Transmission, total current, and conductance

At first, openmx calculates the transmission, the total current, and the conductance. The relevant keywords for the calculation are as follows:

    NEGF.tran.Analysis         on        #  default on
    NEGF.tran.CurrentDensity   on        #  default on
    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

• NEGF.tran.Analysis, NEGF.tran.Channel, NEGF.tran.CurrentDensity

  If NEGF.tran.Analysis is set to on, the transmission, the total current, and the conductance are calculated.

• NEGF.tran.energyrange, NEGF.tran.energydiv

  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'.

• NEGF.tran.Kgrid

  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' to take account of the computational efficiency.

In the calculations of the transmission, the current, and the conductance, following messages are printed in the standard output.

*******************************************************
*******************************************************
 Welcome to TRAN_Main_Analysis.                        
 This is a post-processing code of OpenMX to analyze   
 transport properties such as electronic transmission, 
 current, eigen channel, and current distribution in   
 real space based on NEGF.                             
 Copyright (C), 2002-2015, H. Kino and T. Ozaki        
 TRAN_Main_Analysis 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:  -5.125617225230 (eV)
  Right lead: -5.125617225230 (eV)
NEGF.current.energy.step 1.0000e-02 seems to be large for the calculation of current ...
The recommended Tran.current.energy.step is 0.0000e+00 (eV).
  TRAN_Channel_kpoint  0    0.000000    0.000000
  TRAN_Channel_energy  0    0.000000 eV
  TRAN_Channel_Num 5 

Parameters for the calculation of the current
  lower bound:     -5.125617225230 (eV)
  upper bound:     -5.125617225230 (eV)
  energy step:      0.010000000000 (eV)
  imaginary energy  0.001000000000 (eV)
  number of steps:   0         

  calculating...

  myid0= 0 i2= 0 i3= 0  k2=  0.0000 k3= -0.0000
  myid0= 1 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 calculations, in this case you will obtain three files negf-chain.tran0_0, negf-chain.current,
negf-chain.conductance:

• System.Name.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.

• System.Name.current

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

• System.Name.conductance

  The file stores k-resolved conductance 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 'System.Name.conductance' is shown in Fig. 41.

Figure 41: 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.