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Hetero-Orbital Two-Component Fractional Quantum Hall States in Bilayer Graphene

Ke Huang1, Ajit C. Balram2,3, Hailong Fu1,*, Chengqi Guo1, Kenji Watanabe4, Takashi Taniguchi5, Jainendra K. Jain1,†, and Jun Zhu1,6,‡

  • *Present address: School of Physics, Zhejiang University, Hangzhou 310058, China.
  • †Contact author: jkj2@psu.edu
  • ‡Contact author: jxz26@psu.edu
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Phys. Rev. X 15, 031023 – Published 22 July, 2025

DOI: https://doi.org/10.1103/kfn2-qggs

Abstract

A two-dimensional electron system exposed to a strong magnetic field produces a plethora of strongly interacting fractional quantum Hall (FQH) states, the complex topological orders of which are revealed through exotic emergent particles, such as composite fermions, and fractionally charged Abelian and non-Abelian anyons. Much insight has been gained by the study of multicomponent FQH states, where spin and pseudospin indices of the electron contribute additional correlation. Traditional multicomponent FQH states develop in situations where the components share the same orbital states and the resulting interactions are pseudospin independent; this homo-orbital nature is also crucial to their theoretical understanding. Here, we study “hetero-orbital” two-component FQH states, in which the orbital index is part of the pseudospin, rendering the multicomponent interactions strongly SU(2) anisotropic in the pseudospin space. Such states, obtained in bilayer graphene at the isospin transition between N=0 and N=1 electron Landau levels, are markedly different from previous homo-orbital two-component FQH states. In particular, we observe strikingly different behaviors for the parallel-vortex and reverse-vortex attachment composite fermion states, and an anomalously strong two-component 2/5 state over a wide range of magnetic field before it abruptly disappears at a high field. Our findings, combined with detailed theoretical calculations, reveal the surprising robustness of the hetero-orbital FQH effects, significantly enriching our understanding of FQH physics in this novel regime.

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Popular Summary

Strong electron interactions give rise to the fractional quantum Hall effect (FQHE), a state that supports fractionally charged states in a strong magnetic field. Electrons carry more than just charge; they also have properties such as spin and pseudospin, which enrich their interactions and enable the formation of more complex quantum states. In particular, bilayer graphene has a property known as valley pseudospin, a spinlike internal degree of freedom associated with which layer the electron goes to in the magnetic field. In this study, we discover a new type of two-component FQHE state in bilayer graphene that uniquely combines two different orbital and valley pseudospin states—a combination not seen before.

Typically, two-component FQHE states in 2D electron systems are homo-orbital, meaning both components share the same orbital wave function. However, when two electron energy levels in bilayer graphene with different orbitals and valley pseudospins align—achieved through electrical tuning—we observe a novel hetero-orbital two-component FQHE state. Theoretical calculations confirm the stability of this new two-component state and indicate that it arises from interactions that treat the components differently based on their orbital character.

This finding broadens our understanding of the FQHE by introducing a new class of multicomponent quantum states. It shows that internal degrees of freedom, such as valley and orbital pseudospin, can be effectively utilized to create and control novel phases of matter.

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Phys. Rev. X 15, 031023– Published 22 July, 2025
  • Received 8 January 2025
  • Revised 8 May 2025
  • Accepted 29 May 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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