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Transcript of brillouin
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Free electron bands for fcc structureG – center of the BZ
X – [100] intercept; G - X path D
K – [110] intercept; G - K path S
L – [111] intercept; G - L path L
Band structure of Al (fcc)
3
Free Electron Bands
Ene
rgy
k
†
Ek = Ek k + G( )
1D : E =h2
2mk +
n2pa
Ê
Ë Á
ˆ
¯ ˜
2
; n = 0, ±1, ± 2 ...n=1
n=-2
n=-1
n=0
Brillouin zones - 2DBZ construction•reciprocal lattice
•bisect vectors to the nearest neighbors
•area defined by bisecting linesrepresents 1BZ
Zonas de Brillouin y Superficie de Fermi
* Red cuadrada* Aprox. e libres
(densidad arbitraria)
Ejemplo:
Esquema de zona extendida
The Fermi surface ofalkali metals
kF = (3p2n)1/3,n = 2/a3
à kF = (3/4p)1/3(2p/a)GN=(2p/a)[(1/2)2+(1/2)2]1/2
\ kF = 0.877 GN
First BZ (of a bcc lattice) andthe Fermi sphere
The Fermi surface of copper (similar for Ag and Au)
Band structure
(Cu is amonovalent metalwith fcc lattice)
Fermi surface
(a cross-section)
Periodic zone scheme
The Fermi surface of Al
(Al is a trivalent metalwith fcc lattice)
Empty lattice result
Actual Fermi surface
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Distorting the Fermi Surface
2nd zone 3rd zone 3rd zone in periodic zone scheme
Distortion due to weak periodic potential
2nd zone 3rd zone
3D Fermi Surface
web page: http://www.phys.ufl.edu/fermisurface/
Na Ca Al
1 valence e- 2 valence e- 3 valence e-
Periodic Table of the Fermi Surfaces of Elemental Solids http://www.phys.ufl.edu/fermisurface
Ferromagnets:
Alternate Structures :
Tat-Sang Choy, Jeffery Naset , Selman Hershfield, and Christopher StantonPhysics Department, University of Florida
Seagate TechnologyJian Chen
Source of tight binding parameters (except for fcc Co ferromagnet): D.A. Papaconstantopoulos, Handbook of the band structure of elemental solids, Plenum 1986.This work is supported by NSF, AFOSR, Research Corporation, and a Sun Microsystems Academic Equipment Grant.
(15 March, 2000)
Co_fcc Co_fcc