Flat bands in chiral multilayer graphene
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911851706580992 |
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| author | Makov, Roi Guinea, Francisco Stern, Ady |
| author_facet | Makov, Roi Guinea, Francisco Stern, Ady |
| contents | We study the formation and properties of perfectly-flat zero energy bands in a multi-layer graphene systems in the chiral limit. Employing the degrees of freedoms of the multi-layer system, such as relative twist-angle and relative shifts, in a way that preserves a set of symmetries, we define a two-dimensional parameter plane that hosts lines of two and four flat bands. This plane enables adiabatic continuation of multi-layer chiral systems to weakly coupled bi- and tri-layer systems, and through that mapping provides tools for calculating the Chern numbers of the flat bands. We show that a flat band of Chern number $C$ can be spanned by $C$ effective Landau levels, all experiencing an effective flux of $1/C$ flux quantum per unit cell, and each carrying its own intra-unit-cell wave function. The flat bands do not disperse under the effect of a perpendicular magnetic field, and the gap to the dispersive bands closes when the externally applied flux cancels the $1/C$ effective flux. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_15759 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Flat bands in chiral multilayer graphene Makov, Roi Guinea, Francisco Stern, Ady Mesoscale and Nanoscale Physics Strongly Correlated Electrons We study the formation and properties of perfectly-flat zero energy bands in a multi-layer graphene systems in the chiral limit. Employing the degrees of freedoms of the multi-layer system, such as relative twist-angle and relative shifts, in a way that preserves a set of symmetries, we define a two-dimensional parameter plane that hosts lines of two and four flat bands. This plane enables adiabatic continuation of multi-layer chiral systems to weakly coupled bi- and tri-layer systems, and through that mapping provides tools for calculating the Chern numbers of the flat bands. We show that a flat band of Chern number $C$ can be spanned by $C$ effective Landau levels, all experiencing an effective flux of $1/C$ flux quantum per unit cell, and each carrying its own intra-unit-cell wave function. The flat bands do not disperse under the effect of a perpendicular magnetic field, and the gap to the dispersive bands closes when the externally applied flux cancels the $1/C$ effective flux. |
| title | Flat bands in chiral multilayer graphene |
| topic | Mesoscale and Nanoscale Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2404.15759 |