Quantum Hall spin liquids and their possible realization in moiré systems

Abstract

Recently, Chern insulators with Chern numbers $C=1$ and 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 ${\ensuremath{\nu}}_{T}=1,3$ (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 ${\ensuremath{\nu}}_{T}=1$, 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 antiferromagnetic phases. We briefly comment on the generalization to the filling ${\ensuremath{\nu}}_{T}=2$ and propose possible quantum valley Hall spin liquid without full spin polarization. Finally, we also propose another class of QHSL using fermionic spinons, including phases supporting non-Abelian anyons.