Diamond band structure using cubic supercell instead of primitive cell
"Aryana, Kiumars" <[email protected]> Wed, 7 Feb 2018 12:32:05 -0500
| Newsgroups | gmane.comp.science.photonic-bands |
|---|---|
| Message-ID | <CALjYqUDvHepWdcKC1dtHx0=P1MY41DX-FS+VvM0f5-b=FsLrvA@mail.gmail.com> |
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Dear MPB users,
I'm trying to simulate a complex 3D crystal and I want to use the supercell
instead of primitive cell. I tried to verify my code by doing the same for
diamond unit cell but the band structure that I get for diamond is
different than the one with primitive cell. I still see a bandgap but in a
higher frequency. I would like to know if anyone have any idea how we
should proceed if we were to use the supercell of a crystal?
Here is my code for the diamond supercell:
(set! geometry-lattice (make lattice
(basis-size 1 1 1)
(basis1 1 0 0)
(basis2 0 1 0)
(basis3 0 0 1)))
; Corners of the irreducible Brillouin zone for the fcc lattice,
; in a canonical order:
(set! k-points (interpolate 4 (list
(vector3 0 0.5 0.5) ; X
(vector3 0 0.625 0.375) ; U
(vector3 0 0.5 0) ; L
(vector3 0 0 0) ; Gamma
(vector3 0 0.5 0.5) ; X
(vector3 0.25 0.75 0.5) ; W
(vector3 0.375 0.75 0.375)))) ; K
; define a couple of parameters (which we can set from the command-line)
(define-param eps 13) ; the dielectric constant of the spheres
(define-param r 0.2165) ; the radius of the spheres
(define diel (make dielectric (epsilon eps)))
; A diamond lattice has 18 "atoms" per unit cell:
(set! geometry (list (make sphere (center 0 0 0)
(radius r)
(material diel))
(make sphere (center 1.0000 0 0) (radius r)
(material diel))
(make sphere (center 1.0000 1.0000 0) (radius r)
(material diel))
(make sphere (center 1.0000 1.0000 1.0000) (radius r)
(material diel))
(make sphere (center 0 1.0000 1.0000) (radius r)
(material diel))
(make sphere (center 0 0 1.0000) (radius r)
(material diel))
(make sphere (center 1.0000 0 1.0000) (radius r)
(material diel))
(make sphere (center 0 1.0000 0) (radius r)
(material diel))
(make sphere (center 0.5000 0.5000 0) (radius r)
(material diel))
(make sphere (center 0.5000 0.5000 1.0000) (radius r)
(material diel))
(make sphere (center 0 0.5000 0.5000) (radius r)
(material diel))
(make sphere (center 1.0000 0.5000 0.5000) (radius r)
(material diel))
(make sphere (center 0.5000 0 0.5000) (radius r)
(material diel))
(make sphere (center 0.5000 1.0000 0.5000) (radius r)
(material diel))
(make sphere (center 0.2500 0.2500 0.2500) (radius r)
(material diel))
(make sphere (center 0.2500 0.7500 0.7500) (radius r)
(material diel))
(make sphere (center 0.7500 0.7500 0.2500) (radius r)
(material diel))
(make sphere (center 0.7500 0.2500 0.7500) (radius r)
(material diel))))
(set-param! resolution 16) ; use a 16x16x16 grid
(set-param! mesh-size 5)
(set-param! num-bands 10)
; run calculation, outputting electric-field energy density at the U point:
(run (output-at-kpoint (vector3 0 0.625 0.375) output-dpwr))
Kind regards,
*Kiumars Aryana*
M.Sc. Mechanical Engineering
Miami University
Department of Mechanical and Manufacturing Engineering, 56 Garland Hall
605 E. High St.
Oxford, OH 45056
[email protected]
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<div dir=3D"ltr">Dear MPB users,<div><br></div><div>I'm trying to simul=
ate a complex 3D crystal and I want to use the supercell instead of primiti=
ve cell. I tried to verify my code by doing the same for diamond unit cell =
but the band structure that I get for diamond is different than the one wit=
h primitive cell. I still see a bandgap but in a higher frequency. I would =
like to know if anyone have any idea how we should proceed if we were to us=
e the supercell of a crystal?</div><div><br></div><div>Here is my code for =
the diamond supercell:</div><div><div><br></div><div>(set! geometry-lattice=
(make lattice</div><div>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 (basis-size 1 1 1)</div><div>=C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 (basis1 1 0 0)</div><div>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 (basis2 0 1 0)</div=
><div>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0=
=C2=A0 =C2=A0 =C2=A0 (basis3 0 0 1)))</div><div><br></div><div>; Corners o=
f the irreducible Brillouin zone for the fcc lattice,</div><div>; in a cano=
nical order:</div><div>=C2=A0(set! k-points (interpolate 4 (list</div><div>=
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 (vector3 0 0.5 0.5)=C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 ; X</div><div>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 (vector3 0 0.625 0.375)=C2=A0 =C2=A0 =C2=A0 =C2=A0 ; U</div><div>=C2=A0=
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 (vector3 0 0.5 0)=C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 ; L</div><div>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 (vector3 0 0 0)=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
; Gamma</div><div>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 (vector3 0 0.5 0.5)=
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 ; X</div><div>=C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 (vector3 0.25 0.75 0.5)=C2=A0 =C2=A0 =C2=A0 =C2=A0 ; W=
</div><div>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 (vector3 0.375 0.75 0.375)=
)))=C2=A0 ; K</div><div><br></div><div>=C2=A0; define a couple of parameter=
s (which we can set from the command-line)</div><div>=C2=A0(define-param ep=
s 13) ; the dielectric constant of the spheres</div><div>=C2=A0(define-para=
m r 0.2165)=C2=A0 =C2=A0 ; the radius of the spheres</div><div><br></div><d=
iv>=C2=A0(define diel (make dielectric (epsilon eps)))</div><div><br></div>=
<div>=C2=A0; A diamond lattice has 18 "atoms" per unit cell:</div=
><div>=C2=A0(set! geometry (list <span style=3D"white-space:pre"> </span>(m=
ake sphere (center=C2=A0 =C2=A0 =C2=A0 0=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A00=
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A00) (radius r)</div><div>=C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 (material diel))</div><div><span style=3D"white-space:pre"> </s=
pan>(make sphere (center 1.0000=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A00=C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A00) (radius r)</div><div>=C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 (=
material diel))</div><div><span style=3D"white-space:pre"> </span>(mak=
e sphere (center 1.0000=C2=A0 =C2=A0 1.0000=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A00) (radius r)</div><div>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0=
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 (material diel))</div><di=
v><span style=3D"white-space:pre"> </span>(make sphere (center 1.0000=
=C2=A0 =C2=A0 1.0000=C2=A0 =C2=A0 1.0000) (radius r)</div><div>=C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 (material diel))</div><div><span style=3D"white-space:pre"> =
</span>(make sphere (center=C2=A0 =C2=A0 =C2=A0 0=C2=A0 =C2=A0 1.0000=
=C2=A0 =C2=A0 1.0000) (radius r)</div><div>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 (materia=
l diel))</div><div><span style=3D"white-space:pre"> </span>(make spher=
e (center=C2=A0 =C2=A0 =C2=A0 0=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A00=C2=A0 =
=C2=A0 1.0000) (radius r)</div><div>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 (material diel)=
)</div><div><span style=3D"white-space:pre"> </span>(make sphere (cent=
er 1.0000=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A00=C2=A0 =C2=A0 1.0000) (radius r=
)</div><div>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 (material diel))</div><div><span style=
=3D"white-space:pre"> </span>(make sphere (center=C2=A0 =C2=A0 =C2=A0 =
0=C2=A0 =C2=A0 1.0000=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A00) (radius r)</div><=
div>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 (material diel))</div><div><span style=3D"white=
-space:pre"> </span>(make sphere (center 0.5000=C2=A0 =C2=A0 0.5000=C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A00) (radius r)</div><div>=C2=A0 =C2=A0 =C2=A0=
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 (material diel))</div><div><span style=3D"white-space:pre"> </span=
>(make sphere (center 0.5000=C2=A0 =C2=A0 0.5000=C2=A0 =C2=A0 1.0000) (radi=
us r)</div><div>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 (material diel))</div><div><span sty=
le=3D"white-space:pre"> </span>(make sphere (center=C2=A0 =C2=A0 =C2=
=A0 0=C2=A0 =C2=A0 0.5000=C2=A0 =C2=A0 0.5000) (radius r)</div><div>=C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 (material diel))</div><div><span style=3D"white-space:pre=
"> </span>(make sphere (center 1.0000=C2=A0 =C2=A0 0.5000=C2=A0 =C2=A0=
0.5000) (radius r)</div><div>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 (material diel))</div>=
<div><span style=3D"white-space:pre"> </span>(make sphere (center 0.50=
00=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A00=C2=A0 =C2=A0 0.5000) (radius r)</div>=
<div>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 (material diel))</div><div><span style=3D"white=
-space:pre"> </span>(make sphere (center 0.5000=C2=A0 =C2=A0 1.0000=C2=
=A0 =C2=A0 0.5000) (radius r)</div><div>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 (material di=
el))</div><div><span style=3D"white-space:pre"> </span>(make sphere (c=
enter 0.2500=C2=A0 =C2=A0 0.2500=C2=A0 =C2=A0 0.2500) (radius r)</div><div>=
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 (material diel))</div><div><span style=3D"white-sp=
ace:pre"> </span>(make sphere (center 0.2500=C2=A0 =C2=A0 0.7500=C2=A0=
=C2=A0 0.7500) (radius r)</div><div>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 (material diel)=
)</div><div><span style=3D"white-space:pre"> </span>(make sphere (cent=
er 0.7500=C2=A0 =C2=A0 0.7500=C2=A0 =C2=A0 0.2500) (radius r)</div><div>=C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 (material diel))</div><div><span style=3D"white-space:=
pre"> </span>(make sphere (center 0.7500=C2=A0 =C2=A0 0.2500=C2=A0 =C2=
=A0 0.7500) (radius r)</div><div>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 (material diel))))<=
/div><div><br></div><div><br></div><div>=C2=A0(set-param! resolution 16) ; =
use a 16x16x16 grid</div><div>=C2=A0(set-param! mesh-size 5)</div><div>=C2=
=A0(set-param! num-bands 10)</div><div><br></div><div>=C2=A0; run calculati=
on, outputting electric-field energy density at the U point:</div><div>=C2=
=A0(run (output-at-kpoint (vector3 0 0.625 0.375) output-dpwr))</div><div><=
br></div>Kind regards,<br><div class=3D"gmail_signature"><div dir=3D"ltr"><=
div><div dir=3D"ltr"><div><div dir=3D"ltr"><b style=3D"color:rgb(51,51,51);=
font-family:"Gotham SSm A","Gotham SSm B","Helveti=
ca Neue",Helvetica,Arial,sans-serif;font-size:11px;line-height:16.5px"=
>Kiumars Aryana</b><br style=3D"color:rgb(51,51,51);font-family:"Gotha=
m SSm A","Gotham SSm B","Helvetica Neue",Helvetica=
,Arial,sans-serif;font-size:11px;line-height:16.5px"><span style=3D"color:r=
gb(51,51,51);font-family:"Gotham SSm A","Gotham SSm B",=
"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:11px;line-h=
eight:16.5px">M.Sc.=C2=A0</span><span style=3D"color:rgb(51,51,51);font-fam=
ily:"Gotham SSm A","Gotham SSm B","Helvetica Neue&=
quot;,Helvetica,Arial,sans-serif;font-size:11px;line-height:16.5px">Mechani=
cal Engineering</span></div><div dir=3D"ltr"><font color=3D"#333333" face=
=3D"Gotham SSm A, Gotham SSm B, Helvetica Neue, Helvetica, Arial, sans-seri=
f"><span style=3D"font-size:11px;line-height:16.5px"><br></span></font><div=
><span style=3D"color:rgb(51,51,51);font-family:"Gotham SSm A",&q=
uot;Gotham SSm B","Helvetica Neue",Helvetica,Arial,sans-seri=
f;font-size:11px;line-height:16.5px">Miami University</span><br style=3D"co=
lor:rgb(51,51,51);font-family:"Gotham SSm A","Gotham SSm B&q=
uot;,"Helvetica Neue",Helvetica,Arial,sans-serif;font-size:11px;l=
ine-height:16.5px"><span style=3D"color:rgb(51,51,51);font-family:"Got=
ham SSm A","Gotham SSm B","Helvetica Neue",Helveti=
ca,Arial,sans-serif;font-size:11px;line-height:16.5px">Department of Mechan=
ical and Manufacturing Engineering, 56 Garland Hall</span></div><div><span =
style=3D"color:rgb(51,51,51);font-family:"Gotham SSm A","Got=
ham SSm B","Helvetica Neue",Helvetica,Arial,sans-serif;font-=
size:11px;line-height:16.5px">605 E. High St.</span><br style=3D"color:rgb(=
51,51,51);font-family:"Gotham SSm A","Gotham SSm B",&qu=
ot;Helvetica Neue",Helvetica,Arial,sans-serif;font-size:11px;line-heig=
ht:16.5px"><span style=3D"color:rgb(51,51,51);font-family:"Gotham SSm =
A","Gotham SSm B","Helvetica Neue",Helvetica,Arial=
,sans-serif;font-size:11px;line-height:16.5px">Oxford, OH 45056</span><br s=
tyle=3D"color:rgb(51,51,51);font-family:"Gotham SSm A","Goth=
am SSm B","Helvetica Neue",Helvetica,Arial,sans-serif;font-s=
ize:11px;line-height:16.5px"><span style=3D"color:rgb(51,51,51);font-family=
:"Gotham SSm A","Gotham SSm B","Helvetica Neue&quo=
t;,Helvetica,Arial,sans-serif;font-size:11px;line-height:16.5px"><a href=3D=
"mailto:[email protected]" target=3D"_blank">[email protected]</a></spa=
n></div><div><img src=3D"http://www.miamioh.edu/images/i_logo_horizontal.jp=
g" width=3D"96" height=3D"30"><br></div></div></div></div></div></div></div=
>
</div></div>
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