{VERSION 5 0 "APPLE_PPC_MAC" "5.0" }
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{CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 
0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 
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0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 
1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "restart;\nwith(Linea
rAlgebra):\nwith(plots):\nhji:=Matrix(4,4):" }}{PARA 7 "" 1 "" {TEXT 
-1 50 "Warning, the name changecoords has been redefined\n" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 169 "#For Si\nh2overm:=7.62;\ndis2:=2.3
5**2;\nEs:=-13.55:\nEp:=-6.52:\nsss:=-1.40*h2overm/dis2;\npps:=3.24*h2
overm/dis2;\nppp:=-0.81*h2overm/dis2;\nsps:=1.84*h2overm/dis2;\npss:=-
sps:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(h2overmG$\"$i(!\"#" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%dis2G$\"&D_&!\"%" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%$sssG$!+<QtJ>!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%$ppsG$\"+wReqW!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$pppG$!+%*
fk<6!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$spsG$\"+f,&)QD!\"*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 169 "#For Ge\nh2overm:=7.62;\ndi
s2:=2.44**2;\nEs:=-14.38:\nEp:=-6.36:\nsss:=-1.40*h2overm/dis2;\npps:=
3.24*h2overm/dis2;\nppp:=-0.81*h2overm/dis2;\nsps:=1.84*h2overm/dis2;
\npss:=-sps:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(h2overmG$\"$i(!\"#
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%dis2G$\"&O&f!\"%" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%$sssG$!+Gq&=z\"!\"*" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$ppsG$\"+@\"po9%!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%$pppG$!+!G<n.\"!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$spsG$\"
+%47]N#!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 624 "gethji:=pro
c(v1::Vector)\nglobal hji;\nlocal distance_ij,x,y,z,x2,y2,z2,xy,yz,zx,
yx,zy,xz,ppsmp;\ndistance_ij:=Norm(v1,2);\nx:=v1[1]/distance_ij;\ny:=v
1[2]/distance_ij;\nz:=v1[3]/distance_ij;\nx2:=x*x:y2:=y*y:z2:=z*z:\nxy
:=x*y:yz:=y*z:zx:=z*x:\nyx:=xy:zy:=yz:xz:=zx:\n#s-s\nhji[1,1]:=sss:\n#
s-p\nhji[1,2]:=z*sps:\nhji[1,3]:=x*sps:\nhji[1,4]:=y*sps:\n#p-s\nhji[2
,1]:=z*pss:\nhji[3,1]:=x*pss:\nhji[4,1]:=y*pss:\n#p-p\nppsmp:=pps-ppp:
\nhji[2,2]:=z2*ppsmp+ppp:\nhji[2,3]:=zx*ppsmp:\nhji[2,4]:=zy*ppsmp:\nh
ji[3,2]:=hji[2,3]:\nhji[3,3]:=x2*ppsmp+ppp:\nhji[3,4]:=xy*ppsmp:\nhji[
4,2]:=hji[2,4]:\nhji[4,3]:=hji[3,4]:\nhji[4,4]:=y2*ppsmp+ppp:\nhji:=ev
alf(hji);\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 303 "#Make n
eighbor atom\nSite[1,1]:=Vector([1/4,1/4,1/4]):\nSite[1,2]:=Vector([-1
/4,-1/4,1/4]):\nSite[1,3]:=Vector([1/4,-1/4,-1/4]):\nSite[1,4]:=Vector
([-1/4,1/4,-1/4]):\nSite[2,1]:=Vector([-1/4,-1/4,-1/4]):\nSite[2,2]:=V
ector([1/4,1/4,-1/4]):\nSite[2,3]:=Vector([-1/4,1/4,1/4]):\nSite[2,4]:
=Vector([1/4,-1/4,1/4]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
645 "calc_k:=proc(kvec::Vector)\n#print(kvec):\n#Make Hamiltonian\nloc
al Ihop, iatom, ij_block_init, ij_block,neighb,i,j;\nIhop:=Matrix(8,8)
:\nIhop[1,1]:=Es:\nIhop[2,2]:=Ep:\nIhop[3,3]:=Ep:\nIhop[4,4]:=Ep:\nIho
p[5,5]:=Es:\nIhop[6,6]:=Ep:\nIhop[7,7]:=Ep:\nIhop[8,8]:=Ep:\niatom:=1:
\nij_block_init:=[[0,4],[4,0]]:\n\nfor iatom from 1 to 2 do\nij_block:
=ij_block_init[iatom];\nfor neighb from 1 to 4 do\n  gethji(Site[iatom
,neighb]);\n  for i from 1 to 4 do\n  for j from 1 to 4 do\n    Ihop[i
j_block[1]+i,ij_block[2]+j]:=Ihop[ij_block[1]+i,ij_block[2]+j]\n      \+
+exp(I*DotProduct(kvec,Site[iatom,neighb]))*hji[i,j];\n  od;\n  od;\no
d;\nod;\n\nsort(map(Re,Eigenvalues(Ihop))):\nend:\n" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 24 "calc_k(Vector([0,0,0]));" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#-%'RTABLEG6$\"*C1tz'-%'MATRIXG6#7*7#$!3A++?6Gua@!#
;7#$!3L,++;%zX7*!#<F/F/7#$!3E+++))=d7sF27#$!3u*****Re?af$F2F6F6" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 259 "stepx_max:=2:\nkvec:=Vector
([kx,ky,kz]):\nInit:=Vector([0,0,0]):\nFinal:=Vector([1,0,0]):\nVec:=F
inal-Init:\nStepv:=Vec/stepx_max:\nfor stepx from 0 to stepx_max do\n \+
 kvec:=evalf(Init+Stepv*stepx):\n  kvec:=evalf(2*kvec*Pi);\n  e1:=calc
_k(kvec);\n  print(kvec,e1);\nod:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$-
%'RTABLEG6$\"*[H&)z'-%'MATRIXG6#7%7#$\"\"!F-F+F+-F$6$\"*_vJ!o-F(6#7*7#
$!3')****>6Gua@!#;7#$!3c*****fTzX7*!#<F8F87#$!3:,++))=d7sF;7#$!3?+++%e
?af$F;F?F?" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$-%'RTABLEG6$\"*oof!o-%'M
ATRIXG6#7%7#$\"+aEfTJ!\"*7#$\"\"!F1F/-F$6$\"*O6f!o-F(6#7*7#$!30]p$=7Fu
.#!#;7#$!3cSRMd^7p7F;7#$!3I],!*Q-Oi6F;7#$!37],!*Q-Oi6F;7#$!3U@1ceUYN\\
!#<7#$!3-)[I'\\H,zMFH7#$!3_%\\)*4h(R'4\"FH7#$!3'e\\)*4h(R'4\"FH" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6$-%'RTABLEG6$\"*_D4!o-%'MATRIXG6#7%7#$
\"+3`=$G'!\"*7#$\"\"!F1F/-F$6$\"*/!*G!o-F(6#7*7#$!3A/o1Xfr7<!#;7#$!3h4
c&[%fr7<F;7#$!3w****f`[9F8F;7#$!3%*****f`[9F8F;7#$!3;t3a]0%Gh$!#<7#$!3
#=-N-bSGh$FH7#$\"3m2++g`[9b!#=7#$\"3b1++g`[9bFO" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 638 "#Procedure definition\n\nband:=proc(Init::Vec
tor,Final::Vector)\nlocal stepx_max,Vec,Stepv,stepx,kvec,e1,m,n,E_all,
Vec_step,Vec_dist;\nE_all:=[]:\nstepx_max:=5:\nVec:=Final-Init;\nVec_s
tep:=sqrt(Vec.Vec)/stepx_max:\nStepv:=Vec/stepx_max:\nfor stepx from 0
 to stepx_max do\n  kvec:=evalf(Init+Stepv*stepx):\n  kvec:=evalf(2*kv
ec*Pi):\n  e1:=calc_k(kvec):\n  Vec_dist:=Vec_step*stepx:\n  E_all:=[o
p(E_all),[Vec_dist,e1]]:\nod:\n#plot\nfor m from 1 to 8 do data||m:=[]
;od:\n\nfor n from 1 by 1 to stepx_max+1 do \nfor m from 1 by 1 to 8 d
o\n  data||m:=[op(data||m),[E_all[n,1],Re(E_all[n,2][m])]]; \nod;\nod;
\n\{data1,data2,data3,data4,data5,data6,data7,data8\};\nend:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 129 "#Xpoint(1,1,0)->Gpoint(Sigm
a) K(3/4,3/4,0)\nInit:=Vector([1,1,0]):\nFinal:=Vector([0,0,0]):\nE_al
l3:=band(Init,Final):\nplot(E_all3);" }}{PARA 13 "" 1 "" {TEXT -1 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "#Gpoint->Xpoint(Delta)
 OK\nInit:=Vector([0,0,0]):\nFinal:=Vector([1,0,0]):\nE_all2:=band(Ini
t,Final):\nplot(E_all2);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "#Lpoint(Lambda)->Gpoint\nInit:=Vec
tor([0.5,0.5,0.5]):\nFinal:=Vector([0,0,0]):\nE_all1:=band(Init,Final)
:\nplot(E_all1);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "
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2 0 1 10 0 2 9 1 4 2 1.000000 36.000000 275.000000 0 0 "Curve 1" "Curv
e 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" }}
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}}{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 646 "Eige
n_all:=[op(E_all1)]:\nk_offset:=0.0;\nn_k:=nops(E_all1[1]):\nn_wave:=n
ops(E_all1):\nfor i from 1 to n_wave do\n  for j from 1 to n_k do\n   \+
 Eigen_all[i][j][1]:=E_all1[i][j][1]+k_offset;\n  od:\nod:\nk_offset:=
Eigen_all[1][n_k][1];\nn_k:=nops(E_all2[1]):\nn_wave:=nops(E_all2):\nf
or i from 1 to n_wave do\n  for j from 1 to n_k do\n    Eigen_all[i]:=
[op(Eigen_all[i]),[E_all2[i][j][1]+k_offset,E_all2[i][j][2]]];\n  od:
\nod:\nk_offset:=Eigen_all[1][nops(Eigen_all[1])][1];\nn_k:=nops(E_all
3[1]):\nn_wave:=nops(E_all3):\nfor i from 1 to n_wave do\n  for j from
 1 to n_k do\n    Eigen_all[i]:=[op(Eigen_all[i]),[E_all3[i][j][1]+k_o
ffset,E_all3[i][j][2]]];\n  od:\nod:\n" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%)k_offsetG$\"\"!F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)k_off
setG$\"+SSDg')!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)k_offsetG$\"+/
a-m=!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "plot(\{op(Eigen
_all)\},color=black);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 
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