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Fig. 1: Fermi surface and electron momentum density of copper in the reduced zone schema measured with 2D ACAR. [6]Consider a spin-less ideal Fermi gas of particles. . According to Fermi–Dirac statistics, the mean occupation number of a state with energy is give
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.
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 .
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 relates a Fermi liquid's particle density to the volume of its Fermi surface. In condensed matter physics, Luttinger's theorem [1] [2] is a result derived by J. M. Luttinger and J. C. Ward in 1960 that has broad implications in the field of electron transport.
Fermi–Dirac statistics is a type of quantum statistics that applies to the ... In the limit of low particle density, ... (typically T = 10 000 K on its surface ...
In a quantum oscillation experiment, the external magnetic field is varied, which causes the Landau levels to pass over the Fermi surface, which in turn results in oscillations of the electronic density of states at the Fermi level; this produces oscillations in the many material properties which depend on this, including resistance (the ...
If the new periodicity is a rational fraction or multiple of the lattice constant, the density wave is said to be commensurate; otherwise the density wave is termed incommensurate. A sketch in k-space of a (001) section of the Fermi surface of Cr.