Fermi surfaces

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At zero temperature, a Fermi surface marks the boundary between occupied and empty electron states in momentum space. The wireframe marks the first Brillouin zone; colours distinguish bands. Calculation details and sources are available under About the data.

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Try the following comparisons:

1. Sodium: compare the surface with the sphere predicted by the free-electron model. How much does the direction of momentum matter?
2. Copper: look along \([111]\). Where does the surface meet the zone boundary? A surface crossing a zone face continues in the neighboring reciprocal cell.
3. Aluminium: switch the two bands on and off. Why can a metal have more than one Fermi-surface sheet?