Lead_Keldysh.m

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%%    Eotvos Quantum Transport Utilities - Lead_Keldysh
%    Copyright (C) 2009-2018 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 basic Basic Functionalities
%> @{
%> @file Lead_Keldysh.m
%> @brief A class to calculate the Keldysh lesser and greater Green functions and self energies of a translational invariant lead.
%> @} 
%> @brief A class to calculate the Keldysh lesser and greater Green functions and self energies of a translational invariant lead.
%> The notations and the structure of the Hamiltonian is defined accroding to the following image:
%> @image html Lead_Hamiltonian.jpg
%> @image latex Lead_Hamiltonian.jpg
%> @Available
%> EQuUs v4.9 or later
%%
classdef Lead_Keldysh < FermiDirac & Lead
    
    
properties ( Access = protected ) 
     %>The matrix of the lesser surface Greens function of the semi-infinite ribbon.
    lessergsurf
     %>The matrix of the lesser Greens function of the infinite ribbon.
    lesserginf
     %>The matrix of the lesser surface Greens function of a finite ribbon.
    lessergfin
     %>The lesser self-energy of the semi-infinite ribbon.
    lesserSigma
    %>The bias on the lead in units of the energy unit in the elements of the Hamiltonian
    bias
end    
    
    

methods ( Access = public )
%% Lead_Keldysh
%> @brief Constructor of the class.
%> @param Opt An instance of the structure #Opt.
%> @param param An instance of structure #param.
%> @param varargin Cell array of optional parameters. For details see #InputParsing.
%> @return An instance of the class
    function obj = Lead_Keldysh(Opt, param, varargin)    
        obj = obj@Lead( Opt, param, varargin{:} ); 
        
        obj.lessergsurf = [];
        obj.lesserginf = [];
        obj.lessergfin = [];
        obj.lesserSigma = [];
        obj.bias = [];
    end
    
    
    
%% LesserSurfaceGreenFunction
%> @brief Calculates the lesser Green function of a semi-infinite lead for eregy #E. The calculated Green function is stored by the attribute #lessergsurf.
    function LesserSurfaceGreenFunction( obj, varargin ) 
        
        % Here we calculate the redarded Green function
        obj.SurfaceGreenFunction( 'CalcInverse', false );
            
        % Here we calculate the lesser Green function from the retarted surface Green function.
        if isempty( obj.E )
            error(['EQuUs:', class(obj), ':LesserSurfaceGreenFunction: eigenvalue problem needs to be solved first.'])
        end
        
        % the termal occupation number
        if obj.Opt.BdG
            % if the BdG model is enabled
            if obj.isSuperconducting()
                % in case the lead is superconducting 
                % working only for unbiased lead!!!!!!
                occupation_num = obj.Fermi(obj.E);
            else
                % in case of normal lead in the BdG model
                occupation_num_electron = obj.Fermi(obj.E - obj.bias); % occupation number for electrons
                occupation_num_hole = obj.Fermi(obj.E + obj.bias); % occupation number for electrons
                occupation_num = kron( [occupation_num_electron,0; 0, occupation_num_hole], eye(size(obj.Sigma)/2) );
            end
        else
            % for normal systems
            occupation_num = obj.Fermi(obj.E);
        end
        
        % Eq (56) in Adv. Nat. Sci.: Nanosci. Nanotechnol. 5 (2014) 033001
        obj.lessergsurf = (obj.gsurf' - obj.gsurf)*occupation_num;
            
        
    end   
    
    
%% LesserSelfEnergy
%> @brief Calculates the lesser self energy of a semi-infinite lead for energy #E according to Eq (41) in Adv. Nat. Sci.: Nanosci. Nanotechnol. 5 (2014) 033001. The calculated lesser self energy is stored by attribute #lesserSigma.
%> @return Returns with the calculated self energy.
function ret = LesserSelfEnergy( obj )
             
        % Here we calculate the lesser self energy from the effective coupling of the lead
        if isempty( obj.E )
            error(['EQuUs:', class(obj), ':LesserSelfEnergy: eigenvalue problem needs to be solved first.'])
        end
        
        % calculate the retarded self-energy if it was not already calculated
        if isempty( obj.Sigma )
           obj.SelfEnergy();
        end
        
        % the termal occupation number        
        if obj.Opt.BdG
            % if the BdG model is enabled
            if obj.isSuperconducting()
                % in case the lead is superconducting 
                % working only for unbiased lead!!!!!!
                occupation_num = obj.Fermi(obj.E);
            else
                % in case of normal lead in the BdG model
                occupation_num_electron = obj.Fermi(obj.E - obj.bias); % occupation number for electrons
                occupation_num_hole = obj.Fermi(obj.E + obj.bias); % occupation number for electrons
                occupation_num = kron( [occupation_num_electron,0; 0, occupation_num_hole], eye(size(obj.Sigma)/2) );
            end
        else
            % for normal systems
            occupation_num = obj.Fermi(obj.E);
        end
        
        %obj.display(['EQuUs:', class(obj), ':LesserSelfEnergy: Occupation number = ', num2str( occupation_num ), ', Energy: ', num2str(obj.E), ', temperature = ', num2str(obj.T)]);
        
        % Eq (41) in Adv. Nat. Sci.: Nanosci. Nanotechnol. 5 (2014) 033001
        obj.lesserSigma = ((obj.Sigma)'-obj.Sigma)*occupation_num;
        
        ret = obj.lesserSigma;
           
end  
    


    
end % end public methods



methods ( Access = protected )
    
%% Initialize
%> @brief Initializes class attributes.
    function Initialize(obj)        
        Initialize@Lead(obj); 
    end    
    
end  


methods ( Access = public )
%% CreateClone
%> @brief Creates a clone of the present Lead object.
%> @return Returns with the cloned object.
%> @param varargin Cell array of optional parameters (https://www.mathworks.com/help/matlab/ref/varargin.html):
%> @param 'empty' Set true to create an empty clone, or false (default) to clone all atributes.
    function ret = CreateClone( obj, varargin )     
        
        p = inputParser;
        p.addParameter('empty', false );
        
        p.parse(varargin{:});       
        empty    = p.Results.empty;
        
        ret = Lead_Keldysh(obj.Opt, obj.param,...
                                            'Hanyadik_Lead', obj.Hanyadik_Lead,...
                                            'Lead_Orientation', obj.Lead_Orientation, ...
                                            'mu', obj.mu, ...
                                            'bias', obj.bias, ...
                                            'T', obj.T, ...
                                            'q', obj.q);
                                        
        if empty
            return
        end
                  
        meta_data = metaclass(obj);
        
        for idx = 1:length(meta_data.PropertyList)
            prop_name = meta_data.PropertyList(idx).Name;
            if strcmpi( prop_name, 'SelfEnergyCalc' ) || strcmpi( prop_name, 'GinfCalc' )  
              continue
            elseif strcmpi( prop_name, 'next_SVD_cycle' )
              if ~isempty( obj.next_SVD_cycle )
               ret.next_SVD_cycle = obj.next_SVD_cycle.CreateClone();
              end
            else
                 ret.Write( prop_name, obj.(prop_name));  
            end 
        end   
        
    end   
    
%% setTemperature
%> @brief Sets the temperature in the calculations
%> @param T The value of the temperature in Kelvins.
    function setTemperature( obj, T )
        setTemperature@FermiDirac( obj, T );

        % resetting the temperature dependent attributes
        obj.lessergsurf = [];
        obj.lesserginf = [];
        obj.lessergfin = [];
        obj.lesserSigma = [];
    end              

%% Reset
%> @brief Resets all elements in the class.
    function Reset( obj )
        
        if strcmpi( class(obj), 'Lead_Keldysh' )
            meta_data = metaclass(obj);
            
            for idx = 1:length(meta_data.PropertyList)
                prop_name = meta_data.PropertyList(idx).Name;
                if strcmp(prop_name, 'Opt') || strcmp( prop_name, 'param') || strcmp(prop_name, 'varargin') || strcmp(prop_name, 'k_B') || strcmp(prop_name, 'T_treshold')
                    continue
                end
                obj.Clear( prop_name ); 
            end   
        end 
        
        obj.Initialize();
             
    end

%% Write
%> @brief Sets the value of an attribute in the class.
%> @param MemberName The name of the attribute to be set.
%> @param input The value to be set.
    function Write(obj, MemberName, input)  
       
        if strcmpi(MemberName, 'param') || strcmpi(MemberName, 'params')
            Write@CreateLeadHamiltonians( obj, MemberName, input );
            return
        elseif strcmpi(MemberName, 'T')
            obj.setTemperature( input );
        else
               try
               obj.(MemberName) = input;
               catch
                    error(['EQuUs:', class(obj), ':Read'], ['No property to write with name: ',  MemberName]);
               end
        end
        
    end
%% Read
%> @brief Query for the value of an attribute in the class.
%> @param MemberName The name of the attribute to be set.
%> @return Returns with the value of the attribute.
    function ret = Read(obj, MemberName)
        
        if  strcmp(MemberName, 'd_modusmtx_p')
            obj.calcDualModes()
            ret = obj.d_modusmtx_p;
            return
        elseif strcmp(MemberName, 'd_modusmtx_m')
            obj.calcDualModes()
            ret = obj.d_modusmtx_m;  
            return           
        else
               try
               ret = obj.(MemberName);
               catch
                    error(['EQuUs:', class(obj), ':Read'], ['No property to read with name: ',  MemberName]);
               end            
        end
        
        
    end
%% Clear
%> @brief Clears the value of an attribute in the class.
%> @param MemberName The name of the attribute to be cleared.
    function Clear(obj, MemberName)
          try
          obj.(MemberName) = [];
          catch
               error(['EQuUs:', class(obj), ':Clear'], ['No property to clear with name: ',  MemberName]);
          end  
        
    end

end


methods (Access=protected)   
    

%% InputParsing
%> @brief Parses the optional parameters for the class constructor.
%> @param varargin Cell array of optional parameters (https://www.mathworks.com/help/matlab/ref/varargin.html):
%> @param 'Hanyadik_Lead' The ID number of the current lead. Set to empty (default) for using parameters of the scatter region.
%> @param 'Lead_Orientation' Orientation of the lead. Set +1 (default) is the "incoming" direction of the propagating states is defined in the +x or +y direction, and "-1" otherwise.
%> @param 'q' The transverse momentum. Set to empty (default) for computations without transverse momentums.
%> @param 'T' The absolute temperature in Kelvins.
    function InputParsing( obj, varargin )
        p = inputParser;
        p.addParameter('Hanyadik_Lead', []);
        p.addParameter('Lead_Orientation', 1);
        p.addParameter('q', []);
        p.addParameter('T', 0 );
        p.addParameter('bias', 0, @isscalar);
        
        % keeping unmatched attributes that possibly comes from the derived classes
        p.KeepUnmatched = true;
        
        p.parse(varargin{:});   
        
        InputParsing@FermiDirac( obj, 'T', p.Results.T, 'mu', 0 );
        InputParsing@Lead( obj, 'Hanyadik_Lead', p.Results.Hanyadik_Lead, ...
                            'Lead_Orientation', p.Results.Lead_Orientation, ...
                            'q', p.Results.q );
                        
        obj.bias = p.Results.bias;
        
    end

end % private methods



%------------------------------------------------------------------
end % Global End