Step 3: The transmission and current

After the calculations of the steps 2 and 3, you can proceed calculations of transmission and current by adding the following keywords to the input file used in the calculation of the step 2:

    NEGF.tran.energyrange -10 10 1.0e-3  # default=-10.0 10.0 1.0e-3 (eV)
    NEGF.tran.energydiv        200       # default=200
    NEGF.tran.Kgrid            1 1       # default= 1 1

The energy range where the transmission is calculated is given by the keyword 'NEGF.tran.energyrange', where the first and second numbers correspond to the lower and upper bounds, and the third number is an imaginary number used for smearing out the transmission. The energy range specified by 'NEGF.tran.energyrange' is divided by the number specified by the keyword 'NEGF.tran.energydiv'. The numbers of k-points to discretize the reciprocal vectors ${\bf\tilde{b}}$ and ${\bf\tilde{c}}$ are specified by the keyword 'NEGF.tran.Kgrid'. The set of numbers given by 'NEGF.tran.Kgrid' can be different and tends to be larger than that by 'NEGF.scf.Kgrid' because of computational efficiency.

The calculations of the transmission and current are performed by a program code 'TranMain', which can be compiled in the directory 'source' as follows:

    % make TranMain
  

If the compilation is successful, you will find the executable file 'TranMain', and may copy it your work directory, possibly 'work'. Using the code 'TranMain' you can perform the calculation of the step 3, for example, as follows:

      %./TranMain NEGF-Chain.dat 

      *******************************************************
      *******************************************************
       Welcome to TranMain                                   
       This is a post-processing code of OpenMX to calculate 
       electronic transmission and current.                  
       Copyright (C), 2002-2013, H.Kino and T.Ozaki          
       TranMain comes with ABSOLUTELY NO WARRANTY.            
       This is free software, and you are welcome to         
       redistribute it under the constitution of the GNU-GPL.
      *******************************************************
      *******************************************************


      Chemical potentials used in the SCF calculation
        Left lead:  -7.752843837400 (eV)
        Right lead: -7.752843837400 (eV)
      NEGF.current.energy.step 1.0000e-02 seems to be large for the calculation ....
      The recommended Tran.current.energy.step is 0.0000e+00 (eV).

      Parameters for the calculation of the current
        lower bound:    -7.752843837400 (eV)
        upper bound:    -7.752843837400 (eV)
        energy step:     0.010000000000 (eV)
        imginary energy  0.001000000000 (eV)
        number of steps:   0     

        calculating...

        myid0= 0 i2= 0 i3= 0  k2=  0.0000 k3= -0.0000

      Transmission:  files

        ./negf-chain.tran0_0

      Current:  file

        ./negf-chain.current


      Conductance:  file

        ./negf-chain.conductance

After the calculation, in this case you will obtain three files 'negf-chain.tran0_0', 'negf-chain.current', and 'negf-chain.conductance':

• *.tran#_%

  The file stores transmissions for up- and down-spin states. The fourth column is the energy relative to the chemical potential of the left lead, and the sixth and eighth columns are transmission for up- and down-spin states, respectively. When you employ a lot of k-points which is given by 'NEGF.tran.Kgrid', a file with a different set of '#' and '%' in the file extension is generated for each k-point. The correspondence between the numbers and the k-points can be found in the file.

• *.current

  The file stores k-resolved currents and its average for up- and down-spin states in units of ampere.

• *.conductance

  The file stores k-resolved conductance at 0 K and its average for up- and down-spin states in units of quantum conductance ( $G_0\equiv \frac{e^2}{h}$). Thus, the conductance $G$ is proportional to the transmission $T$ at the chemical potential of the left lead, $\mu_{L}$, as follows:

  $$G = \frac{e^2}{h} T(\mu_{L})$$

As an example, the k-resolved transmission drawn by using the file '*.conductance' is shown in Fig. 31.

Figure 31: k-resolved Transmission at the chemical potential for (a) the majority spin state of the parallel configuration, (b) the minority spin state of the parallel configuration, and (c) a spin state of the antiparallel configuration of Fe$\vert$MgO$\vert$Fe, respectively. For the calculations k-points of $120\times 120$ were used.