%Figure 8.7
%p-type dispersion for single pair excitation
%parabola of integration

clear all;
clf;
colormap(jet);
xmax=4;        %max value of scattered wave vector, q/kf
ymax=20;       %max value of energy loss, omega/Ef
me =0.07;      %electron mass
Yk =10;        %Ek/EF initial electron kinetic energy in conduction band
mhh=0.5;       %heavy hole mass
mlh=0.082;     %light hole mass
xhh=linspace(0,xmax,100);     %{0.01 6.01}, {0.1 60.01}

%Heavy to light hole Fermi energy transition (cyan)
Yhh2lhEf1=1-(sqrt(mlh/mhh)-xhh).^2; 
Yhh2lhEf2=1-(sqrt(mlh/mhh)+xhh).^2;

%Heavy hole to light hole transition from haevy hole Fermi energy (magneta)
Yhh2lhfhhEf1=(mhh/mlh)*((xhh+1).^2)-1; 
Yhh2lhfhhEf2=(mhh/mlh)*((xhh-1).^2)-1;

%Light to heavy hole transition from light hole fermi energy (blue)
Ylh2hhlh1=((xhh+sqrt(mlh/mhh)).^2)-1; 
Ylh2hhlh2=((xhh-sqrt(mlh/mhh)).^2)-1;

%Heavy hole to Heavy hole transition (red)
Yhh2hh1=xhh.*(xhh+2); 
Yhh2hh2=xhh.*(xhh-2);

%Light hole to light hole transition (green)
Ylh2lh1=(mhh/mlh)*(xhh.^2)+(2*sqrt(mhh/mlh))*xhh; 
Ylh2lh2=(mhh/mlh)*(xhh.^2)-(2*sqrt(mhh/mlh))*xhh;

%parabola of integration
Y=Yk-(mhh/me)*((xhh-sqrt((me/mhh)*Yk)).^2);

figure(1);
plot(xhh,Yhh2lhEf1,'c');
hold on;
plot(xhh,Yhh2lhEf2,'c');
plot(xhh,Yhh2lhfhhEf1,'m');
plot(xhh,Yhh2lhfhhEf2,'m');
plot(xhh,Ylh2hhlh1,'b');
plot(xhh,Ylh2hhlh2,'b');
plot(xhh,Yhh2hh1,'r');
plot(xhh,Yhh2hh2,'r');
plot(xhh,Ylh2lh1,'g')
plot(xhh,Ylh2lh2,'g')
plot(xhh,Y,'k')
hold off
axis([0 xmax 0 ymax]);%([0 6 0 6*Ef])
yttl=['Energy loss, Y'];
ylabel(yttl);
xlabel('Wavevector, X_{hh}');

ttl2=['\rm GaAs, m^*_{hh} = ',num2str(mhh),...
    ', m^*_{lh} = ',num2str(mlh),', m^*_{e} = ',num2str(me),...
    ', E_k/E_F = ',num2str(Yk)];
title(ttl2);