Hamiltonian Description of Composite Fermions: Magnetoexciton Dispersions

TL;DR

This paper uses a microscopic Hamiltonian approach to compute magnetoexciton dispersions in fractional quantum Hall states, showing good agreement with numerical data and analyzing effects of sample thickness on stability.

Contribution

It extends the fermionic Chern-Simons formalism to calculate magnetoexciton dispersions and stability in various fractional quantum Hall states, including new insights on the 2/5 state.

Findings

Approximate agreement with numerical magnetoexciton dispersions.

Identified instability thresholds as a function of sample thickness.

Showed the 2/5 state cannot be modeled as a simple quantum ferromagnet.

Abstract

A microscopic Hamiltonian theory of the FQHE, developed by Shankar and myself based on the fermionic Chern-Simons approach, has recently been quite successful in calculating gaps in Fractional Quantum Hall states, and in predicting approximate scaling relations between the gaps of different fractions. I now apply this formalism towards computing magnetoexciton dispersions (including spin-flip dispersions) in the $\nu=1/3$, 2/5, and 3/7 gapped fractions, and find approximate agreement with numerical results. I also analyse the evolution of these dispersions with increasing sample thickness, modelled by a potential soft at high momenta. New results are obtained for instabilities as a function of thickness for 2/5 and 3/7, and it is shown that the spin-polarized 2/5 state, in contrast to the spin-polarized 1/3 state, cannot be described as a simple quantum ferromagnet.