Quantum Anomalous Hall Effect in Rhombohedral Multilayer Graphene/hBN Moiré Superlattices

TL;DR

This topical review synthesizes experimental and theoretical progress on the quantum anomalous Hall effect in rhombohedral multilayer graphene aligned with hBN moiré superlattices, emphasizing how moiré potentials and strong Coulomb interactions yield interaction-driven topological bands. It surveys experimental milestones from Chern insulators in R3G to integer and fractional QAH states in thicker layers, and discusses the role of displacement fields, twist angle, and moiré alignment in stabilizing these phases. Theoretically, the work outlines continuum and tight-binding descriptions, Hartree–Fock analyses, and the emergence of concepts such as the Anomalous Hall Crystal (AHC) and various charge-density-wave–related topological phases, while addressing the limitations of mean-field methods. The review highlights open questions, including the robustness of FQAH states, the precise role of the moiré potential, and proposals for engineered moiré environments to further control topological matter in graphene-based systems. Overall, RMG/hBN moiré platforms offer a versatile setting to study and manipulate correlated topological phases with potential implications for topological electronics and quantum information.

Abstract

The recent discovery of robust quantum anomalous Hall (QAH) effect in rhombohedral multilayer graphene (RMG) aligned with hexagonal boron nitride (hBN) has established a highly versatile platform for correlated topological matter. This review synthesizes the experimental and theoretical progress in understanding these interaction-driven topological phases. Experimentally, the landscape has rapidly expanded from initial Chern insulators in trilayer systems to fully quantized QAH states in thicker systems. Theoretically, it is believed that moiré potential and electron-electron interaction cooperate and produce the QAH effect in such systems. Theoretical calculations also bring interesting questions, such as the formation of an interaction-driven topological phase known as an anomalous Hall crystal (AHC). This review comprehensively covers the experimental hallmarks, the theoretical frameworks, including continuum models and many-body approaches, and the ensuing physical picture that reconciles the roles of interactions, displacement fields, and the moiré potentials. We conclude by outlining outstanding open questions and future directions, positioning RMG/hBN systems at the forefront of topological quantum matter.

Figures (5)

• Figure 1: IQAH in RMG/hBN moiré superlattices. (a) Device schematic and measurement configuration of a standard dual-gate structure (reproduced from Ref. lu2025extended). (b) Magnetic hysteresis of $R_{xy}$ (blue) and $R_{xx}$ (red) at $\nu=1$ and $|D|=0.97~\mathrm{V\,nm^{-1}}$ in R5G/hBN moiré superlattices. At $200 ~\mathrm{mK}$, $R_{xy}$ is quantized at $h/e^{2}$ consistent with a Chern number $C=1$, whereas $R_{xx}$ is strongly suppressed at zero field. Solid (dashed) traces correspond to sweeping $B$ backward (forward) (replotted from data in Ref. lu2024fractional). (c),(d) Landau fan diagrams of $R_{xy}$ (c) and $R_{xx}$ (d) at $|D|=0.97~\mathrm{V\,nm^{-1}}$ in R5G/hBN moiré superlattices. The IQAH state forms a wide plateau whose Landau-fan slope matches the $C=1$ dashed line expected from the Streda formula (reproduced from Ref. lu2024fractional). (e)-(h) Representative IQAH responses at integer moiré filling in different layer numbers: (e) R4G at $\nu=-1$ and $|D|=0.21~\mathrm{V\,nm^{-1}}$ with $C=-4$ (replotted from data in Ref. choi2025superconductivity), (f) R6G at $\nu=1$ and $|D|=0.51~\mathrm{V\,nm^{-1}}$ with $C=1$ (replotted from data in Ref. xie2025tunable), (g) R7G at $\nu=1$ and $|D|=0.64~\mathrm{V\,nm^{-1}}$ with $C=1$ (from Ref. xiang2025continuously), (h) R10G at $\nu=1$ and $|D|=0.81~\mathrm{V\,nm^{-1}}$ with $C=2$ (from Ref. ding2025electric). Moiré filling factors ($\nu$) and Chern numbers ($C$) are labeled above each panel. Solid (dashed) traces correspond to sweeping $B$ backward (forward).
• Figure 2: Fractional and extended QAH in R5G/hBN moiré superlattices. (a) $R_{xy}$ (blue) and $R_{xx}$ (red) as functions of filling factor. $R_{xy}$ plateaus and $R_{xx}$ dips occur at fractional fillings $\nu=2/5, 3/7, 4/9, 5/11, 5/9, 4/7, 3/5$ and $2/3$, at $20~\mathrm{mK}$. (b) Representative magnetic hysteresis scans of $R_{xy}$ and $R_{xx}$ at selected fractional fillings $\nu=2/5, 3/7, 4/9, 4/7, 3/5$ and $2/3$, showing quantized $R_{xy} = h/(\nu e^{2})$ with vanishing $R_{xx}$. (c),(d) Phase diagrams of $R_{xx}$ (c) and $R_{xy}$ (d) at $B=\pm0.1~\mathrm{T}$ as functions of filling factor $\nu$ and displacement field $D$, taken at electron temperature of $200~\mathrm{mK}$ , where $R_{xy}$ plateaus and $R_{xx}$ dips occur in a stripe-like region and fractional features appear at commensurate $\nu=1, 2/3, 3/5$ and $2/5$ (indicated by the dashed lines and arrows). (e),(f) Extended phase diagrams of $R_{xx}$ (e) and $R_{xy}$ (f) at $B=\pm0.1~\mathrm{T}$ as functions of $\nu$ and $D$, taken at $20~\mathrm{mK}$. Three regions (labelled by numbers and arrows) show quantized $R_{xy}$ at $h/e^2$ and vanishing $R_{xx}$, over a wide window (extended QAH regime). The dashed lines correspond to $|D|=0.95~\mathrm{V\,nm^{-1}}$. (g),(h) Temperature-dependent $R_{xx}$ (g) and $R_{xy}$ (h) taken along the dashed line in (e) and (f), showing how the extended quantized region evolves and competes with nearby fractional states. All data were extracted by a symmetrizing/anti-symmetrizing process under magnetic-field reversal, $R_{xx}^{\mathrm{sym}}(\pm B)=\frac{R_{xx}(+B)+R_{xx}(-B)}{2}$, $R_{xy}^{\mathrm{asym}}(\pm B)=\frac{R_{xy}(+B)-R_{xy}(-B)}{2}$. Data in panel (a) are from pentalayer device D2; all other panels [(b)-(h)] are from device D1. (a),(e)-(h) are reproduced from Refs. lu2025extended. (b)-(d) are reproduced from Refs. lu2024fractional with permission. © 2024, 2025 Springer Nature.
• Figure 3: Lattice structure and displacement-field-tunable band structures of RMG. (a). Top view of the honeycomb lattice. For the carbon-carbon bonds along the $y$-axis, the atoms at the lower and upper positions are defined as A (white circles) and B (black circles) sublattices, respectively. $\boldsymbol{R}_1$ and $\boldsymbol{R}_2$ denote the primitive lattice vectors, and $a_G$ is the carbon-carbon bond length. (b). Schematic side view of stacking configurations comparing Bernal (AB) and rhombohedral (ABC) stacking. The dashed lines indicate the vertical alignment and shifting of sublattices across layers. (c). (Cited from dong2024theory) Continuum pentalayer rhombohedral graphene dispersion (without hBN alignment) along the $k_x$ axis for increasing interlayer potential difference $\Delta$ (meV) highlighted by darker shades of blue. The vertical dashed lines indicate the location of the moiré $K$ points when h-BN is aligned with pentalayer graphene.
• Figure 4: Reciprocal space representation of a graphene/hBN heterostructure. The diagram illustrates the Brillouin zones (BZs) of graphene (large orange hexagon) and hBN (blue hexagon), which are misaligned by a twist angle $\theta$. The vectors $g_1^G$ and $g_1^{BN}$ represent the primary reciprocal lattice vectors for graphene and hBN, respectively. The resulting moiré Brillouin zone (mBZ) is shown as the small black hexagon, centered at the $\bar{\Gamma}$ point, which coincides with the $K$ vertex of the graphene BZ. Key high-symmetry points within the mBZ, including $\bar{K}$, $\bar{K}'$, and the M-points ($\bar{M}$, $\bar{M}'$, $\bar{M}"$), are labeled to indicate electronic folding. The reciprocal lattice vector of the mBZ is defined as $G_1 = g_1^{BN} - g_1^G$.
• Figure 5: (Cited from dong2024anomalous) (a),(e) The phase diagram of moiré rhombohedral pentalayer graphene as a function of the interlayer potential difference $\Delta$, and the twist angle $\theta$. The colors label the Chern number of the SCHF ground states, with gapless regions shown in white. On the moiré-distant side ($\Delta < 0$), the anomalous Hall crystal (AHC) phase has $C=1$, whereas the Wigner-like insulator (WLI) has $C=0$. (b),(f) Noninteracting band structures at the yellow star ($-\Delta, \theta) =(50\,\mathrm{meV; 0.77^\circ})$ and purple triangle ($-\Delta, \theta) =(50\,\mathrm{meV; 0.2^\circ})$. Inset in (b): plot of the moiré Brillouin zone. (c),(g) SCHF band structure at $\nu=1$, finding an AHC and WLI at the yellow star and purple triangle, respectively. Insets: Berry curvature $\Omega(k)$ of the occupied band. (d),(h) Charge densities $\rho(r)$ of the AHC (d) and WLI (h). The AHC charge density resembles a honeycomb lattice, whereas the WLI charge density resembles a triangular lattice.