vanadium-based kagome materials, which mix energetically distant states and reshape quantum geometry. These results reveal that twist in tb-LCK suppresses quantum geometric inheritance from the monolayer, and establish loop-current-ordered moiré systems as promising platforms for exploring unconventional quantum geometry in moiré flat bands. We further comment on the experimental feasibility of the proposed system via vanadium-based kagome materials.

Figures (16)

• Figure 1: (a) Lattice structure of LCK highlighting the Star-of-David pattern. Green solid and blue dashed lines mark the $2\times2$ and $1\times1$ cells, respectively. (b) A schematic of the loop currents in LCK. Distinct loops are colored differently.
• Figure 2: (a) Band structures of LCK at $\phi_{\text{LC}} = 0.2\pi$ and $0.3976\pi$, with the 6th lowest band (B6) highlighted in red and nearby bands labeled by their Chern numbers $C$. The green circle marks the band edge of interest, while the orange circle shows where Berry curvature is concentrated. (b) The corresponding Berry curvature of B6.
• Figure 3: Lattice structure of tb-LCK at $\theta_c \approx 9.43^\circ$, with high-symmetry stacking centers marked in different colors. See FIG. S2 for structural details of these regions SM.
• Figure 4: Band structures of tb-LCK with $\phi_{\text{LC}} = 0.2\pi$ with (top row) $t_z=0.3|t|$ or (bottom row) $t_z=0.03|t|$ at $\theta_c\approx3.89^\circ$, where the bands of interest are highlighted in red and are labeled by their nonzero Chern numbers $C$ or modified quantum weight $\tilde{K}$. Band indices are indicated for reference.
• Figure 5: Band structures of tb-LCK with $\phi_{\text{LC}} = 0.3976\pi$ and (a) $t_z=0.3|t|$ or (c) $t_z=0.03|t|$ at $\theta_c\approx3.89^\circ$, where the bands of interest are highlighted in red and are labeled by their modified quantum weight $\tilde{K}$. (b) The $\bar{\sigma}$ and $\tilde{K}$ for all twelve low-energy bands of tb-LCK with $t_z=0.3|t|$ as functions of $\theta_c$. (d) The $\bar{\sigma}$ and $\tilde{K}$ of tb-LCK with $t_z=0.03|t|$ at $\theta_c\approx3.89^\circ$ computed at selective chemical potentials marked by gray dashed lines in (c) with $T=100$K.