Nonlocal Empirical Pseudopotential Method Empirical pseudopotenti...

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Nonlocal Empirical Pseudopotential Method Empirical pseudopotential method is a computationally-efficient bandstructure technique, based on the plane wave expansion of the non-core states. Quite frequently the so-called nonlocal (NL) and energy-dependent corrections are needed. Such improvements were introduced sometime ago by Chelikowsky and Cohen (Phys. Rev. B, V. 14, p. 556, 1976). 6 Ly a 4 15 2 4, x, 521 Th Ly x, 6 Si X, L, 8 Ly - -10 -12 r, 5 t A r A x U.K M r WAVE VECTOR k FIG. 2. Band structure for Si as determined from a local-pseudopotential calculation (dotted line) and an nergy-dependent nonlocal-pseudopotential calculation (solid line). The task is to: Learn about the EPM, and write a local-EPM code for a zinc-blende structure. Then, study the classical CC paper for the NL-EPM and incorporate this into your existing code. Reproduce the bandstructures given in the CC paper for a representative number of materials, and develop a feeling on the effects of the NL contributions.

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function epmV()
% based on Dragica Vasileska Empirical Pseudopotential Method
clc;
clear;

global ao N_pw igx_vec igy_vec igz_vec dkx dky dkz t Vs3 Va3 Vs8 Va8
global Vs11 Va11 ik_curr ik ek

str_fac = load('str_fac.txt');
a0 = load('a0.txt');
scn0 = fileread('semiconductors.txt');
scnames = strsplit(scn0);

Ry2eV=13.6056981d0;
hb=1.054D-34;
h=6.625D-34;
q=1.602d-19;
mo=9.11D-31;
t=hb*hb/2.0d0/mo/q;

NN_neighbours=10;
N_pw = 137;
N_ek=40;
ig2_mag(1:NN_neighbours)=[0, 3, 4, 8, 11, 12, 16, 19, 20, 24];
%sprintf('%s','This program calculates the bandstructure of semiconductors based on the Empirical Pseudopotential Method (EPM)')
%sprintf('%s','The following semiconductors are included')
%sprintf('1 -> Si 2 -> Ge 3 -> Sn 4 -> GaP 5 -> GaAs 6 -> AlSb 7 -> InP')
%sprintf('8 -> GaSb 9 -> InAs 10 -> InSb 11 -> ZnS 12 -> ZnSe 13 -> ZnTe 14 -> CdTe')

ichoose = 12;
ao=a0(ichoose);
Vs3=str_fac(ichoose,1);
Vs8=str_fac(ichoose,2);
Vs11=str_fac(ichoose,3);
Va3=str_fac(ichoose,4);
Va8=str_fac(ichoose,5);
Va11=str_fac(ichoose,6);
ao=ao*1.0d-10;
Vs3=Vs3*Ry2eV;
Vs8=Vs8*Ry2eV;
Vs11=Vs11*Ry2eV;
Va3=Va3*Ry2eV;
Va8=Va8*Ry2eV;
Va11=Va11*Ry2eV;

icount=0;
for i=1:NN_neighbours
    ig2=ig2_mag(i);
    a=sqrt(double(ig2));
    ia=floor(a);
    ic=0;
    for igx=-ia:ia
       igx2=igx*igx;
       for jgy=-ia:ia
            jgy2=jgy*jgy;
            igxy2=igx2+jgy2;
            for kgz=-ia:ia
                kgz2=kgz*kgz;
                igxyz2=igxy2+kgz2;
                if (igxyz2==ig2)
                   ic=ic+1;
                   igx_vec(ic+icount)=igx;
                   igy_vec(ic+icount)=jgy;
                   igz_vec(ic+icount)=kgz;
                end
            end
       end
    end
    icount=icount+ic;
    sprintf('%d %d %d',ig2,ic,icount);
end

fprintf('H1\r\n');
ik_curr=0;
sumx=0.0d0;
X0=0.5d0;
Y0=0.5d0;
Z0=0.5d0;
k_vec = zeros(1,161);
for ik=1:N_ek+1
    dkx=0.50d0*(1.0d0-double(ik-1)/double(N_ek));
    dky=0.50d0*(1.0d0-double(ik-1)/double(N_ek));
    dkz=0.50d0*(1.0d0-double(ik-1)/double(N_ek));
    generate_Hamil();
    sumx=sqrt((X0-dkx)*(X0-dkx)+(Y0-dky)*(Y0-dky)+(Z0-dkz)*(Z0-dkz));
    k_vec(ik+ik_curr)=sumx;...

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