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TightBinding_f.m
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TightBinding_f.m
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%% last update 3Jan2022, lne %%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function[Ek]=TightBinding_f(Vpara,a,k,SpinOrbit)
%sp3s*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%% Semiconductor parameters %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% the "_" is for the "*"
Esa = Vpara(1);
Epa = Vpara(2);
Esc = Vpara(3);
Epc = Vpara(4);
Es_a = Vpara(5);
Es_c = Vpara(6);
Vss = Vpara(7); Vs_s=0; % hopefully...
Vxx = Vpara(8);
Vxy = Vpara(9);
Vsa_pc = Vpara(10);
Vsc_pa = Vpara(11); Vpa_sc = Vsc_pa; % hopefully...
Vs_a_pc = Vpara(12);
Vpa_s_c = Vpara(13);
if SpinOrbit==1
Da = Vpara(14);
Dc = Vpara(15);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for jj=1:length(k(:,1))
kx = k(jj,1)*a/4;
ky = k(jj,2)*a/4;
kz = k(jj,3)*a/4;
g0=+cos(kx)*cos(ky)*cos(kz) -1i*sin(kx)*sin(ky)*sin(kz);
g1=-cos(kx)*sin(ky)*sin(kz) +1i*sin(kx)*cos(ky)*cos(kz);
g2=-sin(kx)*cos(ky)*sin(kz) +1i*cos(kx)*sin(ky)*cos(kz);
g3=-sin(kx)*sin(ky)*cos(kz) +1i*cos(kx)*cos(ky)*sin(kz);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Here is the Vogl notation
% J. Phys. Chem. Solids Vol 44, No. 5, pp365-378, 1983
%Hdiag = [ Esa Esc Epa Epa Epa Epc Epc Epc Es_a Es_c ];
%
%% sa sc pa pa pa pc pc pc sa* sc*
%
%H=[
% 0 Vss*g0 0 0 0 Vsa_pc*g1 Vsa_pc*g2 Vsa_pc*g3 0 0 % sa
% 0 0 -Vpa_sc*g1' -Vpa_sc*g2' -Vpa_sc*g3' 0 0 0 0 0 % sc
% 0 0 0 0 0 Vxx*g0 Vxy*g3 Vxy*g2 0 -Vpa_s_c*g1 % pa
% 0 0 0 0 0 Vxy*g3 Vxx*g0 Vxy*g1 0 -Vpa_s_c*g2 % pa
% 0 0 0 0 0 Vxy*g2 Vxy*g1 Vxx*g0 0 -Vpa_s_c*g3 % pa
% 0 0 0 0 0 0 0 0 Vs_a_pc*g1 0 % pc
% 0 0 0 0 0 0 0 0 Vs_a_pc*g2 0 % pc
% 0 0 0 0 0 0 0 0 Vs_a_pc*g3 0 % pc
% 0 0 0 0 0 0 0 0 0 Vs_s*g0 % sa*
% 0 0 0 0 0 0 0 0 0 0 % sc*
%];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Here is the DiCarlo / Klimeck notation
% Superlattices and Microstructures, Vol. 27, No. 5/6, 2000
% Semicond. Sci. Technol. 18 (2003) R1–R31
Hdiag = [ Esa Epa Epa Epa Es_a Esc Epc Epc Epc Es_c ];
% sa pa pa pa sa* sc pc pc pc sc*
H=[
0 0 0 0 0 Vss*g0 Vsa_pc*g1 Vsa_pc*g2 Vsa_pc*g3 0 % sa
0 0 0 0 0 -Vpa_sc*g1 Vxx*g0 Vxy*g3 Vxy*g2 -Vpa_s_c*g1 % pa
0 0 0 0 0 -Vpa_sc*g2 Vxy*g3 Vxx*g0 Vxy*g1 -Vpa_s_c*g2 % pa
0 0 0 0 0 -Vpa_sc*g3 Vxy*g2 Vxy*g1 Vxx*g0 -Vpa_s_c*g3 % pa
0 0 0 0 0 0 Vs_a_pc*g1 Vs_a_pc*g2 Vs_a_pc*g3 0 % sa*
0 0 0 0 0 0 0 0 0 0 % sc
0 0 0 0 0 0 0 0 0 0 % pc
0 0 0 0 0 0 0 0 0 0 % pc
0 0 0 0 0 0 0 0 0 0 % pc
0 0 0 0 0 0 0 0 0 0 % sc*
];
H=H'+H+diag(Hdiag);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if SpinOrbit==1
H0=zeros(10,10);
H=[H H0 ; H0 H'];
lambdaA=Da/3;
lambdaC=Dc/3;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Hso11=[ 0 0 0 0 0
0 0 -1i 0 0
0 1i 0 0 0
0 0 0 0 0
0 0 0 0 0
];
Hso12=[ 0 0 0 0 0
0 0 0 1 0
0 0 0 -1i 0
0 -1 1i 0 0
0 0 0 0 0
];
Ha11=lambdaA*Hso11; %SO Hamiltonian (up,up) or (1,1) -anion
Hc11=lambdaC*Hso11; %SO Hamiltonian (up,up) or (1,1) -cation
Ha12=lambdaA*Hso12; %SO Hamiltonian (up,down) or (1,2) -anion
Hc12=lambdaC*Hso12; %SO Hamiltonian (up,down) or (1,2) -cation
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
H0=zeros(5,5);
HSO=[ Ha11 H0 Ha12 H0
H0 Hc11 H0 Hc12
Ha12' H0 conj(Ha11) H0
H0 Hc12' H0 conj(Hc11)
];
H=H+HSO;
end
Ek(:,jj) = eig(H);
end
end