Fermi-energy oscillations in a two-dimensional electron gas ($\Delta (1/B)=e/(n_{s}h)$)

At fixed sheet density $n_s$, each resolved Landau level gains degeneracy $eB/h$ per unit area as the magnetic field grows. A partly filled ideal level has chemical potential at its energy; when it empties into lower levels, the chemical potential drops. This produces an inverse-field-periodic sawtooth in the clean zero-temperature model. At fixed field and increasing density the corresponding chemical potential is an upward staircase with density increment $eB/h$. Fixed reservoir chemical potential is a different boundary condition, in which the density responds instead. spin counting, disorder and temperature qualify these ideal pictures.