Fractional Quantum Anomalous Hall Effect

Journal Article · Mon Dec 22 00:00:00 EST 2025 · Annual Review of Condensed Matter Physics

DOI:https://doi.org/10.1146/annurev-conmatphys-031524-071133· OSTI ID:3021157

Cao, Ting ^[1]; Fu, Liang ^[2]; Ju, Long ^[2]; Xiao, Di ^[1]; Xu, Xiaodong ^[1]

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1. University of Washington, Seattle, WA (United States)
2. Massachusetts Institute of Technology, Cambridge, MA (United States)

The realization of the fractional quantum anomalous Hall effect (FQAHE) in a zero-field fractional Chern insulator is a new advancement in condensed matter physics, resulting from the interplay among strong correlations, topology, and spontaneous time-reversal symmetry breaking in lattice systems. In this review, we highlight the experimental and theoretical progress toward achieving FQAHE in two material platforms: twisted bilayer MoTe₂ and rhombohedral-stacked multilayer graphene. These systems host narrow topological bands with nontrivial Chern numbers, enabling interaction-driven fractionalized states analogous to the fractional quantum Hall effect, but without external magnetic fields. We discuss how spontaneous ferromagnetism, moiré lattice reconstruction, and band topological effects underpin the emergence of FQAHE in twisted MoTe₂. We describe experimental discoveries of zero-field fractional Chern insulators in both transport and optical experiments, as well as signatures of composite Fermi liquids and higher-energy Chern band, which may shed light on engineering nonabelian states. In rhombohedral graphene/hexagonal boron nitride moiré superlattices, we review the recent observations of fractionally quantized Hall resistance, connections between FQAHE and extended quantum anomalous Hall phases, and the coexistence of superconductivity and FQAHE. Furthermore, these discoveries not only deepen our understanding of strongly correlated topological matter but also open new frontiers for exploring nonabelian anyons, fault-tolerant quantum computation, and topological opto-spintronics free of magnetic fields.

• Research Organization: University of Washington, Seattle, WA (United States)
• Sponsoring Organization: Air Force Office of Scientific Research (AFOSR); National Science Foundation (NSF); USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division (MSE); Vannevar Bush Faculty Fellowship
• Grant/Contract Number: SC0012509; SC0025325; SC0025327
• Other Award/Contract Number: DMR-2414725; FA9550-22-1-0432; FA9550-21-1-0177; N000142512047
• OSTI ID: 3021157
• Journal Information: Annual Review of Condensed Matter Physics, Journal Name: Annual Review of Condensed Matter Physics; ISSN 1947-5462; ISSN 1947-5454
• Publisher: Annual Reviews
• Country of Publication: United States
• Language: English

Related Subjects

bilayer
quantum Hall effect
rhombohedral-stacked multilayer graphene
topology
twisted MoTe2
zero magnetic field