how to extract the bands of surface states from the band structure plot?

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zzhlax · #1 Post by **zzhlax** » Mon May 24, 2010 3:09 pm

hi, everyone
I have a question about obtaining surface states in the surface calculation. For some substances, the bands of surface states does not occur in the band gap. How to distinguish the surface states from the bulk in the band structure plot?
Thanks.

forsdan · #2 Post by **forsdan** » Mon May 24, 2010 3:33 pm

You can map out the real-space character for each band and each k-point that you are interested in, to see if it is localized to the surface. This should give you information of surface states and resonances. Please have a look at
http://cms.mpi.univie.ac.at/vasp/vasp/B ... eters.html

Comparing the band structure for the surface to the bulk, should give a reasonable starting point of which bands and k-points that are interesting.

At least this is my first thought. I don't know if there is an easier way.

Best regards,
/Dan

<span class='smallblacktext'>[ Edited Mon May 24 2010, 05:39PM ]</span>

panda · #3 Post by **panda** » Wed May 26, 2010 2:36 am

What about the symmetry though? Would not the symmetry of the bulk and surface be different, hence a different space group and Brillouin zone would be required for surface and bulk in order to compare the two? This has been bothering me for some time, could you provide some insight please forsdan? You seem to have a handle on these things...

forsdan · #4 Post by **forsdan** » Wed May 26, 2010 7:34 am

As far as I know the standard way of identifying surface states is to project the bulk band structure on the parallel k-component, which will then form a continuum of states in the surface brillouin zone. Effectively one can then identify the surface states as the states in the band gaps of this continuum.

However, in retrospect I think I am wrong about the above case. The projection will not help to identify the the surface resonances (the hybridized surface-bulk states in the continuum) since the bulk states form a continuum. One probably have to map out the real-space character for all bands and k-point in the surface band structure to determine where the surface resonances are.

Cheers,
/Dan

panda · #5 Post by **panda** » Wed May 26, 2010 7:37 pm

Ok, that makes sense, because it is 3D -> 2D projection. Thanks!

zzhlax · #6 Post by **zzhlax** » Fri May 28, 2010 7:47 am

Thank you, forsdan. I have tried to map out the band decomposed charge density for a certain band and k-point on my surface structure.The charge density distributes on both surface and bulk atoms. Does that mean the surface resonance? and the difference with surface states ?

forsdan · #7 Post by **forsdan** » Fri May 28, 2010 12:49 pm

I don't know the exact mathematical distinction between the two, but the surface resonance is a hybridized bulk state with abnormally high amplitude on the surface atoms. The state also extends down into the bulk, although with decaying amplitude. A surface state on the other hand is confined to the surface atoms.

This is at least what I refer to when I talk about surface states and surface resonaces. The terms may have different meanings for other researchers.

/Dan

<span class='smallblacktext'>[ Edited Fri May 28 2010, 03:45PM ]</span>