Composite Fermions and Parton Wavefunctions in Graphene van der Waals Heterostructures*

In a graphene-hexagonal Boron nitride (hBN) heterostructure, the presence of the hBN layer can lead to a gap and the breaking of the symmetry between carbon sublattices, with multicomponent fractional quantum Hall effect (FQHE) due to the electrons’ correlation. We report on the FQHE at filling factors ν = η/3 with ν > 1, and on the composite fermions (CFs) at in the ν < 1 lowest landau Level ν = 4/5, 5/7 and 2/3, which belong to the series of integral quantum Hall effect (IQHE) of CF electrons at ν = p/(2mp ± 1) and ν = 1- p/(2mp ± 1) for CF holes, where 2m is the number of magnetic flux quanta attached to the CF, or vorticity. Here we focus on the ν = 2/3 fraction and his description with a partons’ wave function; in this model the electron is broken down into sub-particles, the partons, each one residing in an IQHE state, fictitious particles that glued back together recover the physical electrons.