= Free-electron Fermi circle in a square lattice
{title2=$k_Fa=\sqrt{2\pi z}$}
For a two-dimensional <free electron gas> with two spin states and $z$ <electrons> per square cell of side $a$, counting occupied <wavevectors> gives $z/a^2=2\pi k_F^2/(2\pi)^2$. The square <first Brillouin zone> has half-width $\pi/a$. A monovalent circle lies inside its faces; a divalent circle crosses its faces but not its corners. A real <periodic potential> can deform and reconnect the crossings, as in <Fermi-surface reconstruction in a weak square potential>; valence alone is insufficient to prove insulation.
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