leoant said:
As we all known, energy band is very important to everyone who want to go longer in physics, especially in condensed matter physics. However, as a student of physics, I am shamed to say that I cannot interpret the picture of energy bands well, thus would someone be kind to tell me the secret or refer me to some books or articles.
As an example of my problems, I would take the picture attached(electronic structure of magnesium dibrode)as an example: how can one assign some curves belong to a band(in the picture, one could assign one of the curves to sigma bands which belongs to B-B)?
And further more, if the curve stands for the energy of electrons in solids, what can we learn for the band structure? Since one coordinate of the picture is K vector, the change of energy wiht respect to K means what exactly?
Thanks very much!
First of all, what you are asking isn't easy to explain online since it requires me sketch stuff.
To be able to decipher any band structure, you first need to know AND have in front of you the crystal structure of the material, or more specifically, the reciprocal structure of the material, preferably the 1st Brillouin zone. This will allow you to know the designation (those letters) of the different momentum or k directions. Different crystals and structures sometime use different symbols and letters. However, I think \Gamma is universally used to indicate the center of the zone.
Once you have the picture of the 1st Brillouin zone, then you can follow the "path" indicated in the band structure. For example, if you look at the horizontal axis going from Gamma to M, let's say, in your band structure, then you are doing the same thing along that direction in the Brillouin zone. So the horizontal axis simply tells you the momentum or k values, and what bands are there as you go along all the high-symmetry directions of that crystal.
Next, look at where E=0 is. This is your Fermi energy level. For metals, there will be at least ONE band that crosses this level. For insulators, you will usually have no bands crossing this (there are exceptions). If you can find the gap between the lowest energy minima above the Fermi level and the highest energy maxima below the Fermi level, then you have found the band gap of this insulator. If they occur at different different k (different horizontal axis value), then you have an indirect band gap.
The "spaghetti-like" picture that you normally get out of one of these graphs is due to the calculation of several different bands coming from all the constituents of the material. In many cases, you are only interested in the valence band, which is normally the band closest to the Fermi level. Take note that these band-structure calculations typically use the Fermi-liquid model, meaning they don't usually consider strong electron-electron interactions. So for many "exotic" compounds, such as high-Tc superconductors, these things can be spectacularly wrong. This, however, may not be the case for MgB2.
A good reference for band structures would be Walter Harrison's book "Electronic Structure and the Properties of Solids : The Physics of the Chemical Bond". It's a Dover book, so it isn't that expensive to get.
Zz.
