added start of conductivity calculations

2D-Conductivity/conductivity_calc_surface.m

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+%% conductivity_calc_surface.m
+%%
+%% calculate and present 2D sheet conductivty for graphene
+
+close all; clear all; clc;
+
+DISPLAY_HZ = true;
+MAX_F = 1e12; % Hz
+F_TOTAL = 1e3;
+MAX_Y = 10; % ev
+Y_TOTAL = 100;
+
+f_vals = 1:MAX_F/F_TOTAL:MAX_F; % hz
+f_vals = f_vals .* (2*pi); % rads-1
+
+y_vals = 1:MAX_Y/Y_TOTAL:MAX_Y; % ev
+%y_vals = y_vals + 273.15;
+
+cond = zeros(length(f_vals), length(y_vals));
+for freq=1:length(f_vals)
+    for y=1:length(y_vals)
+        % omega (rads-1), fermi_level (J), temp (K), scatter_lifetime (s-1)
+        cond(freq, y) = sheet_conductivity(f_vals(freq), ev_to_j(y_vals(y)), 300, 5e-12);
+    end
+end
+
+if DISPLAY_HZ % divide radians back to hertz
+    f_vals = f_vals ./ (2*pi);
+end
+
+surf(f_vals, y_vals, transpose(abs(cond)));
+
+h = gca;
+rotate3d on
+grid();
+set(h, 'xscale', 'log')
+title('2D Sheet Conductivity');
+ylabel('Fermi Level (ev)');
+zlabel('Conductivity (S/m)');
+if DISPLAY_HZ
+    xlabel('Frequency (Hz)');
+else
+    xlabel('Frequency (rads-1)');
+end

2D-Conductivity/conductivity_calculations.m

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+%% conductivity_calculations.m
+%%
+%% calculate and present 2D sheet conductivty for graphene
+
+close all; clear all; clc;
+
+DISPLAY_HZ = true;
+MAX_F = 1e12;
+F_TOTAL = 1e4;
+
+x_vals = 1:MAX_F/F_TOTAL:MAX_F; % hz
+x_vals = x_vals .* (2*pi); % rads-1
+
+% omega (rads-1), fermi_level (J), temp (K), scatter_lifetime (s-1)
+cond = arrayfun(@(x) sheet_conductivity(x, ev_to_j(3), 300, 5e-12), x_vals);
+
+if DISPLAY_HZ % divide radians back to hertz
+    x_vals = x_vals ./ (2*pi);
+end
+
+%plot(x_vals, cond);
+semilogx(x_vals, cond);
+
+grid();
+title('2D Sheet Conductivity');
+ylabel('Conductivity (S/m)');
+if DISPLAY_HZ
+    xlabel('Frequency (Hz)');
+else
+    xlabel('Frequency (rads-1)');
+end

2D-Conductivity/ev_to_j.m

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+function J = ev_to_j(electron_volts)
+%EV_TO_J Transform electron-volts into Joules
+J = electron_volts * 1.602e-19;
+end
+

2D-Conductivity/hz_to_omega.m

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+function omega = hz_to_omega(Hz)
+%HZ_TO_OMEGA Transform Hz into angular frequency
+omega = 2*pi*Hz;
+end
+

2D-Conductivity/sheet_conductivity.m

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+function conductivity = sheet_conductivity(omega, fermi_level, temp, scatter_lifetime)
+%SHEET_CONDUCTIVITY Calculate 2D sheet conductivity
+
+%% CONSTANTS
+e = 1.602e-19; % coulombs
+kb = physconst('Boltzmann'); % J/K
+hbar = 6.626e-34 / (2*pi); % Js
+
+%% TERM 1
+term1_coeff = (2i*(e^2)*kb*temp) ...
+                    / ...
+                (pi*hbar^2*(omega + (1i/scatter_lifetime)));
+term1 = log(2*cosh(fermi_level ...
+                    / ...
+                (2*kb*temp)));
+
+%% TERM 2
+term2_coeff = (e^2) ...
+                / ...
+            (4*hbar);
+
+term_2_term_1 = 1/2;
+term_2_term_2 = (1/pi) * ...
+            atan((hbar*omega - 2*fermi_level) ...
+                    / ...
+                (2*kb*temp));
+
+term_2_term_3 = (1i/2*pi) * ...
+            log((hbar*omega + 2*fermi_level)^2 ...
+                    / ...
+                ((hbar*omega - 2*fermi_level)^2 + 4*((kb*temp)^2)));
+
+%% OUTPUT
+conductivity = term1_coeff*term1 + term2_coeff*(term_2_term_1 + term_2_term_2 - term_2_term_3);
+
+end
+