conductivity of graphene.rar_Kubo公式_Kubo公式转换_kubo石墨烯_石墨烯电导_表面电导率

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % Calculation of Conductivity of Graphene using Kubo Formula % % Author: Ashkan Vakil % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clc clear; j = sqrt(-1); e = 1.6e-19; KB = 1.3806503e-23; T = 3; hb = (6.626e-34)/(2*pi); % tau = 3e-12; % form GW Hanson paper % tau = .64e-12; % Soljacic paper % gamma = 1/(2*tau); gamma = 0.65460252158e12; % Gusynin J. Phys.: Cond. Mat. sigmamin = 6.085e-5; vf = 10^6; w = pi*2e12*linspace(5,400,200); % CO2 lasers are this range m = length(w); muc = 1.6e-19*[.15]; n = length(muc); muct = repmat(muc,m,1); % generating the matrix for chemical potential wt = repmat(transpose(w),1,n); % generating the matrix forfrequency sigmadintra = ... -j*((e^2*KB*T)./(pi*hb^2*(wt-j*2*gamma))).*((muct)/(KB*T)... +2*log(exp(-muct/(KB*T))+1)); %intraband term sigmadinter = zeros(m,n); % interband term variable definition eps = 1.6e-19*linspace(0,10,600000); q = length(eps); % Interband term calculations for i = 1:n muc = muc(i); fdmeps = 1./(1+exp((-eps-muc)/(KB*T))); fdpeps = 1./(1+exp((eps-muc)/(KB*T))); for k = 1:m sigmadinter(k,i) = ... trapz(eps,-(j*e^2*(w(k)-j*2*gamma)/(pi*hb^2))... *(fdmeps-fdpeps)./((w(k)-j*2*gamma)^2-4*(eps/hb).^2)); end end sigmatot = sigmadinter+sigmadintra; % total conductivity C = { 'k','r','b','c','g','m','y' }; p1 = zeros(1,n); pp1 = zeros(1,n); s1 = cell(1, n); p2 = zeros(1,n); pp2 = zeros(1,n); s2 = cell(1, n); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figure(1) subplot(2,1,1) for i = 1:n hold on p1(i)=plot(1e-12*w/2/pi,(transpose(real((sigmadinter(:,i)))))/... (e^2/hb/4),'Linewidth',2);hold on pp1(i)=plot(1e-12*w/2/pi,(transpose(real((sigmadintra(:,i)))))/... (e^2/hb/4),'Linewidth',2,'Linestyle','-.');hold on s1(i) = sprintf('mu {c,%d} = %d meV',i,1e3*muc(i)/(1.6e-19)); end ind = 1:n; % axis square box on xlabel('f (THZ)','fontsize',20,'fontweight','b'); ylabel('Re(\sigma)','fontsize',20,'fontweight','b'); legend(p1(ind), s1{ind}); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %figure(2) subplot(2,1,2) hold on for i = 1:n hold on p2(i) = ... plot(1e-12*w/2/pi,-(transpose(imag((sigmadinter(:,i)))))/... (e^2/hb/4),'Color', C(i),'Linewidth',2);hold on pp2(i) = ... plot(1e-12*w/2/pi,-(transpose(imag((sigmadintra(:,i)))))/... (e^2/hb/4),'Color', ... C(i),'Linewidth',2,'Linestyle','-.');hold on s2(i) = sprintf('mu {c,%d} = %d meV',i,1e3*muc(i)/(1.6e-19)); end % axis square box on xlabel('f (THZ)','fontsize',20,'fontweight','b'); ylabel('Im(\sigma)','fontsize',20,'fontweight','b'); % legend(p2(ind), s2{ind});