0 Cooper Instability of Composite Fermions

When confined to two dimensions and exposed to a strong magnetic field, electrons screen the Coulomb interaction in a topological fashion; they capture and even number of quantum vortices and transform into particles called 'com-posite fermions' [1–3]. The fractional quantum Hall effect [4] 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 sea [5–8]. But for ν = 5/2, a fractional quantum Hall effect is observed instead [9,10]; this unexpected result is the subject of considerable debate and controversy [11]. 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. The most important property of composite fermions is that they do not experience the external magnetic field B but rather a drastically reduced magnetic field B * = B − 2pρφ 0. Here ρ is the two-dimensional density of fermions, 2p is the number of vortices, carried by the composite fermion, often intuitively envisioned as 2p flux quanta, and φ 0 = h/e is a flux quantum. In effect, each electron absorbs 2p flux quanta of the external field to turn into a composite fermion. Electrons confined in two dimensions have unusual properties