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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.
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.
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 ...
It can be used to determine the Fermi surface of a material. Other quantities also oscillate, such as the electrical resistivity (Shubnikov–de Haas effect), specific heat, and sound attenuation and speed. [1] [2] [3] It is named after Wander Johannes de Haas and his student Pieter M. van Alphen. [4]
The work function W for a given surface is defined by the difference [1] =, where −e is the charge of an electron, ϕ is the electrostatic potential in the vacuum nearby the surface, and E F is the Fermi level (electrochemical potential of electrons) inside the material.
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.