test_Nambu.m

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%%   Eotvos Quantum Transport Utilities
%    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 unit_tests Unit Tests
%> @{
%> @file test_Nambu.m
%> @brief Testfile to check functionalities related to Nambu space representation
%> @Available
%> EQuUs v4.9 or later
%> @}
%> @brief Testfile to check functionalities related to Nambu space representation
function test_Nambu()

filename = mfilename('fullpath');
[directory, fncname] = fileparts( filename );

    % create input structures
    [Opt, param] = parseInput( 'Input_Ribbon.xml');    
    
    % defining the width of the lead 1
    param.Leads{1}.M = 10; 
    
    param.Leads{1}.epsilon = 0.3;
    
    % number of bands in the calculated spectra
    bandNum = param.Leads{1}.M*2;
    
    % logival value deciding whether to plot the calculated spctra or not
    PlotSpectra = false;

    % The temperature in Kelvins
    T = 10;
    
    %% test of the class Lead_Keldysh
    disp( '***** test of functionalities related to Nambu space calculations *****' );

    % turning off Bogoliubov de Gennes model
    Opt.BdG = false;
    
    % create an instance of class Lead_Keldysh of a normal system
    cLead_K_normal = Lead_Keldysh(Opt, param, 'Hanyadik_Lead', 1, 'T', T );

    % create normal Hamiltonians
    cLead_K_normal.CreateHamiltonians();     
    spectrum_normal = cLead_K_normal.CalcSpektrum('ka_min', 1.8, 'ka_max', 2.5, 'ka_num', 100, 'toPlot', PlotSpectra, 'offset', 0, 'db', bandNum);
    
    
    % turning on Bogoliubov de Gennes model
    Opt.BdG = true;
    
    % setting the superconducting pair potential in lead 1 to zero
    param.Leads{1}.pair_potential = 0.4;
    
    % create an instance of class Lead_Keldysh of a BdG model
    cLead_K_BdG = Lead_Keldysh(Opt, param, 'Hanyadik_Lead', 1, 'T', T);

    % create BdG Hamiltonians
    cLead_K_BdG.CreateHamiltonians();   
    spectrum_BdG = cLead_K_BdG.CalcSpektrum('ka_min', 1.8, 'ka_max', 2.5, 'ka_num', 100, 'toPlot', PlotSpectra, 'offset', 0, 'db', 2*bandNum);
    
    
    % calculating manually the spectrum in the BdG model from the normal spectrum
    spectrum_manual = sqrt((spectrum_normal(:,2)).^2 + abs(param.Leads{1}.pair_potential)^2);
    spectrum_manual = [spectrum_manual; -spectrum_manual];
    
    spectrum_manual = [ [spectrum_normal(:,1); spectrum_normal(:,1)], spectrum_manual ];
    
%     figure
%     hold on
%     plot( spectrum_manual(:,1), spectrum_manual(:,2), '.')
%     plot( spectrum_BdG(:,1), spectrum_BdG(:,2), 'r.')
    
    checkpoint = norm(sort( spectrum_BdG(:,2) ) - sort(spectrum_manual(:,2)));
    if checkpoint > 1e-10
        warning(['EQuUs:Tests:', fncname, ':checkpoint failed with error ', num2str( checkpoint)]);
    end
    
%     H0_normal = cLead_K_normal.Read('H0');
%     H0_manual = [H0_normal, eye(size(H0_normal))*param.Leads{1}.pair_potential; eye(size(H0_normal))*param.Leads{1}.pair_potential, -H0_normal];   
%     H0_BdG = cLead_K_BdG.Read('H0');    
%     norm(full(H0_manual-H0_BdG))
%     
%     
%     H1_normal = cLead_K_normal.Read('H1');
%     H1_manual = [H1_normal, zeros(size(H1_normal)); zeros(size(H1_normal)), -H1_normal];    
%     H1_BdG = cLead_K_BdG.Read('H1');    
%     norm(full(H1_manual-H1_BdG))

end