Abstract
When confined to two dimensions and exposed to a strong magnetic field, electrons screen the Coulomb interaction in a topological fashion; they capture an even number of quantum vortices and transform into particles called ‘composite fermions’ (refs 1,2,3). The fractional quantum Hall effect4 occurs in such a system when the ratio (or ‘filling factor’, ν) of the number of electrons and the degeneracy of their spin-split energy states (the Landau levels) takes on particular values. The Landau level filling ν = 1/2 corresponds to a metallic state in which the composite fermions form a gapless Fermi sea5,6,7,8. But for ν = 5/2, a fractional quantum Hall effect is observed instead9,10; this unexpected result is the subject of considerable debate and controversy11. Here we investigate the difference between these states by considering the theoretical problem of two composite fermions on top of a fully polarized Fermi sea of composite fermions. We find that they undergo Cooper pairing to form a p-wave bound state at ν = 5/2, but not at ν = 1/2. In effect, the repulsive Coulomb interaction between electrons is overscreened in the ν = 5/2 state by the formation of composite fermions, resulting in a weak, attractive interaction.
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Acknowledgements
This work was supported in part by the National Science Foundation. We thank the Numerically Intensive Computing Group led by V. Agarwala, J. Holmes and J. Nucciarone, at the Penn State University CAC, for assistance and computing time with the LION-X cluster.
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Scarola, V., Park, K. & Jain, J. Cooper instability of composite fermions. Nature 406, 863–865 (2000). https://doi.org/10.1038/35022524
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DOI: https://doi.org/10.1038/35022524
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