Variational Mapping of Chern Bands to Landau Levels: Application to Fractional Chern Insulators in Twisted MoTe${}_2$

Abstract

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 ${\nu }_h=2/3$ 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.

13 pages, 9 figures. Published in Physical Review B as Editors' Suggestion

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Cited by in corpus (15)

• Quantum Geometry Probed by Chiral Excitonic Optical Response of Chern Insulators
• Observation of Ferromagnetic Phase in the Second Moiré Band of Twisted MoTe2
• Moiré Band Engineering in Twisted Trilayer WSe2
• Characterization of fractional Chern insulator quasiparticles in twisted homobilayer MoTe${}_2$
• Low-energy optical absorption in correlated insulators: Projected sum rules and the role of quantum geometry
• Twistronics and moiré superlattice physics in 2D transition metal dichalcogenides
• Topological magnons and domain walls in twisted bilayer MoTe${}_2$
• Quantum Phases in Twisted Homobilayer Transition Metal Dichalcogenides
• Topological Order in Neural Wavefunctions
• Abelian and non-Abelian fractionalized states in twisted MoTe${}_2$: A generalized Landau-level theory
• Orbital Description of Landau Levels
• Instability of Laughlin FQH liquids into gapless power-law correlated states with continuous exponents in ideal Chern bands: rigorous results from plasma mapping
• Robustness of real-space topology in moiré systems
• Three-dimensional flat bands and possible interlayer triplet pairing superconductivity in the alternating twisted NbSe${}_2$ moiré bulk
• Relaxation and Its Effects on Electronic Structure in Twisted Systems: An Analytical Perspective