Composite fermion

An emergent description of correlated electrons in which an even number of statistical flux quanta is attached to each electron. The resulting effective field can turn selected fractional electronic fillings into integer effective fillings. Flux attachment encodes correlations; it is not attachment of literal external magnetic solenoids to individual electrons.

Attach two statistical flux quanta ${\Phi }_0=h/e$ per electron at density $n_s$. For $B>0$, $B^{\ast }=B-2n_s{\Phi }_0=B(1-2\nu )$ and the signed effective filling is ${\nu }^{\ast }=n_s{\Phi }_0/B^{\ast }=\nu /(1-2\nu )$. Inversion gives $\nu ={\nu }^{\ast }/(2{\nu }^{\ast }+1)$. Integer ${\nu }^{\ast }=p$ gives $p/(2p+1)$, while ${\nu }^{\ast }=-p$ gives $p/(2p-1)$. Using nonnegative effective filling instead requires explicitly tracking the effective-field sign. At half filling the mean effective field vanishes.

A family of fractional quantum Hall effect fillings obtained by attaching $2p$ flux quanta and filling $q$ effective Landau levels of composite fermions. Positive integers $p,q$ and the relative effective-field direction specify the branch.