Speaker: Yahui Zhang (Johns Hopkins University) Title:Â Fractional quantum anomalous hall and Fractional quantum spin Hall effects in moire systems Abstract:Â I will introduce two separate works related to graphene based and TMD based moire Chern band systems. In the first part, I will briefly discuss our theory of the integer and fractional quantum anomalous Hall (QAH) states in ABC stacked multilayer graphene following the experiment on pentalayer graphene by Long Ju's group at MIT. In this system we found that moire potential is only a perturbation and a narrow C=1 Chern band is formed purely from spontaneous crystal formation driven by the interaction. In the second part, I will propose a new time reversal invariant state with fractional quantum spin Hall effect (FQSH) at filling n=1/2+1/2 of a C=1 band from one valley and C=-1 band from the other valley. Starting from the decoupled conjugate composite Fermi liquid (CFL), we argue that the inter-valley Coulomb interaction favors exciton pairing between composite fermions in the two valleys. This leads to a fractional insulator with charge gap, neutral Fermi surface and gapless spin excitations in the bulk, but helical charge edge mode and half FQSH effect. We dub the phase as vortex spin liquid as it can be viewed as a vortex liquid (or composite fermi liquid) of the neutral excitons (magnons). Interestingly the field theory has certain similarity to Son's Dirac theory of CFL at half filled Landau level. We propose that this novel state may be a potential explanation of the recent experiment by the Cornell's group in twisted MoTe2 at around 2.1 degree. This suggests a new platform to look for quantum spin liquid enriched by charge edge modes.