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Irreducible Brillouin Zone 
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#1
Apr1612, 01:31 PM

P: 2

When energy levels for a lattice are constructed the Bloch wave vector is evaluated along the edges of the irruducible zone. Like [itex]\Gamma[/itex]  [itex]X[/itex]  [itex]M[/itex] path for a square lattice.
I wonder why the calculation is NOT performed for values within the zone? And how the energy corresponding to an arbitrary vector within the zone but not laying at the boundary can be obtained from a bandgap diagrams (plotted for example in [itex]\Gamma[/itex]  [itex]X[/itex]  [itex]M[/itex] coordinates) Thanks in advance 


#2
Apr1612, 09:07 PM

P: 67

You're quite free to plot the band structure along any path you like. Much of the time we're only concerned about the behavior at the min and max of the bands, which only requires plotting in a few directions. You might want to know the band gaps, effective masses, and anisotropies near theses extrema. If, for some reason, you're especially concerned about what's happening off the band path, you'll just have to do a calculation of that system yourself (or call authors). Incidentally, there is a theorem that says it's possible to reconstruct the band structure from the band eigenvalues only at the gamma point. From k.p theory I think. You can look it up.



#3
Apr1612, 10:16 PM

P: 2

Thank you!
That's quite interesting that we can reconstruct the band structure from only information at [itex]\Gamma[/itex] Still people plot the diagrams in the particular paths along irreducible zones. You say Thanks again 


#4
Apr1712, 02:11 AM

P: 105

Irreducible Brillouin Zone



#5
Apr2012, 03:45 PM

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#6
Apr2812, 06:22 PM

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