Fermi surface

The boundary in a material’s momentum space between occupied and unoccupied electron states at absolute zero. Its shape reflects the material’s electronic structure and influences its electrical, thermal, and magnetic behavior.

Fermi energy: The energy of the highest occupied electron state at absolute zero. The Fermi surface consists of states at this energy.
Fermi–Dirac statistics: The quantum statistics governing populations of indistinguishable fermions. At zero temperature, its occupation rule creates the sharp boundary in electron-state occupancy.
Angle-resolved photoemission spectroscopy: An experimental technique that measures electron energy and momentum by detecting photoemitted electrons. It maps occupied electronic states and can directly trace Fermi-surface contours.
Fermi sea: The collection of occupied electron states below the Fermi energy at zero temperature. The sea is the filled region; the Fermi surface is its boundary.
Band structure: The allowed electron energies in a solid as functions of crystal momentum. Its energy bands determine where the Fermi energy cuts through momentum space.
Bloch's theorem: A result stating that electrons in a periodic crystal potential have wavefunctions with a characteristic periodic form. It makes crystal momentum a useful label for electronic states in a solid.
De Haas–van Alphen effect: The oscillation of a material's magnetization as an applied magnetic field changes. Its oscillation frequencies reveal extremal cross-sections of the Fermi surface.
Fermi level: The electron chemical potential, commonly used to describe the energy level governing occupancy. It is an energy, whereas the Fermi surface is a set of momenta.
Brillouin zone: A primitive cell in the reciprocal lattice that represents distinct crystal momenta. Fermi surfaces are commonly mapped within this momentum-space cell.
Reciprocal lattice: The lattice of wavevectors associated with a crystal's periodic structure. It provides the momentum-space framework in which crystal Fermi surfaces are described.

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