Nonfoliated fractonic three-dimensional fractional quantum Hall states in infinite helical large-angle twisted transition metal dichalcogenides

We theoretically demonstrate that three-dimensional interlayer-coherent fractional quantum Hall states hosting anyons with irrational statistics and fractional charge can emerge in helical large-angle twisted infinite-layer transition metal dichalcogenides under experimentally accessible magnetic fields. The formation of these exotic states relies critically on strong interlayer Coulomb interactions due to the atomic separataion between the layers and the suppression of interlayer tunneling due to the large-angle twist, which together establish a promising platform for realizing the topological orders. Using Monte Carlo simulations, we compare the energies of various candidate fractional quantum Hall states and crystalline phases, revealing a rich landscape of interlayer-coherent quantum Hall phases as functions of electron density and magnetic field. At low carrier densities and in weak magnetic field, the system hosts irrational anyonic phases characterized by nontrivial braiding statistics. More broadly, two-dimensional materials such as TMDs offer a versatile avenue for engineering such novel three-dimensional quantum phenomena through stacking and twisting.