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Fermi surface, -level, -wavelength, -velocity (Read 11593 times)
Gerrit-Jan Linker
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Fermi surface, -level, -wavelength, -velocity
02.09.09 at 12:20:57
 
Fermi surface, Fermi level, Fermi wavelength, Fermi velocity
 
The Fermi surface is a surface of constant energy of the highest occupied state, the Fermi level, in k-space where k is the wavevector of the electron. At absolute zero temperature the Fermi surface separates the unfilled electronic orbitals from the filled ones. The energy of the highest occupied crystal orbital is known as the Fermi energy or as the Fermi level. The associated wavelength is known as the Fermi wavelength.
 
What is meant by Fermi energy  is essentially that even if we have extracted all possible energy from a metal by cooling it down to near absolute zero temperature (0 kelvin), the electrons in the metal are still moving around; the fastest ones would be moving at a velocity that corresponds to a kinetic energy equal to the Fermi energy. This is the Fermi velocity: vF =dE/dk
 
Relation Fermi temperature and Fermi energy (kB is Bolzmann's constant):
TF=EF/kB
 
Fermi momentum:
pF=√(2meEF)
 
Fermi velocity:
vF=pF/me
 
The shape of the Fermi surface in 1D conductors are separated sheets, in 2D conductors it is a cillinder and in 3D conductors it is spherically shaped.  
Ref:   D. Jιrome, Science, New Series, Vol. 252, No. 5012 (Jun. 14, 1991), pp. 1509-1514
 
Source:
Wikipedia - Fermi surface
http://en.wikipedia.org/wiki/Fermi_surface
Fermi energy - Wikipedia
http://en.wikipedia.org/wiki/Fermi_energy
See also:
Fermi Surface Database
http://www.phys.ufl.edu/fermisurface/
Wave vector
http://www.oraxcel.com/cgi-bin/yabb2/YaBB.pl?num=1247825987
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« Last Edit: 18.12.12 at 10:37:08 by Gerrit-Jan Linker »  

Gerrit-Jan Linker
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