ECE495N-F08-HW_7_solution - sig1=sig*L;sig2=sig*R;

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HW 7 solution Problem 1 Mathematical derivations are already done in the previous HW and practice Exam 2. What you should do here is to multiply by 4 for Density of states and mode density (2 for spin and 2 for valley). clear all % close all L=4e-6;mfp=3e-7; ns=[-1:0.01:1].*2e15; sigma=((4/pi)*mfp*L/(mfp+L))*sqrt(pi*abs(ns)); hold on figure(1) h=plot(ns,sigma, 'r' ); set(h, 'linewidth' ,[2.0]) set(gca, 'Fontsize' ,[20])grid on
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Problem 2 % 2-levels transmission,LDOS clear all g=0.5;zplus=i*1e-12;Np=2;t0=1; H=-t0*diag(ones(1,Np-1),1)-t0*diag(ones(1,Np-1),-1); L=diag([1 zeros(1,Np-1)]);R=diag([zeros(1,Np-1) 1]); H(1,1)=.5;H(2,2)=-.5; ii=1;sigB=zeros(Np);siginB=zeros(Np);dE=0.001; for EE=-2.5:dE:+2.5 sig=-i*0.5*g; %ck=-(EE+zplus)/(2*t0);ka=acos(ck);sig=-t0*exp(i*ka);
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Unformatted text preview: sig1=sig*L;sig2=sig*R; gam1=i*(sig1-sig1');gam2=i*(sig2-sig2'); G=inv(((EE+zplus)*eye(Np))-H-sig1-sig2); A=i*(G-G');D1(ii)=A(1,1)/(2*pi);D2(ii)=A(2,2)/(2*pi); TM(ii)=real(trace(gam1*G*gam2*G')); E(ii)=EE;ii=ii+1; end [V,D]=eig(H) (V(1,1)/V(1,2))*conj(V(1,1)/V(1,2)) (V(2,1)/V(2,2))*conj(V(2,1)/V(2,2)) %% hold on figure(1) h=plot(TM,E, 'b' ); set(h, 'linewidth' ,[2.0]) set(gca, 'Fontsize' ,[36]) xlabel( ' Transmission ---> ' ) ylabel( ' Energy ( eV ) ---> ' ) grid on figure(2) h=plot(D1,E, 'r-.' );hold on ; h=plot(D2,E, 'b-' ); set(h, 'linewidth' ,[2.0]) set(gca, 'Fontsize' ,[36]) xlabel( ' DOS ---> ' ) ylabel( ' Energy ( eV ) ---> ' ) grid on V = -0.5257 -0.8507 -0.8507 0.5257 D = -1.1180 0 0 1.1180 ans = 0.3820 ans = 2.6180...
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ECE495N-F08-HW_7_solution - sig1=sig*L;sig2=sig*R;

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