Hamiltonian theory of the fractional quantum Hall effect: Effect of Landau level mixing

Abstract

We derive an effective hamiltonian in the Lowest Landau Level (LLL) that incorporates the effects of Landau-level mixing to all higher Landau levels to leading order in the ratio of interaction energy to the cyclotron energy, κ = (e 2 /εl)/ωc. We then transcribe the hamiltonian to the composite fermion basis using our hamiltonian approach and compute the effect of LL mixing on transport gaps. 73.50.Jt,

Noncommutativity Parameter and Composite Fermions

“…For many speculations about this approach and related matters, one can see the author's original work [6].…”

“…is exactly the quantity c 2 defined recently by Murthy and Shankar [6] to formulate a Hamiltonian for the FQHE in the CF basis. Then, we can write the above relation as…”

“…In this subsection, we are going to review shortly the recent development of Murthy and Shankar [6] for the FQHE. Indeed, the authors considered a CF Hilbert space, where each fermion is described by a coordinate r and momentum p, by constructing the following opera-…”

“…Now we would like to make contact with the Murthy-Shankar c 2 parameter [6], which is related to the CF theory.…”

“…Indeed, Jain's idea is to explain the FQHE in terms of the integer quantum Hall effect (IQHE) by using the attached flux notion where each electron is assumed to be surrounded by an integer number of flux. Subsequently, by constructing a velocity operator in terms of the standard operator momentum and weakened vector potential, Murthy and Shankar [6,7] proposed a Hamiltonian formalism for the FQHE mapped in terms of the CF degrees of freedom.…”