Q:How to interpret band structure?

  • Thread starter leoant
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  • #1
leoant
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Dear all:
I've been tortrued by this problem for a long time, please help me as possible as you can.
1. I want to know, after one get a dispersion picture of E(k), how to judge one of those curves stems from, say, px/py/pz sigma/pi (bond?)? That is to say, how to judge the curve's charater, which is very important in electronic structure analysis.
2. How to perform symmetry ananlysis in dispersion curves of E(k) and omega(k)-phonon dispersion relation? For phonon dispersion, how to judge their mode, for instance, A1g, E2g?
please refer me to some books or papers or links. Thank you in advance.

Bests
 

Answers and Replies

  • #2
marlon
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The book 'A chemist's view of bonding in extended structures' by Roald Hoffmann is a great read on this. I have it and i can really recommend it.
It also explains the link between the slope of the energy curves versus the DOS

marlon
 
  • #3
Dr Transport
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The curvature (second derivative) of the band is a measure of the effective mass of the particle.
 
  • #4
Gokul43201
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leoant said:
Dear all:
I've been tortrued by this problem for a long time, please help me as possible as you can.
1. I want to know, after one get a dispersion picture of E(k), how to judge one of those curves stems from, say, px/py/pz sigma/pi (bond?)? That is to say, how to judge the curve's charater, which is very important in electronic structure analysis.
2. How to perform symmetry ananlysis in dispersion curves of E(k) and omega(k)-phonon dispersion relation? For phonon dispersion, how to judge their mode, for instance, A1g, E2g?
please refer me to some books or papers or links. Thank you in advance.

Bests
This is an entirely non-trivial question - one that I'm not qualified to answer authoritatively. There's a whole host of information contained in a band diagram (Why do alkali and alkaline Earth metal valence bands look so much like free electrons bands when transition metal valence bands do not ? Why then, is the same also true for Zn and Cd ? How do I extract information about the orientations of crystal directions with respect to orbital directions from the varying degeneracies along different crystal directions ? Where is the effective mass high, low, positive or negative ? What are the optical properties I can expect for a material, given its band structure ?), and extracting good portion of it is a skill that takes work to hone (one, I do not claim to possess).

My starting point was Ashcroft & Mermin. But to do a good job, you will need a good spectroscopy text. This, I believe, is the best way to go, and as far as I'm aware, the chemists do a better job of documenting this (especially, when it comes to "vibration spectra" ) than the physicists. There are very good spectroscopy/analytical chemistry texts that could help.

http://www.spectroscopynow.com/Spy/basehtml/SpyH/1,,6-5-3-0-1-book_list-0-0,00.html [Broken]
 
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  • #6
marlon
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i know the prof thit wrote this book. I have tutored some of his tudents here in Ghent, Belgium.

http://www.spectroscopynow.com/Spy/basehtml/SpyH/1,1181,6-5-3-0-1-book_detail-0-141,00.html [Broken]

very good stuff
marlon
 
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