Contrasting twisted bilayer graphene and transition metal dichalcogenides for fractional Chern insulators: an emergent gauge picture

Abstract

The recent experimental discovery of the zero-field fractional Chern insulator (FCI) in twisted $\mathrm{MoT}{\mathrm{e}}_2$ moiré superlattices has sparked immense interest in this exotic topological quantum state. The FCI has also been observed in previous experiments in magic angle twisted bilayer graphene (TBG) under a finite magnetic field of about 5 Tesla. Generally, the stabilization of FCI requires fine-tuning the topological band to satisfy certain conditions. It would still be helpful to have an intuitive picture to understand the different behaviors in twisted $\mathrm{MoT}{\mathrm{e}}_2$ and TBG. Here, we compare them through the lens of emergent gauge fields. In TBG, the system can be mapped to two Dirac fermions coupled to emergent gauge fields with opposite signs. In contrast, the twisted $\mathrm{MoT}{\mathrm{e}}_2$ reduces to a hole with parabolic dispersion coupled to an emergent gauge field. This contrasting gauge structure provides a new perspective on the observed difference: the zero-field FCI is stable in $\mathrm{MoT}{\mathrm{e}}_2$ but absent in TBG. Based on this understanding, we will explore potential strategies for stabilizing FCI in both moiré superlattices.

References in corpus (35)

• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
• Observation of Fractionally Quantized Anomalous Hall Effect
• Fractional quantum Hall effect in the absence of Landau levels
• Quantum anomalous Hall effect from intertwined moiré bands
• Fractional Chern insulators in magic-angle twisted bilayer graphene
• Integer and fractional Chern insulators in twisted bilayer MoTe2
• Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2
• Exact Landau Level Description of Geometry and Interaction in a Flatband
• Fractional Chern Insulator in Twisted Bilayer MoTe${}_2$
• Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides
• Spin-orbit driven ferromagnetism at half moiré filling in magic-angle twisted bilayer graphene
• Twist-angle dependence of the proximity spin-orbit coupling in graphene on transition-metal dichalcogenides
• Vortexability: A Unifying Criterion for Ideal Fractional Chern Insulators
• Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe${}_2$
• Interplay of Fractional Chern Insulator and Charge-Density-Wave Phases in Twisted Bilayer Graphene
• Magic Angles and Fractional Chern Insulators in Twisted Homobilayer TMDs
• Zero-field composite Fermi liquid in twisted semiconductor bilayers
• Topological and stacked flat bands in bilayer graphene with a superlattice potential
• Polarization-driven band topology evolution in twisted MoTe${}_2$ and WSe${}_2$
• Pressure--enhanced fractional Chern insulators in moiré transition metal dichalcogenides along a magic line
• Adiabatic continuity between Hofstadter and Chern insulator states
• Ideal Chern bands are Landau levels in curved space
• Theory of tunable flux lattices in the homobilayer moiré of twisted and uniformly strained transition metal dichalcogenides
• Topological exact flat bands in two dimensional materials under periodic strain
• Chiral limit and origin of topological flat bands in twisted transition metal dichalcogenide homobilayers
• Giant proximity exchange and flat Chern band in 2D magnet-semiconductor heterostructures
• Massive Dirac fermions in moiré superlattices: a route towards topological flat minibands
• Intertwined fractional quantum anomalous Hall states and charge density waves
• Nearly flat Chern band in periodically strained monolayer and bilayer graphene
• Stability of fractional Chern insulators with a non-Landau level continuum limit
• Twisted-bilayer FeSe and the Fe-based superlattices
• Double and Quadruple Flat Bands tuned by Alternative magnetic Fluxes in Twisted Bilayer Graphene

Cited by in corpus (12)

• Adiabatic Approximation and Aharonov-Casher Bands in Twisted Homobilayer TMDs
• Higher vortexability: zero field realization of higher Landau levels
• Experimental signature of layer skyrmions and implications for band topology in twisted WSe2 bilayers
• Quantum-metric-induced quantum Hall conductance inversion and reentrant transition in fractional Chern insulators
• Chiral superconductivity from spin polarized Chern band in twisted MoTe${}_2$
• Edge-driven transition between extended quantum anomalous Hall crystal and fractional Chern insulator in rhombohedral graphene multilayers
• Twistronics and moiré superlattice physics in 2D transition metal dichalcogenides
• Topologically protected flatness in chiral moiré heterostructures
• Fractional Chern insulator candidate in twisted bilayer checkboard lattice
• Multi-Band Exact Diagonalization and an Iteration Approach to Hunt For Fractional Chern Insulators in Rhombohedral Multilayer Graphene
• Anisotropic moiré band flattening in twisted bilayers of M-valley MXenes
• Mean-field Modelling of Moiré Materials: A User's Guide with Selected Applications to Twisted Bilayer Graphene