Graphene_SOC_Lead_Hamiltonians.m

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%%   Eotvos Quantum Transport Utilities - Graphene_SOC_Lead_Hamiltonians
%    Copyright (C) 2018 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 Graphene_SOC_Lead_Hamiltonians.m
%> @brief A class to create the Hamiltonian of one unit cell in a translational invariant graphene lead, including Rashba-type, intrinsic and valley-Zeeman spin-orbit coupling
%> @} 
%> @brief A class to create the Hamiltonian of one unit cell in a translational invariant graphene lead, including Rashba-type, intrinsic and valley-Zeeman spin-orbit coupling
%%
classdef Graphene_SOC_Lead_Hamiltonians < Hex_Lead_Hamiltonians
    

methods ( Access = public )
    
 

%% Graphene_SOC_Lead_Hamiltonians
%> @brief Creates Hamiltonians H_0 and H_1 of graphene ribbon with zigzag/armchair edge including SOC as well as the structure conatining the coordinates of the atomic sites.
%> @image html graphene_SOC.jpg
%> @image latex graphene_SOC.jpg
%> @param lead_param An instance of structure #Lattice_Graphene_SOC (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, H1_skew_left,H1_skew_right, coordinates] = Graphene_SOC_Hamiltonians(obj, lead_param, M, End_Type )
    
    % check the structure containing the physical parameters
    supClasses = superclasses(lead_param);
    if sum( strcmp( supClasses, 'Lattice_Graphene_SOC' ) ) == 0
        error(['EQuUs:Lattices:', class(obj), ':Graphene_SOC_Lead_Hamiltonians'], 'Invalid type of the input parameter');   
    end
    
    if isempty(M)
        error(['EQuUs:Lattices:', class(obj), ':Graphene_SOC_Lead_Hamiltonians'], 'The input parameter M is empty')
    end    
    
    [H0_spindown,H1_spindown,H1_transverse_spindown,coordinates_spindown] = obj.Graphene_Hamiltonians(lead_param, M, End_Type);
    
    coordinates_spindown.z = zeros(size(coordinates_spindown.x));
    
    H0_spinup = H0_spindown;
    H1_spinup = H1_spindown;
    H1_transverse_spinup = H1_transverse_spindown;
    
    lambda = lead_param.Rashba;
    
    if strcmp(End_Type, 'A')
    
        % ******* Rashba-type SOC *************
        
        % unity vectors pointing towards the neighbour sites
        d1 = [0.5; -sqrt(3)/2]; 
        d2 = [0.5; sqrt(3)/2]; 
        d3 = [-1; 0];           
        
        % the vectorial product of the Pauli matrices and the vectors d_i according to Phys. Rev. B 82, 113405
        d1 = d1(2)+1i*d1(1);
        d2 = d2(2)+1i*d2(1);
        d3 = d3(2)+1i*d3(1);
        
        % The matrix size
        Meff = 2*M;
       
        % The Rashba SOC coupling in H0 from spin down to spin up
        HSO_d1 = sparse(1:2:M, M+1:2:2*M, 1i*lambda*d1,Meff,Meff) + sparse(M+1:2:2*M, 1:2:M,-1i*lambda*d1,Meff,Meff); 
        HSO_d2 = sparse(M+2:2:2*M, 2:2:M, 1i*lambda*d2,Meff,Meff) + sparse(2:2:M ,M+2:2:2*M,-1i*lambda*d2,Meff,Meff);
        HSO_d3 = sparse(2:2:M, 1:2:M, -1i*lambda*d3,Meff,Meff) + sparse(M+3:2:2*M-1, M+2:2:2*M-2, -1i*lambda*d3,Meff,Meff) + sparse(1:2:M, 2:2:M, 1i*lambda*d3,Meff,Meff) + sparse(M+2:2:2*M-2, M+3:2:2*M-1, 1i*lambda*d3,Meff,Meff);   
        HSO    = HSO_d1 + HSO_d2 + HSO_d3;
        
        % setting SOC in H0
        H0     = [H0_spinup,HSO;HSO',H0_spindown];
    
        % The Rshba SOC coupling in H1 from spin down to spin up
        H1_SO_d1 = sparse(M+2:2:2*M, 2:2:M, 1i*lambda*d1, Meff, Meff);
        H1_SO_d2 = sparse(M+1:2:2*M, 1:2:M, -1i*lambda*d2, Meff, Meff);
        H1_SO_spinup_spindown = H1_SO_d1 + H1_SO_d2; 
        
        % The Rshba SOC coupling in H1 from spin up to spin down        
        H1_SO_d1 = sparse(M+2:2:2*M, 2:2:M, 1i*lambda*conj(d1), Meff, Meff);
        H1_SO_d2 = sparse(M+1:2:2*M, 1:2:M, -1i*lambda*conj(d2), Meff, Meff);
        H1_SO_spindown_spinup = H1_SO_d1 + H1_SO_d2; 
        
        % setting SOC in H1
        H1 = [H1_spinup, H1_SO_spinup_spindown; H1_SO_spindown_spinup, H1_spindown];
        
    
        
        % The Rshba SOC coupling in H_transverse from spin down to spin up    
        if ~isempty(H1_transverse_spindown)
            
            H1_transverse_SO_spinup_spindown = sparse(2*M, M+1, 1i*lambda*d3, Meff, Meff);
            H1_transverse_SO_spindown_spinup = sparse(2*M, M+1, 1i*lambda*conj(d3), Meff, Meff);
            
            % setting SOC in H_transverse
            H1_transverse = [ H1_transverse_spindown, H1_transverse_SO_spinup_spindown;
                        H1_transverse_SO_spindown_spinup, H1_transverse_spinup];
                    
                    
            H1_skew_left = [];
            H1_skew_right = [];
                    
            
        else
            H1_transverse = [];
        end        
        
        % ******* Intrinsic and valley-Zeeman SOC *************
        
        SOintrinsic = lead_param.Intrinsic;
        SOvalley_zeeman = lead_param.ValleyZeeman;
        
        % intrinsic SO coupling in the unit cell for the spin up subspace
        Meff = 2*M;
        H0_SOintrinsic = sparse( M+1:2:2*M-1, 2:2:M, 1i*(SOintrinsic-SOvalley_zeeman), Meff, Meff) + ... clockwise deirection, B sublattice
                        sparse( 1:2:M-1, M+2:2:2*M, 1i*(SOintrinsic+SOvalley_zeeman), Meff, Meff) + ... clockwise deirection, A sublattice
                        sparse( M+3:2:2*M-1, 2:2:M-2, 1i*(SOintrinsic-SOvalley_zeeman), Meff, Meff) + ... clockwise deirection, B sublattice
                        sparse( 3:2:M-1, M+2:2:2*M-2, 1i*(SOintrinsic+SOvalley_zeeman), Meff, Meff); ... clockwise deirection, A sublattice
                        
        H0_SOintrinsic = H0_SOintrinsic + H0_SOintrinsic'; % clockwise deirection and counterclockwise directions
        
        % expanding the Hamiltonian to the full spin space
        H0_SOintrinsic = kron( [1,0;0,-1], H0_SOintrinsic);
        H0 = H0 + H0_SOintrinsic;
                    
    
        H1_SOintrinsic = sparse( M+2:2:2*M, 1:2:M-1, 1i*(SOintrinsic+SOvalley_zeeman), Meff, Meff) + ... clockwise deirection, A sublattice
                        sparse( 2:2:M, 2:2:M, 1i*(SOintrinsic-SOvalley_zeeman), Meff, Meff) + ... clockwise deirection, B sublattice
                        sparse( M+1:2:2*M-1, M+1:2:2*M-1, 1i*(SOintrinsic-SOvalley_zeeman), Meff, Meff) + ... clockwise deirection, B sublattice
                        sparse( M+2:2:2*M-2, 3:2:M-1, 1i*(SOintrinsic+SOvalley_zeeman), Meff, Meff) + ... clockwise deirection, A sublattice
                        sparse( M+1:2:2*M-1, 2:2:M, -1i*(SOintrinsic-SOvalley_zeeman), Meff, Meff) + ... counterclockwise deirection, B sublattice
                        sparse( 1:2:M-1, 1:2:M-1, -1i*(SOintrinsic+SOvalley_zeeman), Meff, Meff) + ... counterclockwise deirection, A sublattice                      
                        sparse( M+2:2:2*M, M+2:2:2*M, -1i*(SOintrinsic+SOvalley_zeeman), Meff, Meff) + ... counterclockwise deirection, A sublattice
                        sparse( M+3:2:2*M-1, 2:2:M-2, -1i*(SOintrinsic-SOvalley_zeeman), Meff, Meff); ... counterclockwise deirection, B sublattice
                    
                        
        % expanding the Hamiltonian to the full spin space
        H1_SOintrinsic = kron( [1,0;0,-1], H1_SOintrinsic);
        H1 = H1 + H1_SOintrinsic;
        
        
        
        % The Intrinsic SOC coupling in H_transverse from spin down to spin up    
        if ~isempty(H1_transverse_spindown)
            
            H1_transverse_SOintrinsic = sparse(M, M+1, -1i*(SOintrinsic-SOvalley_zeeman), Meff, Meff) + ... counterclockwise deirection, B sublattice
                                        sparse(2*M, 1, -1i*(SOintrinsic+SOvalley_zeeman), Meff, Meff); ... counterclockwise deirection, A sublattice
            
            % expanding the Hamiltonian to the full spin space
            H1_transverse_SOintrinsic = kron( [1,0;0,-1], H1_transverse_SOintrinsic);
            H1_transverse = H1_transverse + H1_transverse_SOintrinsic;
            
            
            H1_skew_left_SOintrinsic = sparse(2*M, 1, 1i*(SOintrinsic+SOvalley_zeeman), Meff, Meff); ... clockwise deirection, A sublattice
                
            % expanding the Hamiltonian to the full spin space
            H1_skew_left = kron( [1,0;0,-1], H1_skew_left_SOintrinsic); 
            
            
        
            H1_skew_right_SOintrinsic = sparse(M, M+1, 1i*(SOintrinsic-SOvalley_zeeman), Meff, Meff); ...clockwise deirection, B sublattice
                
            % expanding the Hamiltonian to the full spin space
            H1_skew_right = kron( [1,0;0,-1], H1_skew_right_SOintrinsic); 
            
        else
            H1_transverse = [];
            H1_skew_left = [];
            H1_skew_right = [];
        end        
        
        
        
        
               
            
            
    % armchair edged bilayer ribbon: warping checked, but not for H1_transverse
    elseif strcmp(End_Type, 'Z')
        
        % unity vectors pointing towards the neighbour sites
        d1 = [sqrt(3)/2; 0.5]; 
        d2 = [-sqrt(3)/2; 0.5]; 
        d3 = [0; -1];           
              

        % the vectorial product of the Pauli matrices and the vectors d_i according to Phys. Rev. B 82, 113405
        d1 = d1(2)+1i*d1(1);
        d2 = d2(2)+1i*d2(1);
        d3 = d3(2)+1i*d3(1);
        
        % The matrix size
        Meff = 4*M;
   
        % The Rashba SOC coupling in H0 from spin down to spin up
        HSO_d1 = sparse(M+2:2*M, 1:M-1, 1i*lambda*d1, Meff, Meff) + sparse(3*M+1:4*M, 2*M+1:3*M, 1i*lambda*d1, Meff, Meff) + ...
                sparse(1:M-1, M+2:2*M, -1i*lambda*d1, Meff, Meff) + sparse(2*M+1:3*M, 3*M+1:4*M, -1i*lambda*d1, Meff, Meff); 
        HSO_d2 = sparse(M+1:2*M, 1:M, 1i*lambda*d2, Meff, Meff) + sparse(3*M+1:4*M-1, 2*M+2:3*M, 1i*lambda*d2, Meff, Meff) + ...
            sparse(1:M, M+1:2*M, -1i*lambda*d2, Meff, Meff) + sparse(2*M+2:3*M, 3*M+1:4*M-1, -1i*lambda*d2, Meff, Meff);
    
        HSO_d3 = sparse(M+1:2*M, 2*M+1:3*M, 1i*lambda*d3, Meff, Meff) + sparse(2*M+1:3*M, M+1:2*M, -1i*lambda*d3, Meff, Meff);   
        HSO    = HSO_d1 + HSO_d2 + HSO_d3;
        
        % setting SOC in H0
        H0     = [H0_spinup,HSO;HSO',H0_spindown];    
    
        
    
        % The Rashba SOC coupling in H1 from spin down to spin up
        H1_SO_d3 = sparse(3*M+1:4*M, 1:M, 1i*lambda*d3, Meff, Meff);
        H1_SO_spinup_spindown = H1_SO_d3; 
        
        % The Rashba SOC coupling in H1 from spin up to spin down        
        H1_SO_d3 = sparse(3*M+1:4*M, 1:M, 1i*lambda*conj(d3), Meff, Meff);
        H1_SO_spindown_spinup = H1_SO_d3; 
        
        % setting SOC in H1
        H1 = [H1_spinup, H1_SO_spinup_spindown; H1_SO_spindown_spinup, H1_spindown];
        
        
        
        % The Rshba SOC coupling in H_transverse from spin down to spin up    
        if ~isempty(H1_transverse_spindown)
            
            % The Rshba SOC coupling in H1 from spin down to spin up
            H1_transverse_SO_d1 = sparse(M, M+1, -1i*lambda*d1, Meff, Meff);
            H1_transverse_SO_d2 = sparse(4*M, 2*M+1, 1i*lambda*d2, Meff, Meff);
            H1_transverse_SO_spinup_spindown = H1_transverse_SO_d1 + H1_transverse_SO_d2; 
        
            % The Rshba SOC coupling in H1 from spin up to spin down        
            H1_transverse_SO_d1 = sparse(M, M+1, -1i*lambda*conj(d1), Meff, Meff);
            H1_transverse_SO_d2 = sparse(4*M, 2*M+1, 1i*lambda*conj(d2), Meff, Meff);
            H1_transverse_SO_spindown_spinup = H1_transverse_SO_d1 + H1_transverse_SO_d2; 
        
                    
            % setting SOC in H_transverse
            H1_transverse = [ H1_transverse_spindown, H1_transverse_SO_spinup_spindown;
                        H1_transverse_SO_spindown_spinup, H1_transverse_spinup];
                    
            H1_skew_left = [];
            H1_skew_right = [];
                    
            
        else
            H1_transverse = [];
            H1_skew_left = [];
            H1_skew_right = [];
        end     
        
        
        
        % ******* Intrinsic and valley-Zeeman SOC *************
        
        SOintrinsic = lead_param.Intrinsic;
        SOvalley_zeeman = lead_param.ValleyZeeman;
        
        % intrinsic SO coupling in the unit cell for the spin up subspace
        Meff = 4*M;
        H0_SOintrinsic = sparse( 2*M+1:3*M, 1:M, 1i*(SOintrinsic-SOvalley_zeeman), Meff, Meff) + ... clockwise deirection, B sublattice
                        sparse( M+1:2*M-1, M+2:2*M, 1i*(SOintrinsic+SOvalley_zeeman), Meff, Meff) + ... clockwise deirection, A sublattice
                        sparse( 1:M-1, 2*M+2:3*M, 1i*(SOintrinsic-SOvalley_zeeman), Meff, Meff) + ... clockwise deirection, B sublattice
                        sparse( M+2:2*M, 3*M+1:4*M-1, 1i*(SOintrinsic+SOvalley_zeeman), Meff, Meff) + ... clockwise deirection, A sublattice
                        sparse( 2*M+2:3*M, 2*M+1:3*M-1, 1i*(SOintrinsic-SOvalley_zeeman), Meff, Meff) + ... clockwise deirection, B sublattice
                        sparse( 4*M:3*M+1, M+1:2*M-1, 1i*(SOintrinsic+SOvalley_zeeman), Meff, Meff); ... clockwise deirection, A sublattice
                        
        H0_SOintrinsic = H0_SOintrinsic + H0_SOintrinsic'; % clockwise deirection and counterclockwise directions
        
        % expanding the Hamiltonian to the full spin space
        H0_SOintrinsic = kron( [1,0;0,-1], H0_SOintrinsic);
        H0 = H0 + H0_SOintrinsic;
                    
    
        H1_SOintrinsic = sparse( 2*M+1:3*M, 1:M, 1i*(SOintrinsic-SOvalley_zeeman), Meff, Meff) + ... clockwise deirection, B sublattice            
                        sparse( 3*M+1:4*M, M+1:2*M, 1i*(SOintrinsic+SOvalley_zeeman), Meff, Meff) + ... clockwise deirection, A sublattice                        
                        sparse( 2*M+2:3*M, 1:M-1, -1i*(SOintrinsic-SOvalley_zeeman), Meff, Meff) + ... counterclockwise deirection, B sublattice                            
                        sparse( 3*M+1:4*M-1, M+2:2*M, -1i*(SOintrinsic+SOvalley_zeeman), Meff, Meff); ... counterclockwise deirection, A sublattice     
                    
                        
        % expanding the Hamiltonian to the full spin space
        H1_SOintrinsic = kron( [1,0;0,-1], H1_SOintrinsic);
        H1 = H1 + H1_SOintrinsic;
        
        
        
        % The Intrinsic SOC coupling in H_transverse from spin down to spin up    
        if ~isempty(H1_transverse_spindown)
            
            H1_transverse_SOintrinsic = sparse(M, 2*M+1, 1i*(SOintrinsic-SOvalley_zeeman), Meff, Meff) + ... clockwise deirection, B sublattice
                                        sparse(4*M, M+1, -1i*(SOintrinsic+SOvalley_zeeman), Meff, Meff); ... counterclockwise deirection, A sublattice
            
            % expanding the Hamiltonian to the full spin space
            H1_transverse_SOintrinsic = kron( [1,0;0,-1], H1_transverse_SOintrinsic);
            H1_transverse = H1_transverse + H1_transverse_SOintrinsic;
            
            
            H1_skew_left_SOintrinsic = sparse(4*M, M+1, -1i*(SOintrinsic+SOvalley_zeeman), Meff, Meff); ... counterclockwise deirection, A sublattice
                
            % expanding the Hamiltonian to the full spin space
            H1_skew_left = kron( [1,0;0,-1], H1_skew_left_SOintrinsic); 
            
            
        
            H1_skew_right_SOintrinsic = sparse(2*M+1, M, -1i*(SOintrinsic-SOvalley_zeeman), Meff, Meff); ...counterclockwise deirection, B sublattice
                
            % expanding the Hamiltonian to the full spin space
            H1_skew_right = kron( [1,0;0,-1], H1_skew_right_SOintrinsic); 
            
        else
            H1_transverse = [];
            H1_skew_left = [];
            H1_skew_right = [];
        end                
        
        
        
    else
        save('Graphene_SOC_Lead_Hamiltonians_Graphene_SOC_Lead_Hamiltonians.mat');
        error('Undefined lead end type')
    end
    
    % creating structure storing sites with downspin               
    coordinates_spinup = coordinates_spindown;
    coordinates_spinup.spinup = true( size(coordinates_spinup.x) );
    coordinates_spindown.spinup = false( size(coordinates_spindown.x) );
    
    % combining sites with ip and down spins
    coordinates = coordinates_spinup.Combine( coordinates_spindown );
    
    
end

end % end public methods 


end