# HW5soln - for ii=2:length(kpath)

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clear; Vpp=-3; %p_z overlap parameter %nearest-neighbor vectors n1=[1/sqrt(3) 0]; n2=[-1/(2*sqrt(3)) 1/2]; n3=[-1/(2*sqrt(3)) -1/2]; % basis vectors d1=[0 0]; d2=n1; %define path along IBZ perimeter Gamma=[0 0]; K=[0 4*pi/3]; M=[pi/sqrt(3) pi]; kpath=[Gamma; K; M; Gamma]; kpathstring=char('Gamma', 'K', 'M', 'Gamma'); N=100; %number of k points from Gamma to K ks=[]; for ii=1:(length(kpath)-1) thispath=[]; for jj=1:2 thispath=[ thispath [linspace(kpath(ii,jj),kpath(ii+1,jj), round(N*norm(kpath(ii,:)-kpath(ii+1,:))))']]; end ks=[ks; thispath]; text(kpath(ii,1)/pi,kpath(ii,2)/pi,kpathstring(ii,:)); end for kk=1:length(ks) k=ks(kk,:); f=exp(i*k*n1')+exp(i*k*n2')+exp(i*k*n3'); H=[0 Vpp*f; Vpp*f' 0]; eigH(:,kk)=eig(H); end Emax=10; TEXTY=0.75; figure(1); plot(1:length(ks),eigH); hold on; set(gca,'XTick',[]) %no x tick marks ylabel('Energy [eV]') axis([1 length(ks) -Emax Emax]); pathlength=0; text(0,-(Emax+TEXTY),kpathstring(1));

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Unformatted text preview: for ii=2:length(kpath) pathlength(ii)=round(N*norm(kpath(ii,:)-kpath(ii-1,:))); text(sum(pathlength), -(Emax+TEXTY), kpathstring(ii)); end Vlinesx=repmat(cumsum(pathlength),2,1); Vlinesy=repmat([-Emax; Emax], 1, length(kpath)); plot(Vlinesx,Vlinesy,'k'); hold off; Es=-7.3; Ep=0.0; Vsss=-4.8; Vsps=4.75; Vpps=4.39; Vppp=-2.56; H11=diag([Es Ep Ep Ep]); for kk=1:length(ks) k=ks(kk,:); f0=exp(i*k*n1')+exp(i*k*n2')+exp(i*k*n3'); f1=exp(i*k*n2')+exp(i*k*n3'); f2=exp(i*k*n2')-exp(i*k*n3'); H12=[Vsss*f0 Vsps*(exp(i*k*n1')-0.5*f1) Vsps*sqrt(3)/2*f2 0; . ..-Vsps*(exp(i*k*n1')-0.5*f1) Vpps*(exp(i*k*n1')+1/4*f1)+3/4*Vppp*f1 -sqrt(3)/4*(Vpps-Vppp)*f2 0 ; . ..-Vsps*sqrt(3)/2*f2 -sqrt(3)/4*(Vpps-Vppp)*f2 Vppp*(exp(i*k*n1')+1/4*f1)+3/4*Vpps*f1 0 ;... 0 0 0 Vppp*f0]; H=[H11 H12; H12' H11]; eigH(:,kk)=eig(H); end...
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## This note was uploaded on 12/29/2011 for the course PHYSICS 731 taught by Professor Appelbaum during the Fall '11 term at Maryland.

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HW5soln - for ii=2:length(kpath)

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