Moiré Graphene Demonstrates Fractional Chern Insulators with Quantized Hall Conductance in a Trivial Band

The pursuit of novel electronic states in twisted multilayer graphene has revealed surprising connections between topology and correlated electron behaviour, and now, Hui Liu, Raul Perea-Causin, and Zhao Liu, alongside colleagues at Stockholm University and Zhejiang University, demonstrate that fractional topological order can arise even when the material’s underlying band structure is topologically trivial. This research establishes a pathway to realising zero-field fractional Chern insulators, states of matter exhibiting fractional quantum Hall conductance, through long-range Coulomb interactions within the moiré pattern of twisted graphene layers. The team’s findings reveal that strongly varying quantum geometry within the moiré structure reshapes electron interactions, driving the emergence of this topological order independently of the material’s band topology, and opens up possibilities for stabilising similar states in a wider range of moiré materials under realistic experimental conditions. This achievement represents a significant step forward in understanding and controlling many-body topological phases, potentially paving the way for future quantum technologies.

This work demonstrates that fractionalized topological order can arise in realistic conditions, even within a moiré band that is topologically trivial. By incorporating long-range Coulomb interactions into a trivial band of twisted multilayer graphene, the researchers identify a series of incompressible fractional Chern insulator ground states, which exhibit fractional quantized Hall conductance. The Laughlin-like behaviour of these states is further confirmed through analysis of the particle-cut entanglement spectrum, revealing characteristics consistent with theoretical predictions. The origin of this phase is traced to the strongly inhomogeneous distribution of quantum geometry within the material.

Moiré Graphene Reveals Strong Topological Order

This research investigates the relationship between the properties of electronic bands in a material and the emergent order arising from interactions between many electrons within moiré graphene structures. The central finding is that strong topological order, similar to Laughlin states, can exist even when the underlying electronic band structure is not inherently topological. This challenges the conventional understanding that topological order requires non-trivial band topology. The key implication of this work is the decoupling of band topology and many-body order, opening up new possibilities for designing materials with exotic properties and guiding the development of new materials with robust topological properties.

Fractional Chern Insulators From Quantum Geometry

Scientists have demonstrated the emergence of fractional Chern insulators within twisted multilayer graphene, even when the underlying electronic bands possess trivial topology. This work establishes that robust fractional Chern insulators can arise not from conventional band topology, but from the specific distribution of quantum geometry within the material. Researchers considered long-range Coulomb interactions within a topologically trivial moiré band, identifying incompressible ground states exhibiting fractional quantized Hall conductance. Experiments revealed Laughlin-like behavior, confirmed through analysis of the particle-cut entanglement spectrum, which matched the expected characteristics of the 1/3 filling Laughlin state.

Quantum Geometry Drives Fractional Chern Insulators

This research demonstrates the emergence of fractional Chern insulators within moiré materials, even when those materials possess topologically trivial band structures. Scientists have identified incompressible ground states exhibiting fractional quantized Hall conductance by considering long-range Coulomb interactions within a twisted multilayer system. Detailed analysis of the particle-cut entanglement spectrum confirms Laughlin-like behavior, indicating the presence of fractionalized topological order. The key finding is that the distribution of quantum geometry across the moiré Brillouin zone, rather than the single-particle Chern number, drives the stabilization of these fractional Chern insulator states.

This quantum geometric mechanism extends to systems with higher Chern numbers, suggesting a broader range of materials where this phenomenon can be observed. Researchers demonstrated that coupling valleys of opposite chirality can create trivial bands hosting Laughlin-like states, offering a pathway for engineering such behavior in twisted bilayer graphene with commensurate substrates. The authors acknowledge that their results also point to limitations in relying solely on standard topological band arguments, hinting at richer phase diagrams in higher-Chern bands. Future research may focus on investigating the competition between unconventional fractional Chern insulators and Halperin-like states, where the interplay of quantum geometry and layer polarization could be crucial. This work establishes realistic scenarios for realizing many-body topological order beyond the traditional Landau-level paradigm, opening new avenues for exploring exotic quantum matter.