Composite fermions and parton wavefunctions in twisted graphene on hexagonal boron nitride

In a twisted graphene on hexagonal boron nitride, the presence of a gap and the breaking of the symmetry between carbon sublattices lead to multicomponent fractional quantum Hall effect (FQHE) due to the electrons' correlation. Here we report on the FQHE at filling factors nu = k/2 and nu = k/3 with nu > 1, and on the composite fermions at in the nu < 1 lowest Landau level nu = 4/5, 5/7 and 2/3. These fractional states can be described with a partons model, in which the electron is broken down into sub-particles each one residing in an integer quantum Hall effect state; partons are fictitious particles that, glued back together, recover the physical electrons. The parton states host exotic anyons that could potentially form building blocks of a fault-tolerant topological quantum computer.