Re: Point defects in slab structure - resonant frequencies

On Tue, 3 Apr 2007, Rob wrote:
> I feel I can see one band that is approximately flat around
> normalized frequency 0.28, but then there are some other
> bands in there, as well.  Is my problem due to a too-small
> supercell or should these other bands actually be in the gap as well?

Yes, you should see lots of bands in the gap--more and more as you 
increase the supercell size.

The reason is that a slab does not have a complete band gap, when you 
include the light cone.  And when you create a point defect, you break 
translational symmetry, which breaks conservation of k, and therefore all 
of the light cone modes fall into the "gap" in a band-structure 
calculation.

In an MPB calculation, the only way to distinguish a point-defect resonant 
mode is to look at the localization of the field.  A resonant mode will 
have a large fraction of its field concentrated in a small region around 
the defect, whereas other modes will not.  The compute-energy-in-objects 
and output-energy-in-objects functions (if I am remembering their names 
correctly) will help you here.

> Why am I trying to use MPB rather than MEEP to find
> resonant band frequencies? I am new to both of these
> software packages and cannot understand yet how to
> simulate non-rectangular unit cells in MEEP (despite
> your posts on this on theMEEP list).  But that is
> a discussion for a different list.

You have a fundamental misunderstanding if you think that the unit cell is 
at all relevant for a point-defect calculation.  For a point defect, there 
is no translational symmetry so you might as well use a rectangular 
supercell.

Cordially,
Steven G. Johnson