Composite Fermions & FQHE — Jain's Construction

In the fractional quantum Hall effect, electrons capture magnetic flux quanta to form composite fermions (CF). Jain's 1989 theory maps FQHE of electrons at filling ν = p/(2p±1) to the integer QHE of composite fermions, explaining the hierarchy of fractional plateaux.

Filling ν (tune B-field) 1/3

Flux quanta attached 2

Disorder Γ 0.05

Filling ν

1/3

CF filling ν*

σ_xy (e²/h)

—

Jain plateau?

Yes

ν = p/(2p+1) ; CF filling ν* = p (IQHE of CFs) ; σ_xy = ν · e²/h — Laughlin, Jain 1989