Eigenchannel analysis

In the step 3, transmission eigenchannels are calculated optionally. The relevant keywords for this calculation are as follows:

    NEGF.tran.Channel          on        #  default on
    NEGF.Channel.Nkpoint        1        # default=1
    <NEGF.Channel.kpoint
      0.0  0.0
    NEGF.Channel.kpoint>
    # default 0.0 0.0
    NEGF.Channel.Nenergy        1        # default=1
    <NEGF.Channel.energy
      0.0
    NEGF.Channel.energy>
    # default 0.0
    NEGF.Channel.Num    5    # defualt=5(for collinear), 10(for Non-collinear)

In the calculation of eigenchannels, openmx makes the following standard output:

**************************************************
 Calculation of transmission eigenchannels starts
**************************************************

  File index : negf-8zgnr-0.3.traneval#k_#E_#spin negf-8zgnr-0.3.tranevec#k_#E_#spin 

  myid0 =   0, #k :    0, N_{ort} / N_{nonort} : 380 / 380 
  PE    0 generates ./negf-8zgnr-0.3.traneval0_0_0 . Sum(eigenval) :   0.031643 
  PE    0 generates ./negf-8zgnr-0.3.traneval0_0_1 . Sum(eigenval) :   0.000508 

  Eigenchannel calculation finished 
  They are written in plottable files. 
  File index : negf-8zgnr-0.3.tranec#k_#E_#spin_#branch_r.cube(.bin)  
               negf-8zgnr-0.3.tranec#k_#E_#spin_#branch_i.cube(.bin)  

  ./negf-8zgnr-0.3.tranec0_0_0_0_r.cube     ./negf-8zgnr-0.3.tranec0_0_0_0_i.cube 
  ./negf-8zgnr-0.3.tranec0_0_0_1_r.cube     ./negf-8zgnr-0.3.tranec0_0_0_1_i.cube 
  ./negf-8zgnr-0.3.tranec0_0_0_2_r.cube     ./negf-8zgnr-0.3.tranec0_0_0_2_i.cube 
  ./negf-8zgnr-0.3.tranec0_0_0_3_r.cube     ./negf-8zgnr-0.3.tranec0_0_0_3_i.cube 
  ./negf-8zgnr-0.3.tranec0_0_0_4_r.cube     ./negf-8zgnr-0.3.tranec0_0_0_4_i.cube 
  ./negf-8zgnr-0.3.tranec0_0_1_0_r.cube     ./negf-8zgnr-0.3.tranec0_0_1_0_i.cube 
  ./negf-8zgnr-0.3.tranec0_0_1_1_r.cube     ./negf-8zgnr-0.3.tranec0_0_1_1_i.cube 
  ./negf-8zgnr-0.3.tranec0_0_1_2_r.cube     ./negf-8zgnr-0.3.tranec0_0_1_2_i.cube 
  ./negf-8zgnr-0.3.tranec0_0_1_3_r.cube     ./negf-8zgnr-0.3.tranec0_0_1_3_i.cube 
  ./negf-8zgnr-0.3.tranec0_0_1_4_r.cube     ./negf-8zgnr-0.3.tranec0_0_1_4_i.cube

In this case, 22 files, negf-8zgnr-0.3.treval0_0_0, negf-8zgnr-0.3.tranevec0_0_0,
negf-8zgnr-0.3.tranec0_0_0_0_r.cube - negf-8zgnr-0.3.tranec0_0_1_4_r.cube,
negf-8zgnr-0.3.tranec0_0_0_0_i.cube - negf-8zgnr-0.3.tranec0_0_1_4_i.cube, are generated.

***********************************************************
***********************************************************
        Eigenvalues and LCAO coefficients                  
        at the k-points specified in the input file.       
***********************************************************
***********************************************************


   # of k-point = 0
   k2=   0.00000 k3=   0.00000

   # of Energy = 0
   e=   0.00000 

   Spin = Up 

   Real (Re) and imaginary (Im) parts of LCAO coefficients


                          1                   2                   3                   4              
                         0.9778              0.0000              0.0000              0.0000          

                          Re        Im        Re        Im        Re        Im        Re        Im   

   1   C 0 s            -0.00000  -0.00000  -0.00000   0.00000   0.00000   0.00000  -0.00000   0.00000
         1 s            -0.00000  -0.00000  -0.00000  -0.00000   0.00000  -0.00000   0.00000  -0.00000
         0 px           -0.63002  -1.49377  -0.14466   0.00019   0.01644  -0.00032  -0.07885   0.00095
         0 py            0.00000   0.00000   0.00000   0.00000  -0.00000   0.00000   0.00000   0.00000
         0 pz            0.00000  -0.00000   0.00000  -0.00000  -0.00000  -0.00000  -0.00000  -0.00000
   2   C 0 s            -0.00000  -0.00000  -0.00000  -0.00000   0.00000  -0.00000   0.00000  -0.00000
         1 s             0.00000   0.00000  -0.00000  -0.00000  -0.00000   0.00000  -0.00000   0.00000
         0 px            0.18040  -0.03816  -0.00452   0.00009  -0.00545  -0.00010  -0.01970  -0.00004
         0 py           -0.00000  -0.00000  -0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
         0 pz            0.00000  -0.00000  -0.00000   0.00000  -0.00000  -0.00000  -0.00000  -0.00000
   3   C 0 s             0.00000   0.00000   0.00000  -0.00000  -0.00000   0.00000  -0.00000   0.00000
         1 s            -0.00000  -0.00000   0.00000   0.00000   0.00000  -0.00000   0.00000  -0.00000
         0 px            2.06634   0.40490   0.11067   0.00023  -0.06068   0.00009  -0.06690  -0.00042
         0 py            0.00000   0.00000   0.00000  -0.00000  -0.00000   0.00000  -0.00000   0.00000
         0 pz            0.00000   0.00000   0.00000   0.00000  -0.00000  -0.00000   0.00000  -0.00000
   4   C 0 s             0.00000   0.00000   0.00000   0.00000  -0.00000  -0.00000  -0.00000  -0.00000
         1 s            -0.00000  -0.00000  -0.00000  -0.00000  -0.00000   0.00000  -0.00000   0.00000

Figure: (a) Spin dependent transmission under a bias voltage of 0.3 V, (b) spin dependent transmission under a bias voltage of -0.3 V, (c) an eigenchannel at an energy of 0 eV, spin $\uparrow$, and 0.3 V as a bias voltage, (d) an eigenchannel at an energy of 0 eV, spin $\uparrow$, and - 0.3 V as a bias voltage, (e) an eigenchannel at an energy of 0 eV, spin $\downarrow$, and 0.3 V as a bias voltage, and (f) an eigenchannel at an energy of 0 eV, spin $\downarrow$, and - 0.3 V as a bias voltage in 8-zigzag graphene nanoribbon with an antiferromagnetic junction (The spin is $\uparrow$ in the left region and it is $\downarrow$ in the right region.) are depicted. The level of isosurfaces are identical in these figures; when the transmission is small, the eigenchannel itself is also small.
\includegraphics[width=10.0cm]{EigenChannel.eps}