Quantum Hall spin liquids and their possible realization in moiré systems

Abstract

Recently Chern insulators with Chern number $C=1$ and $C=2$ in zero (or very small) magnetic field have been observed in two moire graphene systems: twisted bilayer graphene and ABC trilayer graphene, both aligned with a hexagonal Boron-Nitride (h-BN) substrate. These Chern insulator states arise due to many body effects in the Chern bands of these systems when they are partially filled to a total integer filling ${\nu }_T=1,3$ (including spin and valley degrees of freedom). A simple possible explanation is from Hartree-Fock mean field theory which predicts valley and spin polarization in the zero bandwidth limit, similar to the "quantum Hall ferromagnetism" in Landau levels. Though valley polarization is implied by the existing experiments, the fate of the spin degree of freedom is not presently clear. In this paper we propose alternative valley polarized - but not spin polarized - candidates for the observed QAH effect. For a valley polarized spinful Chern band at filling ${\nu }_T=1$, we describe a class of exotic Chern insulator phases through spin-charge separation: charge is in a conventional Chern insulator phase with quantized Hall conductivity, while the spin forms disordered spin liquid phase with fractionalization, which we dub quantum Hall spin liquids. We construct a simple class of $Z_2$ quantum Hall spin liquid as analogs of the familiar $Z_2$ spin liquid through slave fermion-schwinger boson parton theory. Condensation of the spinon from the $Z_2$ quantum Hall spin liquid can lead to a quantum Hall antiferromagnet which is yet another, less exotic, candidate for the experimentally observed Chern insulator. We offer several experimental proposals to probe the quantum Hall spin liquid and the quantum Hall anti-ferromagnetic phases.

arXiv comment11 pages; 1 figure; v2: add discussions on doped case and experimental detection

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• Competing correlated states and abundant orbital magnetism in twisted monolayer-bilayer graphene
• Evidence of orbital ferromagnetism in twisted bilayer graphene aligned to hexagonal boron nitride
• Quantum Geometry and Stability of Moiré Flatband Ferromagnetism
• Twistronics in graphene-based van der Waals structures
• Quantum Hall Superconductivity from Moir{é} Landau Levels
• Deconfined Metal-Insulator Transitions in Quantum Hall Bilayers
• Designing spin-textured flat bands in twisted graphene multilayers via helimagnet encapsulation
• Tunable moire spinons in magnetically encapsulated twisted van der Waals quantum spin-liquids
• Electronic States and Anomalous Hall Effect in Strongly Correlated Topological Systems
• Topological states in strongly correlated systems
• Considerations for extracting moiré-level strain from dark field intensities in transmission electron microscopy
• Low-frequency and Moiré Floquet engineering: a review