Non-coplanar magnetism, topological density wave order and emergent symmetry at half-integer filling of moiré Chern bands

Abstract

Twisted double- and mono-bilayer graphene are graphene-based moiré materials hosting strongly correlated fermions in a gate-tunable conduction band with a topologically non-trivial character. Using unbiased exact diagonalization complemented by unrestricted Hartree-Fock calculations, we find that the strong electron-electron interactions lead to a non-coplanar magnetic state, which has the same symmetries as the tetrahedral antiferromagnet on the triangular lattice and can be thought of as a skyrmion lattice commensurate with the moiré scale, competing with a set of ferromagnetic, topological charge density waves featuring an approximate emergent O(3) symmetry, "rotating" the different charge density wave states into each other. Direct comparison with exact diagonalization reveals that the ordered phases are accurately described within the unrestricted Hartree-Fock approximation. Exhibiting a finite charge gap and Chern number $|C|=1$, the formation of charge density wave order which is intimately connected to a skyrmion lattice phase is consistent with recent experiments on these systems.

35 pages, 12 figures

References in corpus (13)

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• Spontaneous time-reversal symmetry breaking in twisted double bilayer graphene
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Cited by in corpus (12)

• Origin of Model Fractional Chern Insulators in All Topological Ideal Flatbands: Explicit Color-entangled Wavefunction and Exact Density Algebra
• Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers
• Quantum anomalous Hall crystal at fractional filling of moiré superlattices
• Electron spin resonance and collective excitations in magic-angle twisted bilayer graphene
• Helical trilayer graphene: a moiré platform for strongly-interacting topological bands
• Machine Learning Microscopic Form of Nematic Order in twisted double-bilayer graphene
• Non-Abelian Fractional Chern Insulators and Competing States in Flat Moiré Bands
• A Novel Perspective on Ideal Chern Bands with Strong Short-Range Repulsion: Applications to Correlated Metals, Superconductivity, and Topological Order
• Quantum anomalous Hall effects and emergent $\mathrm{SU}(2)$ Hall ferromagnets at fractional filling of helical trilayer graphene
• Electronic structure and transport in materials with flat bands: 2D materials and quasicrystals
• Displacement-field-tunable superconductivity in an inversion-symmetric twisted van der Waals heterostructure
• Higher Chern bands in helical homotrilayer transition metal dichalcogenides