mirror of
https://github.com/c-sooyoung/fold_slice.git
synced 2026-09-18 00:49:09 +09:00
91 lines
3.5 KiB
Matlab
91 lines
3.5 KiB
Matlab
% Calculate ZincBlende Bandstructure from Walter Harrison's book with an
|
|
% added extra s* state for the Conduction band (labelled as t since * inside
|
|
% variable names is not allowed) as in Vogl's paper
|
|
|
|
%Onsite energies are given for cation then anion (same for elemental)
|
|
% e.g. ecs is energy for cation s, eap is energy for anion p.
|
|
|
|
hm = 7.62; % hbar^2/m in eV.A^2
|
|
|
|
% Cubic lattice constant
|
|
alat = 5.65; % GaAs lattice constant
|
|
|
|
% GaAs
|
|
% Onsite Matrix elements (in eV)
|
|
eas = -8.3431;
|
|
eap = 1.0414;
|
|
eat = 8.5914;
|
|
|
|
ecs = -2.6569;
|
|
ecp = 3.6686;
|
|
ect = 6.7386;
|
|
|
|
|
|
%vectors to neighboring cations
|
|
d1 = alat/4 * [1 1 1];
|
|
d2 = alat/4 * [1 -1 -1];
|
|
d3 = alat/4 * [-1 1 -1];
|
|
d4 = alat/4 * [-1 -1 1];
|
|
d = [d1; d2; d3; d4];
|
|
|
|
%phase factors
|
|
g0 = inline('exp(i*k*transpose(d(1,:)))+exp(i*k*transpose(d(2,:)))+exp(i*k*transpose(d(3,:)))+exp(i*k*transpose(d(4,:)))','k','d');
|
|
g1 = inline('exp(i*k*transpose(d(1,:)))+exp(i*k*transpose(d(2,:)))-exp(i*k*transpose(d(3,:)))-exp(i*k*transpose(d(4,:)))','k','d');
|
|
g2 = inline('exp(i*k*transpose(d(1,:)))-exp(i*k*transpose(d(2,:)))+exp(i*k*transpose(d(3,:)))-exp(i*k*transpose(d(4,:)))','k','d');
|
|
g3 = inline('exp(i*k*transpose(d(1,:)))-exp(i*k*transpose(d(2,:)))-exp(i*k*transpose(d(3,:)))+exp(i*k*transpose(d(4,:)))','k','d');
|
|
|
|
%Interatomic Matrix Elements (eV) using Harrison's universal parameters
|
|
dn = norm(d1);
|
|
|
|
% Composite Matrix elements
|
|
Ess = -1.4054* hm/dn^2;
|
|
Esp = 1.0392*(hm/dn^2);
|
|
Exx = 0.3111*(hm/dn^2);
|
|
Exy = 0.8298*(hm/dn^2);
|
|
Etp = 0.9549* hm/dn^2; % Harrison parameter for s*ps from Vtps*dn^2/hm
|
|
Ett = 0; % In Dow's model no coupling between s* states on adjacent atoms is allowed
|
|
|
|
|
|
% Zone boundary and number of k points
|
|
qbz = 2*pi/alat;
|
|
nk=20;
|
|
j=1;
|
|
|
|
E=1;clear E;
|
|
kx=1; clear kx;
|
|
for q=0:qbz/nk:qbz,
|
|
k = [q 0 0];
|
|
|
|
%LCAO hamiltonian for the zincblende structure
|
|
% Calculate Upper Half of the LCAO Hamiltonian Matrix and use its
|
|
% Hermiticity to get lower half
|
|
Hu = [[ ecs/2 Ess *g0(k,d) 0 0 0 Esp*g1(k,d) Esp * g2(k,d) Esp* g3(k,d) 0 0];
|
|
[ 0 eas/2 -Esp * conj(g1(k,d)) -Esp * conj(g2(k,d)) -Esp * conj(g3(k,d)) 0 0 0 0 0];
|
|
[ 0 0 ecp/2 0 0 Exx * g0(k,d) Exy * g3(k,d) Exy * g2(k,d) 0 -Etp * g1(k,d)];
|
|
[ 0 0 0 ecp/2 0 Exy * g3(k,d) Exx * g0(k,d) Exy * g1(k,d) 0 -Etp * g2(k,d) ];
|
|
[ 0 0 0 0 ecp/2 Exy * g2(k,d) Exy * g1(k,d) Exx * g0(k,d) 0 -Etp * g3(k,d)];
|
|
[ 0 0 0 0 0 eap/2 0 0 Etp * g1(k,d) 0 ];
|
|
[ 0 0 0 0 0 0 eap/2 0 Etp * g2(k,d) 0 ];
|
|
[ 0 0 0 0 0 0 0 eap/2 Etp * g3(k,d) 0 ];
|
|
[ 0 0 0 0 0 0 0 0 eat/2 Ett *g0(k,d) ];
|
|
[ 0 0 0 0 0 0 0 0 0 eat/2];
|
|
];
|
|
|
|
%Its adjoint
|
|
Hd = (Hu)';
|
|
|
|
%The full Hermitian Matrix
|
|
H = Hu+Hd;
|
|
|
|
%Calculate Eigenvalues
|
|
E(j,:) = eig(H)';
|
|
kx(j)=q;
|
|
j=j+1;
|
|
|
|
end;
|
|
|
|
|
|
plot(kx,E,'k');
|
|
ylabel('Energy (eV)');
|
|
|