Lattice_TMDC_Bilayer_SOC.m

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%%    Eotvos Quantum Transport Utilities - Lattice_TMDC_Bilayer_SOC
%    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 structures Structures
%> @{
%> @file Lattice_TMDC_Bilayer_SOC.m
%> @brief Class containing physical parameters of the lattice of bilayer transitional dichalcogenides including spin-orbit coupling according to <a href="https://journals.aps.org/prb/pdf/10.1103/PhysRevB.92.205108">PRB 92, 205108 (2015)</a>.
%> @} 
%> @brief Class containing physical parameters of the lattice of bilayer transitional dichalcogenides including spin-orbit coupling according to <a href="https://journals.aps.org/prb/pdf/10.1103/PhysRevB.92.205108">PRB 92, 205108 (2015)</a>.
%> @Available
%> EQuUs v5.0 or later
%%
classdef Lattice_TMDC_Bilayer_SOC < Lattice_TMDC_Monolayer_SOC

    properties
        %> parameter describing the distance between two succesive layers in units of \f$ \AA \f$ according to table I in <a href="https://journals.aps.org/prb/pdf/10.1103/PhysRevB.92.205108">PRB 92, 205108 (2015)</a>.
        c
        %> The width of one layer in units of \f$ \AA \f$ according to table I in <a href="https://journals.aps.org/prb/pdf/10.1103/PhysRevB.92.205108">PRB 92, 205108 (2015)</a>.
        d_XX
        %> parameter used to calculate the strength of the \f$ \sigma \f$ bond according to EQ (17) in <a href="https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.205108">PRB 92 205108</a>.
        nu_sigma
        %> parameter used to calculate the strength of the \f$ \sigma \f$ bond according to EQ (17) in <a href="https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.205108">PRB 92 205108</a>.
        R_sigma
        %> parameter used to calculate the strength of the \f$ \sigma \f$ bond according to EQ (17) in <a href="https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.205108">PRB 92 205108</a>.
        eta_sigma
        %> parameter used to calculate the strength of the \f$ \pi \f$ bond according to EQ (17) in <a href="https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.205108">PRB 92 205108</a>.
        nu_pi
        %> parameter used to calculate the strength of the \f$ \pi \f$ bond according to EQ (17) in <a href="https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.205108">PRB 92 205108</a>.
        R_pi
        %> parameter used to calculate the strength of the \f$ \pi \f$ bond according to EQ (17) in <a href="https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.205108">PRB 92 205108</a>.
        eta_pi
    end



methods (Access=public)
    
%% Contructor of the class
%> @brief Constructor of the class.
%> @return An instance of the class
    function obj = Lattice_TMDC_Bilayer_SOC() 
        
        % initializing class members
        % according to MoS2 parameetrs in the table V in <a href="https://journals.aps.org/prb/pdf/10.1103/PhysRevB.92.205108">PRB 92, 205108 (2015)</a>. 
        obj.nu_sigma = 2.627;
        obj.R_sigma = 3.128;
        obj.eta_sigma = 3.859;
        obj.nu_pi = -0.708;
        obj.R_pi = 2.923;
        obj.eta_pi = 5.724;
        % according to MoS2 parameetrs in the table VIII in <a href="https://journals.aps.org/prb/pdf/10.1103/PhysRevB.92.205108">PRB 92, 205108 (2015)</a>.      
        obj.c = 12.29/2;
        obj.d_XX = 3.13;
    end  
    
%% Calc_Hopping
%> @brief Calculates the hopping amplitude between sites separated by vector r_vec, according to EQ (15) in <a href="https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.205108">PRB 92 205108</a>.
%> @param r_vec Three-dimensional vector connecting the pair of sites.
%> @return Returns with the structure containing the hopping amplitudes.
    function ret = Calc_Hopping( obj, r_vec )
        
        % distence between the sites
        r = norm(r_vec);
        
        % calculating the strength of the sigma and pi bonds
        V_pp_sigma = obj.Calc_V_pp_sigma( r );        
        V_pp_pi    = obj.Calc_V_pp_pi( r );
        
        ret.xx = (V_pp_sigma - V_pp_pi)*r_vec(1)*r_vec(1)/r^2 + V_pp_pi;
        ret.xy = (V_pp_sigma - V_pp_pi)*r_vec(1)*r_vec(2)/r^2;
        ret.xz = (V_pp_sigma - V_pp_pi)*r_vec(1)*r_vec(3)/r^2;
        ret.yx = (V_pp_sigma - V_pp_pi)*r_vec(2)*r_vec(1)/r^2;
        ret.yy = (V_pp_sigma - V_pp_pi)*r_vec(2)*r_vec(2)/r^2 + V_pp_pi;
        ret.yz = (V_pp_sigma - V_pp_pi)*r_vec(2)*r_vec(3)/r^2;
        ret.zx = (V_pp_sigma - V_pp_pi)*r_vec(3)*r_vec(1)/r^2;
        ret.zy = (V_pp_sigma - V_pp_pi)*r_vec(3)*r_vec(2)/r^2;
        ret.zz = (V_pp_sigma - V_pp_pi)*r_vec(3)*r_vec(3)/r^2 + V_pp_pi;
        
    end        
    

%% Calc_V_pp_sigma
%> @brief Calculates the strength of the \f$ \sigma \f$ bond between the p orbitals according to EQ (17) in <a href="https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.205108">PRB 92 205108</a>.
%> @param r The radial distance in units of \f$ \AA \f$
%> @return Returns with the strength of the \f$ \sigma \f$ bond between the p orbitals.
    function ret = Calc_V_pp_sigma( obj, r )
        
        ret = obj.nu_sigma*exp(-(r/obj.R_sigma)^obj.eta_sigma);
        
    end    
    
    
%% Calc_V_pp_pi
%> @brief Calculates the strength of the \f$ \pi \f$ bond between the p orbitals according to EQ (17) in <a href="https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.205108">PRB 92 205108</a>.
%> @param r The radial distance in units of \f$ \AA \f$
%> @return Returns with the strength of the \f$ \sigma \f$ bond between the p orbitals.
    function ret = Calc_V_pp_pi( obj, r )
        
        ret = obj.nu_pi*exp(-(r/obj.R_pi)^obj.eta_pi);
        
    end        

    
end % public methods end

end