8 Apr 2010 17:01

### Two kinds of lattice

```hello,

I want to model a two dimensional arrangement of hexagons like a
graphite structure. Problem is that description require a superposed of
two kinds of lattice (4 basis vectors).
Is it possible with mpb?

Thanks.
```
8 Apr 2010 22:05

### Re: Two kinds of lattice

```Hi!

It not it possible to create a graphite structure by using rectangular lattice
with two objects at one lattice point?

Quoting Julien Arlandis <julien.arlandis <at> laposte.net>:

> hello,
>
> I want to model a two dimensional arrangement of hexagons like a
> graphite structure. Problem is that description require a superposed of
> two kinds of lattice (4 basis vectors).
> Is it possible with mpb?
>
> Thanks.
>
>
>
>
> _______________________________________________
> mpb-discuss mailing list
> mpb-discuss <at> ab-initio.mit.edu
> http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss
>
```
9 Apr 2010 14:18

### Problem with super-lattice

```Hello,

I define a super lattice composed of two distinct holes (radius R1 and
R2), my problem is that diagram band is not equal for R1=R2 and R1 ~ R2.

For example :

(define-param R1 0.15)
(define-param R2 0.15)

(set! geometry-lattice (make lattice (size xsize ysize no-size)
(basis1 1 0)
(basis2 0 1)))

(set! geometry
(list
(make cylinder (center -0.25 -0.25 0) (radius R1) (height infinity)
(material air))
(make cylinder (center +0.25 -0.25 0) (radius R1) (height infinity)
(material air))
(make cylinder (center -0.25 +0.25 0) (radius R2) (height infinity)
(material air))
(make cylinder (center +0.25 +0.25 0) (radius R2) (height infinity)
(material air))
))

==> I get this result :
<http://juliendusud.free.fr/band2.png>

But if I replace (define-param R2 0.15) by (define-param R2 0.1499) I
```

16 Apr 2010 08:05

### How to specify the basises of triangular lattice?

Dear Johnson,
Recently I focus on the triangular lattice and its reciprocal lattice. By using the lattice properties from "Tutorial", just like:

(set! geometry-lattice (make lattice (size 3 3 no-size)
(basis1 (/ (sqrt 3) 2) 0.5)
(basis2 (/ (sqrt 3) 2) -0.5)

and I fill the geometries manually to see its position in cartesian coordinate:

(set! geometry (list
(make cylinder
(center 0 0 0) (radius 0.2) (height infinity)
(material (make dielectric (epsilon 12))))
(make cylinder
(center 1 0 0) (radius 0.1) (height infinity)
(material (make dielectric (epsilon 12))))
(make cylinder
(center 0 1 0) (radius 0.3) (height infinity)
(material (make dielectric (epsilon 12))))
(make cylinder
(center 1 1 0) (radius 0.4) (height infinity)
(material (make dielectric (epsilon 12))))

then I obtain the epsilon.h5 file and convert it to png. I found it inexplicable!
where the cylinder centered at (1 0 0) with radius of 0.1 is actually located at (1, 0) in cartesian coordinate;
the cylinder centered at (0 1 0) with radius of 0.3 is actually located at (0.5, sqrt(3)/2);
and the cylinder centered at (1 1 0) with radius of 0.4 is actually located at (1.5, sqrt(3)/2).
Even the basis vector coordinate is changed from right-hand type to left-hand type, why does this happen?

I also alternate the basises to

(set! geometry-lattice (make lattice (size 3 3 no-size)
(basis1 1 0)
(basis2 0.5 (/ (sqrt 3) 2))
))

and obtain the same picture.

Besides, I use the (set! ensure-periodicity false), but it come no effect.

Regards,

```_______________________________________________
mpb-discuss mailing list
mpb-discuss <at> ab-initio.mit.edu
http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss```
27 Apr 2010 12:49

### defect modes in W0.90 slab

Dear Steven and MPB's users,

I would like to calculate the defect modes existing in a triangular PC slab whith a line defect of W0.90. I have formed a geometry by moving up and down the  air holes around the linear defect but the band structure obtained is wrong: defect modes appear outside the expected band gap region.Could you please help me finding the way to obtain the correct structure?

(define-param h 0.5) ; the thickness of the slab
(define-param a1 0.5) ; lattice vector x triangular distribution
(define-param a2 0.867) ; lattice vector y triangular distribution
(define-param wd 0.7803) ; ;es el valor de h
(define-param eps 11.97) ; the dielectric constant of the slab
(define-param loweps 1.0) ; the dielectric constant of the substrate
(define-param r 0.275) ; the radius of the holes
(define-param supercell-h 4) ; height of the supercell
(set! default-material (make dielectric (epsilon 11.97)))
(define-param supercell-y (+ 12  (* 2 wd))) ; the (odd) number of lateral supercell periods
(set! geometry-lattice (make lattice
(basis1 1 0)
(basis2 0 (/ (sqrt 3) 2))
(size 1 supercell-y supercell-h)))

(set! geometry
(list (make block (material (make dielectric (epsilon loweps)))
(center 0 0 (* 0.25 supercell-h))
(size infinity infinity (* 0.5 supercell-h)))
(make block (material (make dielectric (epsilon eps)))
(center 0) (size infinity infinity h))
))
(set! geometry
(append geometry  (list
(make cylinder (material air)
(center 0.5 wd 0) (radius r) (height supercell-h))
(make cylinder (material air)
(center 0.5 (- 0 wd) 0) (radius r) (height supercell-h))
(make cylinder (material air)
(center 0 (+ wd a2) 0) (radius r) (height supercell-h))
(make cylinder (material air)
(center 0 (- 0 (+ wd a2)) 0) (radius r) (height supercell-h))
(make cylinder (material air)
(center 0.5 (+ wd (* 2 a2)) 0) (radius r) (height supercell-h))
(make cylinder (material air)
(center 0.5 (- 0 (+ wd (* 2 a2))) 0) (radius r) (height supercell-h))
(make cylinder (material air)
(center 0 (- 0 (+ wd (* 3 a2))) 0) (radius r) (height supercell-h))
(make cylinder (material air)
(center 0 (+ wd (* 3 a2)) 0) (radius r) (height supercell-h))
(make cylinder (material air)
(center 0.5 (- 0 (+ wd (* 4 a2))) 0) (radius r) (height supercell-h))
(make cylinder (material air)
(center 0.5 (+ wd (* 4 a2)) 0) (radius r) (height supercell-h))
(make cylinder (material air)
(center 0 (- 0 (+ wd (* 5 a2))) 0) (radius r) (height supercell-h))
(make cylinder (material air)
(center 0 (+ wd (* 5 a2)) 0) (radius r) (height supercell-h))

)))

(define Gamma (vector3 0 0 0))
(define K' (lattice->reciprocal (vector3 0.5 0 0))) ; edge of Brillouin zone.
(set! k-points (interpolate 4 (list Gamma K')))

(define-param extra-bands 5) ; number of extra bands to compute above the gap
(set-param! num-bands 10)
(define-param res 32) ; the resolution (grid points/a)
(set! grid-size (vector3 res (* res supercell-y) 1))
(run-zeven (output-at-kpoint K' fix-hfield-phase output-hfield-z))
(display-eigensolver-stats)

Regards, Imanol Andonegui

```_______________________________________________
mpb-discuss mailing list
mpb-discuss <at> ab-initio.mit.edu
http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss```
27 Apr 2010 16:46

### Re: defect modes in W0.90 slab

```_______________________________________________