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picture1_Matrix Pdf 174256 | Negf Formulas In Pictures


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File: Matrix Pdf 174256 | Negf Formulas In Pictures
how to use negf matrix formulas step by step tutorial in pictures branislav k nikoli department of physics astronomy university of delaware newark de 19716 u s a https wiki ...

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   How to Use NEGF Matrix Formulas: 
     Step-by-Step Tutorial in Pictures
                 Branislav K. Nikolić 
    Department of Physics & Astronomy, University of Delaware, Newark, DE 19716, U.S.A.
                  https://wiki.physics.udel.edu/phys824
 PHYS824: Nanophysics and Nanotechnology    NEGF in pictures
      Step 1: Construct Matrix Representation of 
  the Tight-Binding Hamiltonian of Central Region
                                                   eV =μμ−
                                                     bLR
    3x3 lattice of atoms in the central region
   rix I         II         III
   t                                                                     3x3 submatrix describing
   n ma                                                      0           second row of atoms
   nia
   o
   t
   mil
   a                                                                    3x3 submatrix describing
   H
                                          0                             hoppings from third to 
   9x9                                                                  second row of atoms
 PHYS824: Nanophysics and Nanotechnology                                                NEGF in pictures
        Step 2: Construct Self-Energy Matrices 
  for the Left and the Right Semi-Infinite Lead
   9x9 self-energy matrix                                9x9 self-energy matrix
   for the left electrode                                for the right electrode
               0        0        3x3 submatrix of            0        0        0
                                non-zero elements
      0        0         0       which is returned           0        0         0
                                       by the 
                                      Function 
      0        0         0         self_energy.m             0        0
     Since self-energies are summed with the Hamiltonian before inversion to get the Green 
   function of an open system,  they MUST be defined on the same Hilbert space of 9 orbitals
    H(1:3,1:3)=H1;                         MATLAB           This self-energy (i.e., its non-zero 3x3 
    H(7:9,7:9)=H3;
    for energy=-4:0.02:4                                block returned by the function) is added onto 
        sigma=self_energy(3,1,energy,t_lead,t_couple);     the corners (representing edge layers of 
        H(1:3,1:3)= H(1:3,1:3)+sigma;                        the 3x3 sample) of the ORIGINAL 
        H(7:9,7:9)= H(7:9,7:9)+sigma;                      Hamiltonan recorded outside of the loop
        Gr=inv(energy*eye(Hsize,Hsize)-H);
 PHYS824: Nanophysics and Nanotechnology                                             NEGF in pictures
     Step 3: Construct Retarded Green Function 
                    for an Open Quantum System
            This 3x3 submatrix is               I         II        III
            composed of quantum-
            mechanical probability          3          6         9
   rix    amplitudes for electron to                                        This 3x3 submatrix is 
   t     propagate between I and |||                                        composed of quantum-
   ma    row of atoms. This, it must                                        mechanical probability 
   n     be related to the scattering       2          5         8        amplitudes for electron to 
   io       matrix concept in the                                         propagate between ||| and I 
   t      Landauer formalism (which                                       row of atoms. For example, 
   unc       contains probability                                          matrix element G  gives 
         amplitude to propagate from                                                       29
   n f   a conducting channel in left       1          4         7         probability amplitude to 
   e     led to a conducting channel                                       propagate from atom 9 to 
   Gre        in the right lead)                                                   atom 2.
   d 
   rde   This 3x3 submatrix allows 
   a
   t      us to compute the local 
         density of states on each 
           atom from row | using                
                               −ImG/π
   9x9 reThe total density of states 
        is then obtained by summing 
           all elements of on the 
                          −ImG/π
                diagonal of  
 PHYS824: Nanophysics and Nanotechnology                                             NEGF in pictures
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...How to use negf matrix formulas step by tutorial in pictures branislav k nikoli department of physics astronomy university delaware newark de u s a https wiki udel edu phys nanophysics and nanotechnology construct representation the tight binding hamiltonian central region ev blr x lattice atoms rix i ii iii t submatrix describing n ma second row nia o mil h hoppings from third self energy matrices for left right semi infinite lead electrode non zero elements which is returned function m since energies are summed with before inversion get green an open system they must be defined on same hilbert space orbitals matlab this e its block added onto sigma couple corners representing edge layers sample original hamiltonan recorded outside loop gr inv eye hsize retarded quantum composed mechanical probability amplitudes electron propagate between it related scattering io concept landauer formalism example unc contains element g gives amplitude f conducting channel led atom gre d rde allows us...

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