Posted in | News | Graphene

Understanding Fractional Correlated Insulating States of Twisted Graphene

Magic-angle twisted bilayer graphene has been recently discovered to exhibit superconductivity, which has inspired theoretical studies on integer fillings. However, studies of fractional filling are sparse.

Understanding Fractional Correlated Insulating States of Twisted Graphene

​​​​​​​Study: Fractional correlated insulating states at one-third filled magic angle twisted bilayer grapheneImage Credit: OliveTree/

An article published in Communications Physics presented the “fractional correlated insulator” state of the Wannier orbital’s three-peak structure that emerged at fractional filling (ν) of n ± 1/3 (with n integer). This study showed that the filling of one-third (1/3) electrons in each moiré unit cell resulted in short-range interactions leading to an increased entropy because of “breathing” degree of freedom owing to the irregularity in lattice induced by defect lines.

Furthermore, strongly interacting electrons lifted the degeneracy and selected the ferromagnetic nematic state, breaking AB/BA sublattice symmetry. Thus, the suggested fractional correlated insulating state proposed in the present work might suppress the superconductivity at ν = 2 − 1/3 filling.

Magic-Angle Twisted Bilayer Graphene and its Superconductivity

Twisted bilayer graphene is fabricated by the stacking of two monolayers of graphene with a specific twisting angle (θ). In this structure, the moiré pattern has been observed to emerge with a higher periodicity.

Recently, the twisted bilayer graphene has been often reported with extraordinary optical and electronic properties, which were a result of the development of the moiré patterns. The strong electron interactions in the minibands formed in the moiré superlattices of twisted bilayer graphene make them a fascinating platform for studying strongly correlated states.

In most systems, correlated states appear when the moiré lattice is filled with an integer number of electrons per moiré unit cell. The experimental findings on orbital ferromagnetism, other isospin polarizations, and nematic tendencies have led to significant advancements.

However, studies of fractional filling were less explored, even though phase diagrams revealed potentially complex phenomena at partial fills, such as the suppression of superconductivity close to the filling of v = 2-1/3.

From the theoretical point of view, interest in integer filling originates from the complexity of magic-angle-twisted bilayer graphene. Additionally, the experimental findings reveal that magic-angle twisted bilayer graphene exhibits a triangular superlattice centered on Wannier orbitals, which are obstructed by the topology and symmetry of the Bloch wave functions.

Alternatively, the three lobes of the wavefunction extend to the three nearby AA sites, and the Wannier orbitals are centered at the AB or BA sites. Such extended Wannier orbitals make it difficult to create a local model because they require the inclusion of interactions and further-range hopping elements.

One-Third Filled Magic Angle Twisted Bilayer Graphene

Previous researchers discovered a drop in the superconducting conductivity at ν = 2 − 1/3, which was inspired by the dip in superconductivity in cuprates at a commensurate partial filling of 1/8 holes per plane of copper oxide. This decrease in superconductivity causes the system to insulate even at the lowest temperatures.

The present study focused on the effects of Wannier orbitals and Wannier obstruction in magic-angle-twisted bilayer graphene at ν = 1/3 electrons per unit cell. The strong-coupling limit allowed the mapping of the present problem to the tiling issue.

This mapping helped assert the extensive degeneracy of the ground state at ν of 1/3, which was confined to short-range interactions. The Monte Carlo simulation helped to identify several ground states at low temperatures in the no-touching model, which was consistent with the predicted extensive degeneracy.

In contrast to krypton adsorbed on graphite, the "no-touching" model limited to local interactions had a zero Hamiltonian because the flip lines and Y-junctions used no energy. A long-range density-density Coulomb interaction would not disrupt the degeneracy because it consists of states with the same uniform charge density but different Wannier state layouts.


In summary, the present work revealed a translationally symmetric fractional correlated insulating state mechanism in magic-angle twisted bilayer graphene. The significant effect of the Wannier obstruction in magic-angle twisted graphene was due to the incompressibility of the n ± 1/3 states.

The shortest interaction encouraged a uniform charge distribution, where one-third of the charge was concentrated at each AA site, with the weight of the Wannier orbitals divided into three lobes, resulting in the fractional filling.

This study demonstrated that the short-range no-touching restriction alone would imply extensive entropy by linking the model to the trimer-tiling issue. The ferromagnetic arrangement was favored by further-range interactions, equivalent to direct exchange.

Direct exchange increased degeneracy and selected a complicated state that destroyed the AB/BA sublattice symmetry and C3 rotational symmetry. In addition to the spin ferromagnetic arrangement, the twisted bilayer graphene featured an antiferromagnetic arrangement of the AB/BA Wannier centers. Thus, this study focused on exchange interactions and hopping as disturbances to obtain results on degeneracy splitting.


Zhang, K., Zhang, Y., Fu, L., Kim, E-A. (2022). Fractional correlated insulating states at one-third filled magic angle twisted bilayer graphene. Communications Physics.

Disclaimer: The views expressed here are those of the author expressed in their private capacity and do not necessarily represent the views of Limited T/A AZoNetwork the owner and operator of this website. This disclaimer forms part of the Terms and conditions of use of this website.

Bhavna Kaveti

Written by

Bhavna Kaveti

Bhavna Kaveti is a science writer based in Hyderabad, India. She has a Masters in Pharmaceutical Chemistry from Vellore Institute of Technology, India, and a Ph.D. in Organic and Medicinal Chemistry from Universidad de Guanajuato, Mexico. Her research work involved designing and synthesizing heterocycle-based bioactive molecules, where she had exposure to both multistep and multicomponent synthesis. During her doctoral studies, she worked on synthesizing various linked and fused heterocycle-based peptidomimetic molecules that are anticipated to have a bioactive potential for further functionalization. While working on her thesis and research papers, she explored her passion for scientific writing and communications.


Please use one of the following formats to cite this article in your essay, paper or report:

  • APA

    Kaveti, Bhavna. (2022, October 19). Understanding Fractional Correlated Insulating States of Twisted Graphene. AZoNano. Retrieved on February 24, 2024 from

  • MLA

    Kaveti, Bhavna. "Understanding Fractional Correlated Insulating States of Twisted Graphene". AZoNano. 24 February 2024. <>.

  • Chicago

    Kaveti, Bhavna. "Understanding Fractional Correlated Insulating States of Twisted Graphene". AZoNano. (accessed February 24, 2024).

  • Harvard

    Kaveti, Bhavna. 2022. Understanding Fractional Correlated Insulating States of Twisted Graphene. AZoNano, viewed 24 February 2024,

Tell Us What You Think

Do you have a review, update or anything you would like to add to this news story?

Leave your feedback
Your comment type
Azthena logo powered by Azthena AI

Your AI Assistant finding answers from trusted AZoM content

Azthena logo with the word Azthena

Your AI Powered Scientific Assistant

Hi, I'm Azthena, you can trust me to find commercial scientific answers from

A few things you need to know before we start. Please read and accept to continue.

  • Use of “Azthena” is subject to the terms and conditions of use as set out by OpenAI.
  • Content provided on any AZoNetwork sites are subject to the site Terms & Conditions and Privacy Policy.
  • Large Language Models can make mistakes. Consider checking important information.

Great. Ask your question.

While we only use edited and approved content for Azthena answers, it may on occasions provide incorrect responses. Please confirm any data provided with the related suppliers or authors. We do not provide medical advice, if you search for medical information you must always consult a medical professional before acting on any information provided.

Your questions, but not your email details will be shared with OpenAI and retained for 30 days in accordance with their privacy principles.

Please do not ask questions that use sensitive or confidential information.

Read the full Terms & Conditions.