Electronic states at twist stacking faults in rhombohedral graphite

TL;DR

This work establishes that twist stacking faults in rhombohedral graphite create topologically protected, nearly flat interface bands due to an interplay between moiré periodicity and Zak phase topology. By combining Slater-Koster tight-binding and a low-energy continuum model, and analyzing both ideal (chiral) and non-chiral regimes, it identifies a critical twist angle near $\theta \approx 2.6^{\circ}$ where $\,\mathcal{Z}=\pi$ regions approach the $\Gamma$ point, yielding flat bands across the moiré Brillouin zone. It further shows that non-chiral terms and disorder tune the Chern numbers of these flat bands, with valley Chern numbers being redistributed between interface and surface states and eventually diminishing under strong disorder. The results illuminate a tunable topological platform in twisted rhombohedral graphite, relevant for exploring correlated and topological phases in layered carbon systems.

Abstract

Flat bands in graphitic materials emerged as a platform for realizing tunable correlated physics. As a nodal-line semimetal, rhombohedral graphite features flat drumhead surface states in the vicinity of the Dirac points, which carry a nontrivial topological charge. We present a comprehensive study on rhombohedral graphite with twist stacking faults. Using both the continuum models and the realistic tight-binding models, we show that the twist angle between the graphene layers can tune the interface states at such stacking faults. The evolution of interface states originates from the interplay between the moiré periodicity and Zak phase topology, predicting the occurrence of nearly flat bands throughout the moiré Brillouin zone. We further investigate the disorder-induced layer polarization and tunable Chern number for flat band, and characterize the relationship between the disorder strength and Chern number in twisted rhombohedral graphite.

Figures (10)

• Figure 1: Tiwst stacking faults in rhombohedral graphite with (a) ABC-CBA stacking configuration ($C_{2x}$ symmetry) and (b) ABC-ABC stacking configuration ($C_{2y}$ symmetry). (c) Moiré Brillouin Zone of twisted rhombohedral graphite (black hexagons) at different twist angles. Yellow cicles delimit the region of $\mathcal{\mathcal{}}{Z(k_x,k_y)}=\pi$.
• Figure 2: Maps of the Zak phase of rhombohedral graphite for moiré periodicities that correspond to twist angle (a) $\theta = 6.01^{\circ}$ and (b) $\theta = 3.15^{\circ}$ showing the regions of $\mathcal{Z}=\pi$ in orange. Momentum resolved DOS of twisted rhombohedral graphite at (c) $\theta = 6.01^{\circ}$ and (d) $\theta = 3.15^{\circ}$ calculated using the TB model along the $k$-point path $K-\Gamma-M-K'$.
• Figure 3: Evolution of the DOS of rhombohedral graphite (semi-infinite) interface states at $\Gamma$ point versus twist angles, the twist angle from $4.41^{\circ}$ to $0.8^{\circ}$; (a) Tight-binding model result; (b) continuum model result, $w_{AA}=20\,$meV; (c) continuum model result, chiral limit, $w_{AA}=0\,$meV.
• Figure 4: Spectral weight of the (a) interface and (b) surface bands on the interface layers calculated for the 8+8-layer ABC-CBA configuration. (c,d) Berry curvature maps of the respective bands.
• Figure 5: The evolution of total Chern number of the flat bands with the number of layers and the random scattering disorder amplitude. The black line is the remote band gap strength, the color represents the difference between Chern number and its theoretical value $(N-2)-C$.