Intertwined fractional quantum anomalous Hall states and charge density waves

Abstract

Motivated by the recent experimental breakthrough on the observation of the fractional quantum anomalous Hall (FQAH) effects in semiconductor and graphene moiré materials, we explore the rich physics associated with the coexistence of FQAH effect and the charge density wave (CDW) order that spontaneously breaks the translation symmetry. We refer to a state with both properties as "FQAH-crystal". We show that the interplay between FQAH effect and CDW can lead to a rich phase diagram including multiple topological phases and topological quantum phase transitions at the same moiré filling. In particular, we demonstrate the possibility of direct quantum phase transitions from a FQAH-crystal with Hall conductivity ${\sigma }_H=-2/3$ to a trivial CDW insulator with ${\sigma }_H=0$, and more interestingly, to a QAH-crystal with ${\sigma }_H=-1$.

9 pages

References in corpus (22)

• 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
• Fractional Chern insulators in magic-angle twisted bilayer graphene
• Integer and fractional Chern insulators in twisted bilayer MoTe2
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2
• Fractional Chern Insulator in Twisted Bilayer MoTe${}_2$
• Fractional quantum anomalous Hall states in twisted bilayer MoTe${}_2$ and WSe${}_2$
• Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides
• Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe${}_2$
• Zero-field composite Fermi liquid in twisted semiconductor bilayers
• Pressure--enhanced fractional Chern insulators in moiré transition metal dichalcogenides along a magic line
• Topological Phases in AB-Stacked MoTe${}_2$/WSe${}_2$: ${\mathbb{Z}}_2$ Topological Insulators, Chern Insulators, and Topological Charge Density Waves
• Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers
• Interaction-driven topological phase diagram of twisted bilayer MoTe${}_2$
• Continuous transitions between composite Fermi liquid and Landau Fermi liquid: a route to fractionalized Mott insulators
• Giant proximity exchange and flat Chern band in 2D magnet-semiconductor heterostructures
• Deconfined criticalities and dualities between chiral spin liquid, topological superconductor and charge density wave Chern insulator

Cited by in corpus (22)

• Quantum anomalous Hall crystal at fractional filling of moiré superlattices
• Theory of Generalized Landau Levels and Implication for non-Abelian States
• Higher vortexability: zero field realization of higher Landau levels
• Contrasting twisted bilayer graphene and transition metal dichalcogenides for fractional Chern insulators: an emergent gauge picture
• Topological quantum phase transitions driven by a displacement field in the twisted MoTe2 bilayers
• Efficient prediction of superlattice and anomalous miniband topology from quantum geometry
• Single-particle spectral function of fractional quantum anomalous Hall states
• Layer-Dependent Quantum Anomalous Hall Effect in Rhombohedral Graphene
• From Fractional Quantum Anomalous Hall Smectics to Polar Smectic Metals: Nontrivial Interplay Between Electronic Liquid Crystal Order and Topological Order in Correlated Topological Flat Bands
• Quantum anomalous Hall crystals in moiré bands with higher Chern number
• Spectra of Magnetoroton and Chiral Graviton Modes of Fractional Chern Insulator
• Fractional Chern Insulator and Quantum Anomalous Hall Crystal in Twisted MoTe${}_2$
• Berry Phase Dynamics of Sliding Electron Crystals
• Twistronics and moiré superlattice physics in 2D transition metal dichalcogenides
• Topological magnons and domain walls in twisted bilayer MoTe${}_2$
• Quantum anomalous Hall effects and emergent $\mathrm{SU}(2)$ Hall ferromagnets at fractional filling of helical trilayer graphene
• Identifying Instabilities with Quantum Geometry in Flat Band Systems
• Free and Interacting Fermionic Conformal Field Theories on the Fuzzy Sphere
• Designing (higher) Hall crystals
• Generic integer and fractional quantum anomalous Hall crystals from interaction-driven band folding
• Continuous transition and gapless roton inside fractional quantum anomalous Hall states
• Topological Order Without Band Topology in Moiré Graphene