[Wien] Band Identity in spaghetti

[Dr. Sharat Chandra]

Dear Andrei

Thanks for the reply. It is quite helpful.

Regards
Sharat

On Thu, 7 Apr 2005, Andrei Postnikov wrote:

> On Thu, 7 Apr 2005, Dr. Sharat  Chandra wrote:
> 
> | Dear Wien experts
> | 
> | In the band structure plot generated by spaghetti, when any two bands are 
> | crossing at some point in the plot, the resulting degeneracy is lifted at 
> | the point of crossing and the two bands are separated. This results in a 
> | change of band identity. Suppose, at first band 1 is lower in energy, then 
> | after the point of crossing band 2 will be lower in energy. But after the 
> | point of band bending, band 2 will be higher in energy throughout the 
> | range. I want to know in what way the identity of the bands are given. Are 
> | they set after all the crossings are taken into account, or they are 
> | labelled starting from the band which is lowest in energy?
> 
> Dear Sharat,
> 
> the bands are numbered in the order of increasing energy
> (not only in WIEN but probably in any bandstructure code).
> There reason is, there is no other systematic way of numbering the
> bands. Moreover the crossings usually occur at high-symmetry points
> (along which you'd usually plot your spaghetties),
> but if you want to trace a band, and go around a high-symmetry
> point, you can end up with different numbering, depending on
> your path. Moreover the exact numbering does not affect any
> properties (physically, I mean). Certainly there can be
> a numerical inaccuracy if you use a finitely sparse k-mesh and 
> interpolation. This can be a problem especially in calculations
> involving matrix elements (e.g. optics, of Green's function),
> yet the error can be controllably suppressed by using finer k-mesh.
> 
> | This becomes a problem, if the identies of the bands change after the 
> | crossing is taken into account. For example, I am interested in 
> | calculating the contribution to DOS from each band separately using the 
> | joint program. But this can be done correctly, only if the band identities 
> | do not change.
> 
> The following argument has been offered to me long ago by Igor Mazin,
> in a similar discussion: you start to trace a band from any (symmetric)
> point in the BZ, you go around the BZ along a non-trivial path, and
> good chance that you'll return to the same k-point at different energy
> hence in another band. (Try it!) Hence there is no unambiguous
> band numbering other than by increasig energy.
> 
> Andrei Postnikov
> 
>  +-- Dr. habil. Andrei Postnikov ----- Tel. +49-541-969.2377 -- Fax .2351 ---+
>  | Institut fuer Festkoerperforschung - FZ Juelich, D-52425 Juelich, Germany |
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