Yang-Mills flows for multilayered graphene
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arXiv
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| Format: | Preprint |
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2025
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| author | Iugov, Vasilii Nekrasov, Nikita |
| author_facet | Iugov, Vasilii Nekrasov, Nikita |
| contents | We clarify the origin of magic angles in twisted multilayered graphene using Yang-Mills flows in two dimensions. We relate the effective Hamiltonian describing the electrons in the multilayered graphene to the ${\bar\partial}_{A}$ operator on a two dimensional torus coupled to an $SU(N)$ gauge field. Despite the absence of a characteristic class such as $c_{1}$ relevant for the quantum Hall effect, we show that there are topological invariants associated with the zero modes occuring in a family of Hamiltonians. The flatbands in the spectrum of the effective Hamiltonian are associated with Yang-Mills connections, studied by M.Atiyah and R.Bott long time ago. The emergent $U(1)$ magnetic field with nonzero flux is presumably responsible for the observed Hall effect in the absence of (external) magnetic field. We provide a numeric algorithm transforming the original single-particle Hamiltonian to the direct sum of ${\bar\partial}_{A}$ operators coupled to abelian gauge fields with non-zero $c_1$'s. Our perspective gives a simple bound for magic angles: if the gauge field $A(α)$ is such that the YM energy $\Vert F_{A(α)} \Vert^2$ is smaller than that of $U(1)$ magnetic flux embedded into $SU(2)$, then $α$ is not magic. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_19097 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Yang-Mills flows for multilayered graphene Iugov, Vasilii Nekrasov, Nikita High Energy Physics - Theory Superconductivity We clarify the origin of magic angles in twisted multilayered graphene using Yang-Mills flows in two dimensions. We relate the effective Hamiltonian describing the electrons in the multilayered graphene to the ${\bar\partial}_{A}$ operator on a two dimensional torus coupled to an $SU(N)$ gauge field. Despite the absence of a characteristic class such as $c_{1}$ relevant for the quantum Hall effect, we show that there are topological invariants associated with the zero modes occuring in a family of Hamiltonians. The flatbands in the spectrum of the effective Hamiltonian are associated with Yang-Mills connections, studied by M.Atiyah and R.Bott long time ago. The emergent $U(1)$ magnetic field with nonzero flux is presumably responsible for the observed Hall effect in the absence of (external) magnetic field. We provide a numeric algorithm transforming the original single-particle Hamiltonian to the direct sum of ${\bar\partial}_{A}$ operators coupled to abelian gauge fields with non-zero $c_1$'s. Our perspective gives a simple bound for magic angles: if the gauge field $A(α)$ is such that the YM energy $\Vert F_{A(α)} \Vert^2$ is smaller than that of $U(1)$ magnetic flux embedded into $SU(2)$, then $α$ is not magic. |
| title | Yang-Mills flows for multilayered graphene |
| topic | High Energy Physics - Theory Superconductivity |
| url | https://arxiv.org/abs/2504.19097 |