= Rectangular-lattice Fermi-surface reconstruction
Consider a spin-degenerate two-dimensional <free electron model> with rectangular periods $a>b$ and two <Electrons> per <unit cell>. Write $K=\pi/a$, $L=\pi/b$, and $k_F^2=4\pi/(ab)$. If $K<k_F<L$, the circular <Fermi contour> crosses only the vertical boundaries of the first <Brillouin zone>. Folding translates its protruding caps back by a <reciprocal lattice> vector $(2K,0)$. A weak <periodic potential> mixes the intersecting <plane waves>, reconnecting the contours into two open first-band sheets and a closed second-band pocket. The pocket is centred on a zone boundary: its halves on opposite sides of a reduced-zone plot are identified periodically and belong to one closed sheet.
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