Filling factor (quantum Hall effect, ${\nu }_f=n_{s}h/(eB)$)

For a two-dimensional electron gas in a perpendicular magnetic field of magnitude $B>0$, the filling factor is the Electron number per unit area $n_s$ divided by the orbital degeneracy per unit area $eB/h$ of one spin branch of a Landau level. Here $e$ is the positive elementary charge and $h$ the Planck constant. The nominal filling factor varies continuously with $n_s/B$; it need not be an integer.

One resolved spin branch of a two-dimensional Landau level has degeneracy $eB/h$ per area. Thus the total carrier density is $n_s=\nu eB/h$, where the filling factor $\nu$ counts all occupied spin and other internal branches, including partial filling. If consecutive unsplit orbital peaks change filling by an unresolved degeneracy $g_d$,For only spin degeneracy, $g_d=2$. Once spin splitting is resolved, adjacent individual branches differ by one rather than two; counting split subpeaks as unsplit orbital peaks gives a factor-two error.