Variational Mapping of Chern Bands to Landau Levels: Application to Fractional Chern Insulators in Twisted MoTe$_2$
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| Format: | Preprint |
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2024
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| _version_ | 1866913736805056512 |
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| author | Li, Bohao Wu, Fengcheng |
| author_facet | Li, Bohao Wu, Fengcheng |
| contents | We present a theoretical study of mapping between Chern bands and generalized Landau levels in twisted bilayer MoTe$_2$ ($t$MoTe$_2$), where fractional Chern insulators down to zero magnetic fields have been observed. We construct an exact Landau-level representation of moiré bands, where the basis functions, characterized by a uniform quantum geometry, are derived from Landau-level wavefunctions dressed by spinors aligned or antialigned with the layer pseudospin skyrmion field. We further generalize the dressed zeroth Landau level to a variational wavefunction with an ideal yet nonuniform quantum geometry and variationally maximize its weight in the first moiré band. The variational wavefunction has a high overlap with the first band and quantitatively captures the exact diagonalization spectra of fractional Chern insulators at hole-filling factors $ν_h=2/3$ and $3/5$, providing a clear theoretical mechanism for the formation and properties of the fractionalized states. Our work introduces a variational approach to studying fractional states by mapping Chern bands to Landau levels, with application to other systems beyond $t$MoTe$_2$ also demonstrated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20307 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Variational Mapping of Chern Bands to Landau Levels: Application to Fractional Chern Insulators in Twisted MoTe$_2$ Li, Bohao Wu, Fengcheng Mesoscale and Nanoscale Physics Strongly Correlated Electrons We present a theoretical study of mapping between Chern bands and generalized Landau levels in twisted bilayer MoTe$_2$ ($t$MoTe$_2$), where fractional Chern insulators down to zero magnetic fields have been observed. We construct an exact Landau-level representation of moiré bands, where the basis functions, characterized by a uniform quantum geometry, are derived from Landau-level wavefunctions dressed by spinors aligned or antialigned with the layer pseudospin skyrmion field. We further generalize the dressed zeroth Landau level to a variational wavefunction with an ideal yet nonuniform quantum geometry and variationally maximize its weight in the first moiré band. The variational wavefunction has a high overlap with the first band and quantitatively captures the exact diagonalization spectra of fractional Chern insulators at hole-filling factors $ν_h=2/3$ and $3/5$, providing a clear theoretical mechanism for the formation and properties of the fractionalized states. Our work introduces a variational approach to studying fractional states by mapping Chern bands to Landau levels, with application to other systems beyond $t$MoTe$_2$ also demonstrated. |
| title | Variational Mapping of Chern Bands to Landau Levels: Application to Fractional Chern Insulators in Twisted MoTe$_2$ |
| topic | Mesoscale and Nanoscale Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2405.20307 |