Cooper instability of composite fermions

Abstract

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 ‘composite 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.