Re: PC slab and modes simmetry

On Mon, 27 Nov 2006, paolo bettotti wrote:
> I am trying to simulate a PC asymmetric slab. I've used the run-yeven/yodd run function but if I ask the program to print mode parity, in order to recover the quasi-TE/TM like modes, I've got the following error after the first k-point calculation, while the program is trying to find out parity of the last band:
>
> "Finished solving for bands 2 to 10 after 107 iterations.
> yevenfreqs:, 1, 0, 0, 0, 0, 0, 0.110314, 0.120346, 0.223496, 0.239816, 0.339623,
> 0.357412, 0.458293, 0.476587, 0.53817
> elapsed time for k point: 5 minutes, 52 seconds.
> yevenzparity:, 1, -1.0, 0.817931093575246, -0.804035178956196, 0.416573429618825
> , -0.280294019299509, -0.0453411909561938, 0.186153766371718, -0.213838267739919
> , -0.112659261038628, -0.979660245893559
> CHECK failure on line 512
> of ../../../mpb-ctl/mpb.c: k vector is incompatible wi
> th specified parity
> solve_kpoint (0,0.0454545,0):"
>
> Why is not possible to calculate that parity (and how to solve the 
> problem to find the quasi-TE/TM modes for an asymmetric slab)?

First, you can calculate any parity you want.  What MPB is complaining 
about is that you are telling it to run-yeven but your k-point breaks the 
y=0 symmetry (really, the symmetry in the direction of the 2nd lattice 
vector).

The deeper problem is that you can't really use run-yeven/run-yodd with a 
non-orthogonal computational cell.  Or at least, it won't really do what 
you want.   You should just do "(run)".

It only really makes sense to use the yeven/yodd if you want to do a
line-defect calculation.  In that case, you could rearrange your
computational cell into a rectangular one by making your (super)cell
something like:

        o     o     o     o     o     o     o     o     o     o     o
        	  o    	o     o     o     x     o     o     o     o     o
        o     o     o     o     o     o     o     o     o     o     o

where I've put an "x" to indicate where your defect(s) would go.

You don't want to use such a rectangular cell when you are computing
the band diagram of the slab with no defect, because there you want to
use the primitive cell to prevent band-folding.  However, for the band
structure you need k-points in all directions so you are not going to
have any particular mirror symmetry anyway.

Steven