-
Notifications
You must be signed in to change notification settings - Fork 7
/
kp_6bands_Luttinger_DKK_f.m
66 lines (46 loc) · 1.76 KB
/
kp_6bands_Luttinger_DKK_f.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
function[E]=kp_6bands_Luttinger_DKK_f(k_list, Dso, g1, g2, g3)
% DKK model: Dresselhaus, Kip and Kittel
% Calin Galeriu
% PhD thesis: "k.p Theory of semiconductor nanostructures" (2005)
% Chapter 3, page 26
% Download:
% https://web.wpi.edu/Pubs/ETD/Available/etd-120905-095359/unrestricted/cgaleriu.pdf
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%% Constants %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
h=6.62606896E-34; %% Planck constant [J.s]
hbar=h/(2*pi);
e=1.602176487E-19; %% charge de l electron [Coulomb]
m0=9.10938188E-31; %% electron mass [kg]
H0=hbar^2/(2*m0) ;
Dso=Dso*e;
L = H0*(-1-g1-4*g2);
M = H0*(-1-g1+2*g2);
N = -H0*6*g3;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%% Building of the Hamiltonien %%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i=1:length(k_list(:,1))
kx = k_list(i,1);
ky = k_list(i,2);
kz = k_list(i,3);
k=sqrt(kx.^2 + ky.^2 + kz.^2);
Hdiag = H0*k^2 - Dso/3*ones(1,6);
H_DKK=[
L*kx^2+M*(ky^2+kz^2) N*kx*ky N*kx*kz
N*kx*ky L*ky^2+M*(kx^2+kz^2) N*ky*kz
N*kx*kz N*ky*kz L*kz^2+M*(kx^2+ky^2)
];
Hso=[
0 1 0 0 0 1i
-1 0 0 0 0 1
0 0 0 -1i -1 0
0 0 -1i 0 -1 0
0 0 1 1 0 0
1i -1 0 0 0 0
];
H = diag(Hdiag) + [H_DKK zeros(3,3) ; zeros(3,3) H_DKK] + Hso*Dso/(3i);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
E(:,i) = eig(H)/e ;
end
end