A First-Landau-Level Laughlin/Jain Wave Function for the Fractional Quantum Hall Effect
Abstract
We show that the introduction of a more general closed-shell operator allows one to extend Laughlin's wave function to account for the richer hierarchies (1/3, 2/5, 3/7 ...; 1/5, 2/9, 3/13, ..., etc.) found experimentally. The construction identifies the special hierarchy states with condensates of correlated electron clusters. This clustering implies a single-particle (ls)j algebra within the first Landau level (LL) identical to that of multiply filled LLs in the integer quantum Hall effect. The end result is a simple generalized wave function that reproduces the results of both Laughlin and Jain, without reference to higher LLs or projection.
Keywords
Cite
@article{arxiv.cond-mat/9510133,
title = {A First-Landau-Level Laughlin/Jain Wave Function for the Fractional Quantum Hall Effect},
author = {Joe Ginocchio and Wick Haxton},
journal= {arXiv preprint arXiv:cond-mat/9510133},
year = {2009}
}
Comments
Revtex. In this replacement we show how to generate the Jain wave function explicitly, by acting with the generalized ls closed-shell operator discussed in the original version. We also walk the reader through a classical 1d caricature of this problem so that he/she can better understand why 2s+1, where s is the spin, should be associated with the number of electrons associated with the underlying clusters or composites. 11 pages