Triangle_Lead_Hamiltonians.m

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%%   Eotvos Quantum Transport Utilities - Triangle_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 Triangle_Lead_Hamiltonians.m
%> @brief Class to create the Hamiltonian of one unit cell in a translational invariant lead made of Triangle lattice structure.
%> @} 
%> @brief Class to create the Hamiltonian of one unit cell in a translational invariant lead made of Triangle lattice structure.
%%
classdef Triangle_Lead_Hamiltonians


methods (Access = public, Static = true)
%% Triangle_Hamiltonians
%> @brief Creates Hamiltonians related to triangular lattice structure
%> @image html lattice_triangle.jpg
%> @image latex lattice_triangle.jpg
%> @param lead_param An instance of structure #Lattice_Triangle (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] The skew coupling between unit cells in the left direction. 
%> @return [5] A structure Coordinates containing the coordinates of the sites. 
    function [H0, H1, H1_transverse, H1_skew_left, cCoordinates] = Triangle_Hamiltonians( lead_param, M )
        
        % check the structure containing the physical parameters
        supClasses = superclasses(lead_param);
        if sum( strcmp( supClasses, 'Lattice_Triangle' ) ) == 0
            error(['EQuUs:Lattices:Triangle_Lead_Hamiltonians:TriangleLattice_Lead_Hamiltonians'], 'Invalid type of the input parameter');   
        end
        
        if isempty(M)
            error(['EQuUs:Triangle_Lead_Hamiltonians:TriangleLattice_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) + ... on-site terms
            sparse( 2:M, 1:M-1, vargamma, M, M) + ... hopping term
            sparse( 1:M-1, 2:M, vargamma, M, M); ... hopping term
            
        H1 = sparse( 1:M, 1:M, vargamma, M, M) + ... horizontal hopping terms
            sparse( 1:M-1, 2:M,  vargamma, M, M);
            
        % creating coordinates
        cCoordinates = structures('coordinates');
        cCoordinates.LatticeConstant = 1;
        cCoordinates.a = [1; 0];
        cCoordinates.b = [-0.5; sqrt(3)/2 ]*M;
        
        cCoordinates.x = cCoordinates.b(1)*(1:M);
        cCoordinates.y = cCoordinates.b(2)*(1:M);
            
        % Transverse coupling    
        H1_transverse = sparse( M, 1, vargamma, M, M);   
        
        % skew coupling in the left direction
        H1_skew_left = sparse( M, 1, vargamma, M, M);
    
    end
    
    
end % end static methods



end