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In condensed matter physics, the Fermi surface is the surface in reciprocal space which separates occupied electron states from unoccupied electron states at zero temperature. [1] The shape of the Fermi surface is derived from the periodicity and symmetry of the crystalline lattice and from the occupation of electronic energy bands .
The periodicity of these oscillations can be measured, and in turn can be used to determine the cross-sectional area of the Fermi surface. [8] If the axis of the magnetic field is varied at constant magnitude, similar oscillations are observed. The oscillations occur whenever the Landau orbits touch the Fermi surface.
The Fermi level does not necessarily correspond to an actual energy level (in an insulator the Fermi level lies in the band gap), nor does it require the existence of a band structure. Nonetheless, the Fermi level is a precisely defined thermodynamic quantity, and differences in Fermi level can be measured simply with a voltmeter.
Luttinger's theorem states that the volume enclosed by a material's Fermi surface is directly proportional to the particle density.. While the theorem is an immediate result of the Pauli exclusion principle in the case of noninteracting particles, it remains true even as interactions between particles are taken into consideration provided that the appropriate definitions of Fermi surface and ...
The area in momentum space that remains ungapped is called the Fermi arc. [2] Fermi arcs also appear in some materials with topological properties such as Weyl semimetals where they represent a surface projection of a two dimensional Fermi contour and are terminated onto the projections of the Weyl fermion nodes on the surface.
The Fermi momentum can also be described as =, where = /, called the Fermi wavevector, is the radius of the Fermi sphere. [ 4 ] n {\displaystyle n} is the electron density. These quantities may not be well-defined in cases where the Fermi surface is non-spherical.
Within the Brillouin zone, a constant-energy surface represents the loci of all the -points (that is, all the electron momentum values) that have the same energy. Fermi surface is a special constant-energy surface that separates the unfilled orbitals from the filled ones at zero kelvin.
The Fermi energy surface in reciprocal space is known as the Fermi surface. The nearly free electron model adapts the Fermi gas model to consider the crystal structure of metals and semiconductors , where electrons in a crystal lattice are substituted by Bloch electrons with a corresponding crystal momentum .