Square_Lead_Hamiltonians.m

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%%   Eotvos Quantum Transport Utilities - Square_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 Square_Lead_Hamiltonians.m
%> @brief Class to create the Hamiltonian of one unit cell in a translational invariant lead made of square lattice structure, including the SSH model.
%> @} 
%> @brief Class to create the Hamiltonian of one unit cell in a translational invariant lead made of square lattice structure, including the SSH model.
%%
classdef Square_Lead_Hamiltonians


methods (Static = true)
%% SquareLattice_Lead_Hamiltonians
%> @brief Creates Hamiltonians H_0 and H_1 for square lattice structure
%> @param lead_param An instance of structure #Lattice_Square (or its subclass) containing the physical parameters.
%> @param M Number of sites in the cross section of the lead.
%> @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] = SquareLattice_Lead_Hamiltonians( lead_param, M )
        
        % check the structure containing the physical parameters
        supClasses = superclasses(lead_param);
        if sum( strcmp( supClasses, 'Lattice_Square' ) ) == 0
            error(['EQuUs:Lattices:Square_Lead_Hamiltonians:SquareLattice_Lead_Hamiltonians'], 'Invalid type of the input parameter');   
        end
        
        if isempty(M)
            error(['EQuUs:Square_Lead_Hamiltonians:SquareLattice_Lead_Hamiltonians'], 'The input parameter M is empty')
        end        
    
        epsilon  = lead_param.epsilon;
        vargamma = lead_param.vargamma;
            
        H0 = sparse(1:M,1:M,epsilon,M,M) - sparse(1:M-1,2:M,vargamma,M,M) - sparse(2:M,1:M-1,vargamma,M,M);
        H1 = sparse(1:M,1:M,-vargamma,M,M);
            
        coordinates = structures('coordinates');
        coordinates.x = transpose(1:M);
        coordinates.y = zeros(M,1);
        coordinates.a = [0; 1];
            
        if M == 1
            H0 = full(H0);
            H1 = full(H1);
        end
            
        coordinates.b = [M,0];
        H1_transverse = sparse(M,1,-vargamma,M,M);   
    
    
    end

%% SSH_Lead_Hamiltonians
%> @brief Creates Hamiltonians H_0 and H_1 of the SSH model.
%> @param lead_param An instance of structure #Lattice_SSH (or its subclass) containing the physical parameters.
%> @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] = SSH_Lead_Hamiltonians( lead_param )
        
        % check the structure containing the physical parameters
        supClasses = superclasses(lead_param);
        if sum( strcmp( supClasses, 'Lattice_SSH' ) ) == 0
            error(['EQuUs:Lattices:Square_Lead_Hamiltonians:SSH_Lead_Hamiltonians'], 'Invalid type of the input parameter');   
        end
    
        epsilon  = lead_param.epsilon;
        vargamma1 = lead_param.vargamma1;
        vargamma3 = lead_param.vargamma3;
        deltaAB = lead_param.deltaAB;
        if isempty( deltaAB )
            deltaAB = 0;
        end
    
        H0 = zeros(2,2);
        H1 = zeros(2);
    
        H0(1,2) = -vargamma1;
        H0(2,1) = -vargamma1;
        H0(1,1) = deltaAB/2 + epsilon;
        H0(2,2) = -deltaAB/2 + epsilon;
    
        H1(2,1) = -vargamma3;
    
        H1_transverse = [];
                
        coordinates = structures('coordinates');
        coordinates.x = transpose(1:2);
        coordinates.y = zeros(2,1);
        coordinates.a = [0; 1];  
    
    
    end

%% Lieb_Lead_Hamiltonians
%> @brief Creates Hamiltonians H_0 and H_1 for Lieb lattice structure
%> @param lead_param An instance of structure #Lattice_Lieb (or its subclass) containing the physical parameters.
%> @param M Number of sites in the cross section of the lead.
%> @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] = Lieb_Lead_Hamiltonians( lead_param, M )
        
        % check the structure containing the physical parameters
        supClasses = superclasses(lead_param);
        if sum( strcmp( supClasses, 'Lattice_Lieb' ) ) == 0
            error(['EQuUs:Lattices:Square_Lead_Hamiltonians:Lieb_Lead_Hamiltonians'], 'Invalid type of the input parameter');   
        end
        
        if isempty(M)
            error(['EQuUs:', class(obj), ':Lieb_Lead_Hamiltonians'], 'The input parameter M is empty')
        end
    

        epsilon  = lead_param.epsilon;
        vargamma = lead_param.vargamma;
        N = 3*M;
           

        h00=toeplitz([epsilon,-vargamma,0]);    
        h01=-vargamma*[0 0 0; 0 0 0; 0 1 0];
        h1=-vargamma*[0 1 0; 0 0 0; 0 0 0];
          
        H0=sparse([],[],[], N,N);
        H1=sparse([],[],[], N,N);

        for l=1:3;
              for m=1:3;
                H0 = H0 + sparse(l:3:N,m:3:N,h00(l,m),N,N) + sparse(l:3:N-3,m+3:3:N,h01(l,m),N,N) + sparse(l+3:3:N,m:3:N-3,h01(m,l),N,N);
                H1 = H1 + sparse(l:3:N,m:3:N,h1(l,m),N,N);
              end
            end

        coordinates = structures('coordinates');
        coordinates.x = zeros(N,1);
        coordinates.x(1:3:N) = transpose(1:M);
        coordinates.x(2:3:N) = transpose(1:M);
        coordinates.x(3:3:N) = transpose(1:M)+0.5;
        coordinates.y = zeros(N,1);
     coordinates.y(1:3:N) = 0.5;
        coordinates.a = [0; 1];
            
        if M == 1
            H0 = full(H0);
            H1 = full(H1);
        end
                
        H1_transverse = sparse([],[],[], N,N);
        for l=1:3;
         for m=1:3;
           H1_transverse = H1_transverse + sparse(3*M-3+l,m,h01(l,m),3*M,3*M);   
         end
        end
        coordinates.b = [M,0];
        
    end

end % methods static


end