Hex_Lead_Hamiltonians.m

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%%   Eotvos Quantum Transport Utilities - Hex_Lead_Hamiltonians
%    Copyright (C) 2009-2015 Peter Rakyta, Ph.D.
%
%    This program is free software: you can redistribute it and/or modify
%    it under the terms of the GNU General Public License as published by
%    the Free Software Foundation, either version 3 of the License, or
%    (at your option) any later version.
%
%    This program is distributed in the hope that it will be useful,
%    but WITHOUT ANY WARRANTY; without even the implied warranty of
%    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
%    GNU General Public License for more details.
%
%    You should have received a copy of the GNU General Public License
%    along with this program.  If not, see http://www.gnu.org/licenses/.
%
%> @addtogroup lattices Lattices
%> @{
%> @file Hex_Lead_Hamiltonians.m
%> @brief A class to create the Hamiltonian of one unit cell in a translational invariant lead made of hexagonal lattice structure (graphene).
%> @} 
%> @brief A class to create the Hamiltonian of one unit cell in a translational invariant lead made of hexagonal lattice structure (graphene).
%%
classdef Hex_Lead_Hamiltonians
    

methods ( Access = public )
    

%% Graphene_Lead_Hamiltonians
%> @brief Creates Hamiltonians H_0 and H_1 of silicene ribbon with zigzag/armchair edge as well as the structure conatining the coordinates of the atomic sites.
%> @image html graphene.jpg
%> @image latex graphene.jpg
%> @param lead_param An instance of structure #Lattice_Graphene (or its subclass) containing the physical parameters.
%> @param M Number of sites in the cross section of the lead.
%> @param End_Type The orientation of the lattice. Set 'A' for lattice with armchair orientation (meaning zigzag edges) or 'Z' for zizgaz orientation (meaning arm-chair edges)
%> @return [1] The Hamiltonian of one slab in the ribbon. 
%> @return [2] The coupling between the slabs. 
%> @return [3] The transverse coupling between the slabs for transverse calculations. 
%> @return [4] A structure Coordinates containing the coordinates of the sites. 
function [H0, H1, H1_transverse, coordinates] = Graphene_Hamiltonians(obj, lead_param, M, End_Type )
    
    % check the structure containing the physical parameters
    supClasses = superclasses(lead_param);
    if sum( strcmp( supClasses, 'Lattice_Graphene' ) ) == 0
        error(['EQuUs:Lattices:', class(obj), ':Graphene_Hamiltonians'], 'Invalid type of the input parameter');   
    end
    
    if isempty(M)
        error(['EQuUs:', class(obj), ':Graphene_Hamiltonians'], 'The input parameter M is empty')
    end
    
    epsilon = lead_param.epsilon;
    vargamma = lead_param.vargamma;
    deltaAB = lead_param.deltaAB;
    


    if strcmp(End_Type, 'A')
        [H0,H1, H1_transverse, coordinates] = obj.Armchair_End(epsilon,vargamma,M);
    elseif strcmp(End_Type, 'Z')
        [H0, H1, H1_transverse, coordinates] = obj.Zigzag_End(epsilon,vargamma,M);
    else
        error(['EQuUs:', class(obj), ':Graphene_Hamiltonians'], 'Unrecognized Lead type');
    end
    
    % staggered A-B potential tuned by perpendicular electric field   
    H_DeltaAB = sparse( 1:2:M, 1:2:M, deltaAB, size(H0,1), size(H0,2)) + sparse( M+2:2:2*M, M+2:2:2*M, deltaAB, size(H0,1), size(H0,2)) + ...
            sparse( 2:2:M, 2:2:M, -deltaAB, size(H0,1), size(H0,2)) + sparse( M+1:2:2*M, M+1:2:2*M, -deltaAB, size(H0,1), size(H0,2));   
        
    H0 = H0 + H_DeltaAB;
    
%     if ~isempty(q)
%         H0 = H0 + H1_transverse*exp(1i*q) + H1_transverse'*exp(-1i*q);
%     end
    
    
    
    
end


end % methods public

methods ( Access = protected )
    
%> @brief Creates Hamiltonians H_0 and H_1 of silicene ribbon with zigzag edge as well as the structure conatining the coordinates of the atomic sites.
%> @param epsilon The onsite potential.
%> @param vargamma The hopping amplitude.
%> @param M Number of sites in the cross section of the lead.
%> @param q The transverse momentum quantum number.
%> @return [1] The Hamiltonian of one slab in the ribbon. 
%> @return [2] The coupling between the slabs. 
%> @return [3] The transverse coupling between the slabs for transverse calculations. 
%> @return [4] A structure Coordinates containing the coordinates of the sites. 
function [H0,H1,H1_transverse,coordinates] = Armchair_End(obj, epsilon,vargamma,M)
    
    if isempty(M)
        error(['EQuUs:', class(obj), ':Armchair_End'], 'The input parameter M is empty')
    end
    
    
    H0 = sparse( 1:2:M-1, 2:2:M, -vargamma, 2*M, 2*M) + ...
        sparse( M+2:2:2*M-1, M+3:2:2*M, -vargamma, 2*M, 2*M) + ...
        sparse( 1:M, M+1:2*M, -vargamma, 2*M, 2*M);
    H0 = H0 + H0' + sparse( 1:2*M, 1:2*M, epsilon, 2*M, 2*M);
    
    H1 = sparse( M+1:2*M, 1:M, -vargamma, 2*M, 2*M);
    
     
     coordinates = structures('coordinates');
     coordinates.a = zeros(2,1);
     coordinates.x = zeros(2*M,1);
     coordinates.y = zeros(2*M,1);
     deltax1 = 2;
     deltax2 = 1;
     deltay  = sqrt(3)/2;
          
    coordinates.x(1:2:M) = ((1:2:M)-1)*(deltax1+deltax2)/2; %in units rCC
     coordinates.x(2:2:M) = ((2:2:M)-2)*(deltax1+deltax2)/2 + deltax2; %in units rCC
     coordinates.x(M+(1:2:M)) = ((1:2:M)-1)*(deltax1+deltax2)/2 - deltax2/2; %in units rCC
     coordinates.x(M+(2:2:M)) = ((2:2:M)-2)*(deltax1+deltax2)/2 + deltax1 - deltax2/2; %in units rCC        
     coordinates.y = [zeros(M,1); ones(M,1)*deltay]; %in units rCC
    coordinates.a = [0; 2*deltay];% 1D lattice constant in uits of rCC 
    
    if mod(M,2) == 0
        H1_transverse = sparse( 2*M, M+1, -vargamma, 2*M, 2*M);
        %H1_transverse = sparse( M+1, 2*M, -vargamma, 2*M, 2*M);
        coordinates.b = [M/2*3; 0];
    else
           
        H1_transverse = [];
    end
        
end

%% Zigzag_End
%> @brief Creates Hamiltonians H_0 and H_1 of silicene ribbon with armchair edge as well as the structure conatining the coordinates of the atomic sites.
%> @param epsilon The onsite potential.
%> @param vargamma The hopping amplitude.
%> @param M Number of sites in the cross section of the lead.
%> @param q The transverse momentum quantum number.
%> @param varargin Optional parameters (https://www.mathworks.com/help/matlab/ref/varargin.html):
%> @return [1] The Hamiltonian of one slab in the ribbon. 
%> @return [2] The coupling between the slabs. 
%> @return [3] The transverse coupling between the slabs for transverse calculations. 
%> @return [4] A structure Coordinates containing the coordinates of the sites. 
function [H0, H1, H1_transverse, coordinates] = Zigzag_End(obj, epsilon,vargamma,M)
    
    if isempty(M)
        error(['EQuUs:', class(obj), ':Zigzag_End'], 'The input parameter M is empty')
    end

    coordinates = structures('coordinates');
    coordinates.a = [0;3]; %in units rCC
    
    vargamma_nnn = 0*vargamma;
    H0nnn = sparse(1:M, 2*M+1:3*M, -vargamma_nnn, 4*M, 4*M) + sparse(1:M-1, 2*M+2:3*M, -vargamma_nnn, 4*M, 4*M) + sparse(1:M-1, 2:M, -vargamma_nnn, 4*M, 4*M) +...
            sparse(M+1:2*M, 3*M+1:4*M, -vargamma_nnn, 4*M, 4*M) + sparse(M+2:2*M, 3*M+1:4*M-1, -vargamma_nnn, 4*M, 4*M) + sparse(M+1:2*M-1, M+2:2*M, -vargamma_nnn, 4*M, 4*M) +...
            sparse(2*M+1:3*M-1, 2*M+2:3*M, -vargamma_nnn, 4*M, 4*M) + ...
            sparse(3*M+1:4*M-1, 3*M+2:4*M, -vargamma_nnn, 4*M, 4*M);
        
    H1nnn = sparse(3*M+1:4*M, M+1:2*M, -vargamma_nnn, 4*M, 4*M) + sparse(3*M+1:4*M-1, M+2:2*M, -vargamma_nnn, 4*M, 4*M) + ...
        sparse(2*M+1:3*M, 1:M, -vargamma_nnn, 4*M, 4*M) + sparse(2*M+2:3*M, 1:M-1, -vargamma_nnn, 4*M, 4*M);
    
    H0 = sparse(1:M, M+1:2*M, -vargamma, 4*M, 4*M) + sparse(1:M-1, M+2:2*M, -vargamma, 4*M, 4*M) + ...
        sparse(M+1:2*M, 2*M+1:3*M, -vargamma, 4*M, 4*M) + ...
        sparse(2*M+1:3*M, 3*M+1:4*M, -vargamma, 4*M, 4*M) + sparse(2*M+2:3*M, 3*M+1:4*M-1, -vargamma, 4*M, 4*M);
    H0 = H0 + H0' + sparse( 1:4*M, 1:4*M, epsilon, 4*M, 4*M) + H0nnn + H0nnn';
    
    H1 = sparse(3*M+1:4*M, 1:M, -vargamma, 4*M, 4*M) + H1nnn;
    
    
     coordinates.x = zeros(4*M,1); %in units rCC
     coordinates.y = zeros(4*M,1); %in units rCC
    
    coordinates.x(1:M) = sqrt(3)*(1:M) - sqrt(3)/2;  %in units rCC
    coordinates.y(1:M) = 0;  %in units rCC
    
    coordinates.x(M+1:2*M) = sqrt(3)*(0:M-1);  %in units rCC
    coordinates.y(M+1:2*M) = 0.5;  %in units rCC
    
    coordinates.x(2*M+1:3*M) = sqrt(3)*(0:M-1);  %in units rCC
    coordinates.y(2*M+1:3*M) = 1.5;  %in units rCC
    
    coordinates.x(3*M+1:4*M) = sqrt(3)*(1:M) - sqrt(3)/2;  %in units rCC
    coordinates.y(3*M+1:4*M) = 2;  %in units rCC
    
    H1_transverse = sparse(M, M+1, -vargamma, 4*M, 4*M) + sparse(4*M, 2*M+1, -vargamma, 4*M, 4*M);
    %H1_transverse = sparse(M+1, M, -vargamma, 4*M, 4*M) + sparse(2*M+1, 4*M, -vargamma, 4*M, 4*M);
    coordinates.b = [sqrt(3)*M; 0];
    
end

end % methods protected

end