%Figure 8.4
%p-type dispersion for single pair excitation

clear all;
clf;
colormap(jet);
xmax=4;                 %max value of scattered wave vector, q/kf
ymax=20;                %max value of energy loss, omega/Ef
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 (blue)
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 (red)
Yhh2lhfhhEf1=(mhh/mlh)*((xhh+1).^2)-1; 
Yhh2lhfhhEf2=(mhh/mlh)*((xhh-1).^2)-1;

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

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

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



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

ttl2=['GaAs, m^*_{hh} = ',num2str(mhh),...
    ', m_{lh} = ',num2str(mlh)];
title(ttl2);



