D:\Learning\NES\Nano_Structure_and_Nanot...\graphene_E_k_script.m Page 1May 11, 2015 3:40:33 PM

% Script for generating the E-k diagram of Graphene

%------------ Input parameters ---------------------%E0 = 0; % coloumb integralV = -2.7; % hopping integralacc = 1.41; % c-c bond lengthlattice = acc*sqrt(3); % Lattice constant

% Creating necessary k-vectorsk_vec_x = linspace(-2*pi/lattice,2*pi/lattice,100);k_vec_y = linspace(-2*pi/lattice,2*pi/lattice,100);[k_mesh_x,k_mesh_y] = meshgrid(k_vec_x, k_vec_y);

% Energy values with the preset parametersenergy_mesh = NaN([size(k_mesh_x,1),size(k_mesh_y,2),2]);for a = 1 : size(k_mesh_x,1) energy_mesh(:,a,1) = (E0 + V*sqrt(1 + (4.*((cos(k_mesh_y(:,a)/2*lattice)).^2)) + (4.*(cos(sqrt(3)/2*lattice*k_mesh_x(:,a))).*(cos(k_mesh_y(:,a)/2*lattice))))); energy_mesh(:,a,2) = (E0 - V*sqrt(1 + (4.*((cos(k_mesh_y(:,a)/2*lattice)).^2)) + (4.*(cos(sqrt(3)/2*lattice*k_mesh_x(:,a))).*(cos(k_mesh_y(:,a)/2*lattice)))));end

% Plottingsurf(k_mesh_x, k_mesh_y, real(energy_mesh(:,:,1)));hold onsurf(k_mesh_x, k_mesh_y, real(energy_mesh(:,:,2)));colormap('jet');shading interphx = xlabel('k_x');hy = ylabel('k_y');hz = zlabel('E(k)');% axis equalhold off