Emergent fermion dynamical symmetry for monolayer graphene in a strong magnetic field

Abstract

We review the physics of monolayer graphene in a strong magnetic field, with emphasis on highly collective states that emerge from the weakly interacting system because of correlations (emergent states). After reviewing the general properties of graphene and of electrons in a magnetic field, we give a brief introduction to the integer quantum Hall effect (IQHE) and the fractional quantum Hall effect (FQHE) in a 2D electron gas as foundation to show that monolayer graphene in a magnetic field exhibits both effects, but with properties modified by the influence of the graphene crystal. After giving an introduction to standard methods of dealing with emergent states for this system, we show that an SO(8) fermion dynamical symmetry governs the emergent degrees of freedom and that the algebraic and group properties of the dynamical symmetry provide a new view of strongly correlated states observed in monolayer graphene subject to a strong magnetic field.

Graphical abstract

Keywords

graphene / group theory / dynamical symmetry / emergent states / Lie algebras / quantum phases

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Declarations

The authors declare no competing interests and no conflicts.

Electronic supplementary materials

The online version contains supplementary material available at https://doi.org/10.15302/frontphys.2025.014302.

Acknowledgements

We wish to thank Yang Sun for useful discussions and Matthew Murphy for help with some of the calculations and illustrations that were used here. L.-A. W. was supported by the Basque Country Government (Grant No. IT1470- 22) and Grant No. PGC2018-101355-B-I00 funded by MCIN/AEI/10.13039/501100011033. F. W. was supported partially by LightCone Interactive LLC during the completion of this work.

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