Jackson P. Butler | Searcharxiv

arXiv2026

1/3 Fractional and Gapless Integer Quantum Anomalous Hall States in Rhombohedral Graphene

The fractional quantum anomalous Hall (FQAH) effect occurs in moir\'e superlattices in both twisted bilayer MoTe$_2$ and rhombohedral $n$-layer graphene aligned to hexagonal boron nitride (R$n$G/hBN) as a novel quantum phase driven by intertwined electron correlation and topology. Although several fractional states in the Jain sequence have been identified, the $1/3$ state, the most robust and fundamental state in conventional fractional quantum Hall (FQH) systems, was missing in either FQAH system. Determining whether it exists would have a major impact on understanding the mechanism of FQAH, especially in the theoretically still-debated R$n$G/hBN system. Here we report the FQAH effect at moir\'e filling factor $\nu = 1/3$ in R$5$G/hBN moir\'e superlattice devices, through a combination of quantum capacitance and transport measurements. By tuning the displacement field, we observed a topological phase transition from a $1/3$ fractional Chern insulator (FCI) to a trivial charge density wave state. With the inclusion of the $1/3$ state, the FQAH states in R$5$G/hBN now exhibit a surprising level of particle-hole symmetry about half-filling, closely resembling the behavior of FQH states in the lowest Landau level. Additionally, we perform compressibility and transport measurements at a filling of one electron per moir\'e unit cell, $\nu =1$, and also for $\nu \lesssim 1$, where previous transport measurements displayed the extended quantum anomalous Hall (EQAH) effect. While our transport measurements show no change between the integer quantum anomalous Hall state (IQAH) and the EQAH region, compressibility measurements reveal a distinct transition from a gapped IQAH state to a gapless and highly compressible EQAH state. Our direct thermodynamic characterization of the rich phase diagram paves the way to engineering of anyon braiding and non-Abelian quasiparticles at zero magnetic field.

cond-mat.mes-hall↗

arXiv2026

Evidence of Metallic Wigner Crystal in Rhombohedral Graphene

When the Coulomb interaction dominates over kinetic energy, electrons can crystallize into a Wigner crystal (WC). This paradigmatic correlated electronic phase has been realized in two-dimensional electron gases with parabolic band dispersion and completely flat Landau levels under high magnetic fields. Beyond these conventional contexts of electron crystallization, more exotic electron crystals have been postulated but remain unexplored. For example, a metallic Wigner crystal (mWC), in which itinerant carriers coexist with a pinned electron lattice, has been proposed theoretically but considered difficult to realize. Non-parabolic electron bands and quantum geometry may facilitate mWC and other novel topological electron crystals. Here we report transport evidence for WC and mWC in rhombohedral tetra-, penta-, and hexalayer graphene in the charge density range 0.3-0.5x10^12 cm^-2. By flattening the conduction band with a gate-controlled displacement field D, we observe an insulating state at nonzero charge density that shows nonlinear, hysteretic current-voltage relations, signatures of a pinned WC, that are absent from the lower-density insulator. Further increasing D reveals transport dominated by hole-like carriers with density up to only 15% of the nominal electron density, consistent with mWC. This mWC state is closely tied to the WC state, as both collapse simultaneously with increasing temperature or bias voltage. The mWC state shows quantum Hall onset near 0.4 T and disobeys the Streda relation, indicating compressible charge exchange between itinerant holes and the transport-inert WC background. Our results establish rhombohedral graphene as a platform for exploring novel electron crystals, as well as possible nontrivial topology, and new collective modes.

cond-mat.mes-hall↗