A First-Landau-Level Laughlin/Jain Wave Function for the Fractional Quantum Hall Effect

TL;DR

This paper introduces a generalized wave function for the fractional quantum Hall effect that captures hierarchical states through correlated electron clusters, aligning with Laughlin and Jain results without needing higher Landau levels.

Contribution

It develops a new wave function using a closed-shell operator to describe hierarchy states directly within the first Landau level.

Findings

Reproduces Laughlin and Jain wave functions

Accounts for experimentally observed hierarchy states

Eliminates the need for higher Landau level projections

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.