Fermi surface
Materials with complex crystal structures can have quite intricate Fermi surfaces. The figure 2 illustrates the anisotropic Fermi surface of graphite, which has both electron and hole pockets in its Fermi surface due to multiple bands crossing the Fermi energy along the formula_20 direction. Often in a metal the Fermi surface radius formula_17 is larger than the size of the first Brillouin zone which results in a portion of the Fermi surface lying in the second (or higher) zones. As with the band structure itself, the Fermi surface can be displayed in an extended-zone scheme where formula_22 is allowed to have arbitrarily large values or a reduced-zone scheme where wavevectors are shown modulo formula_23 (in the 1-dimensional case) where a is the lattice constant. In the three-dimensional case the reduced zone scheme means that from any wavevector formula_22 there is an appropriate number of reciprocal lattice vectors formula_25 subtracted that the new formula_22 now is closer to the origin in formula_22-space than to any formula_25. Solids with a large density of states at the Fermi level become unstable at low temperatures and tend to form ground states where the condensation energy comes from opening a gap at the Fermi surface. Examples of such ground states are superconductors, ferromagnets, Jahn–Teller distortions and spin density waves.