Nature of quasiparticle excitations in the fractional quantum Hall effect

Composite fermions in a partially filled quasi-Landau level may be viewed as quasielectrons of the underlying fractional quantum Hall state, suggesting that a quasielectron is simply a dressed electron, as often is true in other interacting electron systems, and as a result has the same intrinsic charge and exchange statistics as an electron. This paper discusses how this result is reconciled with the earlier picture in which quasiparticles are viewed as fractionally-charged ...

A novel hierarchy of fractional quantum Hall (FQH) states in the lowest Landau level (LL) is proposed to explain recently observed FQH fractions such as nu=5/13, 3/8, or 4/11. Based on the analysis of their interaction pseudopotentials, it is argued that the Laughlin quasiparticles (particles/holes in a partially filled composite fermion LL) form pairs. These pairs are proposed to have Laughlin correlations with one another and to form condensed states at a sequence of fracti...

Motivated by the quasiparticle wavefunction in the composite fermion (CF) theory for fractional quantum Hall filling factor $\nu = 1/m$, I consider a suitable quasiparticle operator in differential form, as a modified form of Laughlin's quasiparticle operator, that reproduces quasiparticle wave function as predicted in the CF theory. I further consider the conjugate of this operator as quasihole operator for obtaining a novel quasihole wave function for $1/m$ state. Each of t...

We give a brief introduction to the phenomenon of the Fractional Quantum Hall effect, whose discovery was awarded the Nobel prize in 1998. We also explain the composite fermion picture which describes the fractional quantum Hall effect as the integer quantum Hall effect of composite fermions.

Phonon excitations of fractional quantum Hall states at filling factors nu = 1/3, 2/5, 4/7, 3/5, 4/3, and 5/3 are experimentally shown to be based on Landau level transitions of Composite Fermions. At filling factor nu = 2/3, however, a linear field dependence of the excitation energy in the high-field regime rather hints towards a spin transition excited by the phonons. We propose to explain this surprising observation by an only partially polarized 2/3-ground-state making t...

We review the recently proposed Dirac composite fermion theory of the half-filled Landau level. This paper is based on a talk given at the Nambu Symposium at University of Chicago, March 11-13, 2016.

The energy spectra and wavefunctions of up to 14 interacting quasielectrons (QE's) in the Laughlin nu=1/3 fractional quantum Hall (FQH) state are investigated using exact numerical diagonalization. It is shown that at sufficiently high density the QE's form pairs or larger clusters. This behavior, opposite to Laughlin correlations, invalidates the (sometimes invoked) reapplication of the composite fermion picture to the individual QE's. The series of finite-size incompressibl...

We review the recently proposed Dirac composite fermion theory of the half-filled Landau level.

In this work, two quasiparticle excitation energies per particle are calculated analytically for systems with up to $N = 7$ electrons in both Laughlin and composite fermions (CF) theories by considering the full jellium potential which consists of three parts, the electron-electron, electron-background, and background-background Coulomb interactions. The exact results we have obtained confirm the fact that the CF-wavefunction for two quasiparticles has lower energy than Laugh...

We construct model wavefunctions for a family of single-quasielectron states supported by the $\nu=1/3$ fractional quantum Hall (FQH) fluid. The charge $e^*$ = $e/3$ quasielectron state is identified as a composite of a charge-$2e^*$ quasiparticle and a $-e^*$ quasihole, orbiting around their common center of charge with relative angular momentum $n\hbar > 0$, and corresponds precisely to the "composite fermion" construction based on a filled $n=0$ Landau level plus an extra ...