Parton description of non-Abelian paired states*

The fractional quantum Hall effect (FQHE) forms a paradigm in our understanding of strongly correlated systems. FQHE in the lowest Landau level (LLL) predominantly occurs at odd-denominator fillings and can be understood in terms of weakly interacting composite fermions, which are bound states of electrons and vortices. In the second LL (SLL), FQHE has been observed at even-denominator fillings such as 5/2 and 2+3/8 and a description of these states lies beyond the purview of non-interacting composite fermions. In this talk, I will demonstrate that these states can be understood using the "parton" theory which generalizes the idea of composite fermion. In particular, I will elucidate our recent work on the parton construction of wave functions to describe non-Abelian paired states that potentially capture the underlying physical mechanism for the FQHE observed in the SLL [1,2], at 1/4 in wide quantum wells of GaAs [3] and at 1/2 in the third LL of monolayer graphene [4]. More generally, our work suggests that the parton theory provides a unified description of the quantum Hall effects [5].