Non-Abelian Chern band in rhombohedral graphene multilayers

Abstract

Moiré flat bands in rhombohedral multilayer graphene provide a platform for exploring interaction-driven topological phases, where a single isolated band often forms a Chern band. However, non-Abelian degenerate Chern bands with internal symmetries such as $\mathrm{SU}(N)$ have so far been realized only in highly engineered systems. Here, we show that a doubly degenerate non-Abelian Chern band with Chern number $|C|=1$ emerges spontaneously at filling $ν=2$ in rhombohedral 3-, 4-, and 5-layer graphene, regardless of the presence of an hBN substrate. Using self-consistent Hartree-Fock calculations, we map out phase diagrams as functions of displacement field and electronic periodicity, and analytically demonstrate that the Fock term drives spontaneous symmetry breaking and generates non-Abelian Berry curvature. We further show that this non-Abelian topology is characterized by $\mathrm{SU}(2)$ gauge flux threading the noncontractible cycles of the Brillouin zone, leading to a global non-Abelian holonomy. Our findings unveil a new class of interaction-driven non-Abelian topological phases, distinct from quantum anomalous Hall and fractional Chern phases.

Figures (9)

• Figure 1: Phase diagram of rhombohedral multilayer graphene at filling factor $\nu = 2$ as a function of the interlayer potential difference $u_D$ and the twist angle $\theta$ (with corresponding moiré period $L^M$). The upper, middle, and bottom rows correspond to $N_L = 3$, $4$, and $5$, respectively, and the left and right panels show results without and with $V_{\rm{hBN}}$, respectively. Gray, green, and red regions indicate the metallic phase, the QSH phase, and the non-Abelian phase, respectively.
• Figure 2: Band structure, local charge density and local spin texture of (a) the non-Abelian state and (b) the QSH state obtained by HF calculations for the 5-layer graphene, which are marked by red and green stars, respectively, in Fig. \ref{['fig:PhaseDiagram']}. The hexagon in the middle and right figures represent the superlattice unit cell. In the right panel, the color map represents the local spin-density $S_z$ while the arrow represents $S_x$ and $S_y$ components.
• Figure 3: (a) BZ of the model Hamiltonian in Eq. \ref{['eq_H_simple']} with reciprocal vectors $\bm{G}_i$. (b) BZ torus with noncontractible cycles corresponding to paths from $\Gamma$ to $\bm{G}_i$$(i=1,2,3)$. Thick lines indicate $\mathrm{SU}(2)$ gauge fluxes associated with $\tau_1$ (vertical line) and $\tau_2$ (circular loop inside the torus). (c) Band structure for the parameter $L=1$, $\hbar^2/(2m)=1$ and $V_0=0.05$. Each band is two-fold degenerate on the whole BZ. (d) Local spin density When the lowest band doublet is fully occupied, plotted in the same manner as in Fig. \ref{['fig:NA_QSH']}.
• Figure 4: Band structures of a 5-layer system without hBN at $u_D = 40$ meV and $\theta = 0.77^\circ$, comparing HF calculations with 7 (left panel) and 14 (right panel) conduction bands per spin and valley.
• Figure 5: Total energy differences relative to the non-Abelian HF ground state as a function of the number of conduction bands $N_b$ per spin and valley (5-layer without hBN, $u_D = 40$ meV, $\theta = 0.77^\circ$). The plotted $\Delta E_{\rm{tot}}$ values show systematic convergence with increasing $N_b$, while the quantum spin Hall (QSH) and metallic states remain energetically higher for all $N_b$. From these results, we conclude that $N_b = 7$ is sufficient to reliably distinguish the ground state.