Nature of quasiparticle excitations in the fractional quantum Hall effect

The mean field (MF) composite Fermion (CF) picture successfully predicts low lying states of fractional quantum Hall systems. This success cannot be attributed to a cancellation between Coulomb and Chern-Simons interactions beyond the mean field and solely depends on the short range (SR) of the Coulomb pseudopotential in the lowest Landau level (LL). The class of pseudopotentials for which the MFCF picture can be applied is defined. The success or failure of the MFCF picture ...

The current state of the theory of the Fractional Quantum Hall Effect is critically analyzed, especially the generally accepted concept of composite fermions. It is argued that there is no sound theoretical foundation for this concept. A simple one-dimensional model is proposed, which presumably has an energy spectrum similar to that of the FQHE system.

The excitations of the 7/3 fractional Hall state, one of the most prominent states in the second Landau level, are not understood. We study the effect of screening by composite fermion excitons and find that it causes a strong renormalization at 7/3, thanks to a relatively small exciton gap and a relatively large residual interaction between composite fermions. The excitations of the 7/3 state are to be viewed as composite fermions dressed by a large exciton cloud. Their wide...

We show that the excitation spectrum of interacting electrons at filling factor $\nu=\nu^*/(2\nu^*+1)$ is well described in terms of non-interacting composite fermions at filling factor $\nu^*$, but does not have a one-to-one correspondence with the excitation spectrum of non-interacting electrons at $\nu^*$. In particular, the collective modes of the fractional quantum Hall states are not analogous to those of the integer quantum Hall states. We also speculate on the nature ...

The low-energy excitations of filled Landau levels (LL's) of electrons involve promotion of a single electron from the topmost filled LL to the lowest empty LL. These are called excitons or collective modes. The incompressible fractional quantum Hall states are understood as filled LL's of composite fermions, and the low-energy neutral excitations are excitons of composite fermions. New techniques are developed to study large systems, which provide detailed information about ...

The low energy neutral excitations of incompressible fractional quantum Hall states are called collective modes or magnetic excitons. This work develops techniques for computing their dispersion at general filling fractions for reasonably large systems. New structure is revealed; in particular, the collective mode at 1/3 is found to possess several minima, with the energy of the principal minimum significantly smaller than the earlier estimate. \pacs{73.40.Hm, 73.20.Dx, 73.20...

New trial wave functions corresponding to half filling quantum Hall states are proposed. These wave functions are constructed by first pairing up the quasielectrons of the 1/3 Laughlin quantum Hall state, with the same relative angular momentum for each pair, and then making the paired quasielectrons condense into a 1/4 Laughlin state. The quasiparticle excitations of the proposed wave functions carry $\pm1/4$ of electron charge, and obey Abelian fractional statistics. In the...

We report the observation of a new fractional quantum Hall state in the second Landau level of a two-dimensional electron gas at the Landau level filling factor $\nu=2+6/13$. We find that the model of noninteracting composite fermions can explain the magnitude of gaps of the prominent 2+1/3 and 2+2/3 states. The same model fails, however, to account for the gaps of the 2+2/5 and the newly observed 2+6/13 states suggesting that these two states are of exotic origin.omposite fe...

In this paper we study fractional quantum Hall composite fermion wavefunctions at filling fractions \nu = 2/3, 3/5, and 4/7. At each of these filling fractions, there are several possible wavefunctions with different spin polarizations, depending on how many spin-up or spin-down composite fermion Landau levels are occupied. We calculate the energy of the possible composite fermion wavefunctions and we predict transitions between ground states of different spin polarizations a...

The fractional quantum Hall effect was experimentally discovered in 1982. It was observed that the Hall conductivity $\sigma_{yx}$ of a two-dimensional electron system is quantized, $\sigma_{yx}=e^2/3h$, in the vicinity of the Landau level filling factor $\nu=1/3$. In 1983, Laughlin proposed a trial many-body wave function, which he claimed described a ``new state of matter'' -- a homogeneous incompressible liquid with fractionally charged quasiparticles. Here I develop an ex...