Graphene conductance and dielectric permittivity

Hello,

I'm trying to reproduce the conductance and the dielectric permittivity of graphene, as described in this link: https://support.lumerical.com/hc/en-us/articles/360042244874-Graphene-surface-conductivity-material-model .

To do this, I wrote the following code in MATLAB:

wls_interval=0.3:0.01:5; % wavelength in microns

c=3*10^8; % speed of light

f=(c./(wls_interval*10^-6)); %Hz

w=2*pi.*f; %rad/s

f=f.*10^-12; % frequency in THz

E=1240./(wls_interval*10^3); % energy expressed as 1240/(wls in nanometers)

htag=6.582*10^-16; % reduced Planck constant in eV*s

hconst=htag*2*pi; % Planck constant in eV*s

%w=2*pi*c./(wls_interval.*10^-6);

epsr=1; % relative permittivity of vacuum

e=-1.602*10^-19; % Electron's charge in C

kb=8.617*10^-5; % Boltzmann constant in eV/K

T=300; % Temperature in °K

mu_c=0.2; % Chemical potential in eV

eps0=8.854*10^-12; % Vacuum dielectric permittivity (F/m)

n_sheets=1; %number of sheets by which the graphene layer is made of

t_sheet=0.336*10^-9; % thickness of a graphene sheet in nm

tg=n_sheets*t_sheet; % total thickness of the graphene layer

Gamma=0.41*10^-3; % Scattering rate in eV

parfor i=1:length(E)

%----- Interband contribution numerical -----

FD=@(x) 1./(exp((x-mu_c)./(kb*T))+1); %Fermi-Dirac distribution

den=@(x) (E(i)+1i*2*Gamma).^2-4*(x./htag).^2;

fun=@(x) (FD(-x)-FD(x))./den(x);

eta(i)=1i*e^2*(E(i)+1i*2*Gamma)/(pi*htag^2);

int_term(i)=integral(fun,0,E(i));

sigma_inter(i)=eta(i)*int_term(i);

%----------------------------------------------------------------------------

%----- Intraband contribution analytical -----

alpha(i)=1i*e^2*kb*T/(pi*htag^2*(E(i)+2*1i*Gamma));

beta=mu_c/(kb*T);

sigma_intra(i)=alpha(i)*(beta+2*log(exp(-beta)+1));

sigma_tot(i)=sigma_intra(i)+sigma_inter(i);

eps_graph_par(i)=eps0*(epsr(i)+1i*sigma_tot(i)/(eps0*E(i)*tg));

refind(i)=sqrt(eps_graph_par(i));

end

The results I'm supposed to get are plotted in panel "a" and "b", while the ones I actually get are in panel "d-g". Even though you may notice that the real interband conductivity may resemble to some extent the real total conductivty I'm supposed to get, this is not the case for the imaginary part, that is totally different. Moreover, the order of magnitude is completely out of scale (see panel "c,d"), therefore, the contribution of the interband part is minimal also in the visible range, while it should be significant.

Can you please help me in finding the error?

Thank you so much!

[MINAS KOUROUMPLAKIS]

Try the matlab file Sigma_Graphene.m on this link

https://www.comsol.com/community/exchange/361/

it gives the same result as lumenrical

[mohammad]

Dear Minas Can you please just put the file Sigma_Graphene.m here? Because I think acess to comsol is restricted.

[Prosper]

hi,

i want to use matlab to produce the thermoelectric amplification phonons in graphene ,and i need your assistance