Fractional Quantum Hall States in Graphene

TL;DR

This paper investigates the fractional quantum Hall effect in graphene by extending Laughlin and composite fermion theories to Dirac particles, revealing how interactions can be generated via gauge transformations.

Contribution

It generalizes Laughlin and composite fermion wavefunctions to Dirac fermions in graphene, connecting free and interacting Hamiltonians through gauge transformations.

Findings

Generalized Laughlin potential for graphene

Realized composite fermion filling factors in graphene

Linked free and interacting Dirac operators via gauge transformation

Abstract

We quantum mechanically analyze the fractional quantum Hall effect in graphene. This will be done by building the corresponding states in terms of a potential governing the interactions and discussing other issues. More precisely, we consider a system of particles in the presence of an external magnetic field and take into account of a specific interaction that captures the basic features of the Laughlin series \nu={1\over 2l+1}. We show that how its Laughlin potential can be generalized to deal with the composite fermions in graphene. To give a concrete example, we consider the SU(N) wavefunctions and give a realization of the composite fermion filling factor. All these results will be obtained by generalizing the mapping between the Pauli--Schr\"odinger and Dirac Hamiltonian's to the interacting particle case. Meantime by making use of a gauge transformation, we establish a relation between the free and interacting Dirac operators. This shows that the involved interaction can actually be generated from a singular gauge transformation.