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

Joe Ginocchio·Wick Haxton
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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.

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Joe Ginocchio, Wick Haxton. 1996-04-11. A First-Landau-Level Laughlin/Jain Wave Function for the Fractional Quantum Hall Effect. https://doi.org/10.1103/physrevlett.77.1568

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