Excitonic fractional quantum Hall hierarchy in Moiré heterostructures

Abstract

We consider fractional quantum Hall states in systems where two flat Chern number $C=\pm 1$ bands are labeled by an approximately conserved 'valley' index and interchanged by time reversal symmetry. At filling factor $\nu =1$ this setting admits an unusual hierarchy of correlated phases of excitons, neutral particle-hole pair excitations of a fully valley-polarized `orbital ferromagnet' parent state where all electrons occupy a single valley. Excitons experience an effective magnetic field due to the Chern numbers of the underlying bands. This obstructs their condensation in favor of a variety of crystalline orders and gapped and gapless liquid states. All these have the same quantized charge Hall response and are electrically incompressible, but differ in their edge structure, orbital magnetization, and hence valley and thermal responses. We explore the relevance of this scenario for Moiré heterostructures of bilayer graphene on a hexagonal boron nitride substrate.

5+4 pages, 1+3 figures

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• Hybrid Wannier Chern bands in magic angle twisted bilayer graphene and the quantized anomalous Hall effect
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Cited by in corpus (12)

• Topological Lattice Models with Constant Berry Curvature
• Quantum-metric-enabled exciton condensate in double twisted bilayer graphene
• Halperin States of Particles and Holes in Ideal Time Reversal Invariant Pairs of Chern Bands and The Fractional Quantum Spin Hall Effect in Moiré MoTe${}_2$
• Kekulé spiral order at all nonzero integer fillings in twisted bilayer graphene
• Excitons in the Fractional Quantum Hall Effect
• Long-lived Topological Flatband Excitons in Semiconductor Moiré Heterostructures: a Bosonic Kane-Mele Model Platform
• Non-Abelian spin Hall insulator
• Textured Exciton Insulators
• Continuous phase transitions between fractional quantum Hall states and symmetry-protected topological states
• Variational wavefunctions for fractional topological insulators
• Exciton fractional Chern insulators in moiré heterostructures
• Tuning between a fractional topological insulator and competing phases at ${\nu }_{\mathrm{T}}=2/3$