Resolving optical calculations

Purpose

This tutorial is designed to describe the procedure and output of OPTICS_PART=1,OPTICS_PART=2 and OPTICS_PART=3. See also this tutorial, which resolves the density-of-states by k in a magnetic metal.

Prerequsites

This tutorial follows from the self-consistent and optics tutorial preformed on PbTe, it is highly recomended that you go through those before this tutorial, for this tutorials the lm or lmf are needed.

Resolve by Individual Band to Band Contributions

The imaginary part of the dielectric function and density of states can both be resolved by band to band contribution, to preform such calculation it is only necessery to set OPTICS_PART=1 with in the control file, such that

  OPTICS  MODE=1 NPTS=1001 WINDOW=0 1 LTET=3
          FILBND=9,10 EMPBND=11,12
          PART=1

and preform the calculation as befor.

  lm -vnit=1 ctrl.pbte --rs=1,0

It is worth noting that caution should be taken with such settings as the output file (popt.exe) can become very large very quickly. For the exampel above where the bands are restricted to 2 for conduction and valnce bands there will be 12 values for each energy point. Thes values correspond to contirbution to the imaginary part of the dielectric from band 9 to band 11 for x orientation of electric field followed by y and z counter parts, the next three digits correspond to contributions form transitions from band 9 to 12 (three values for x,y and z) followed by transitions from valence band 10 to conduction band 11 and finaly band 10 to band 12.

Resolving by k-points

In both the lm and lmf implementations of the code it is possible to separate the contribution to the optical properites by individual k-points. Note: You can also k-resolve the density-of-states, as described in this tutorial. This calculation can be performed by adding PART=2 to the optics category, however few additional steps are needed to interpret the output. Lets start by running an optics calculation for PbTe with the following setup in the control file:

OPTICS MODE=1 NPTS=1001 WINDOW=0 1 ESCISS=0 LTET=3 PART=2

we can preform this calculation just as any other optics calculation, simply invoke:

lm pbte -voptmod=1 -vnit=1 –rs=1,0

through this the program will write a new file name popt.pbte. The format of this file is different to opt.pbte and jdos.pbte which you have previously encountered; here the first number in each row represtnts the energy while the next 3X numbers are the contributions from X ireducible k-points for the three orientation of the electric field. Below you can see a section of the popt.pbte for 4X4X4 k-mesh:

0.262000     0.000000     1.456862     2.730097     0.665279     0.869784     3.001192
             0.064389     1.856153     0.000000     1.456862     2.730097     0.665279
             0.869784     3.001192     0.064389     1.856153     0.000000     1.456862
             2.730097     0.665279     0.869784     3.001192     0.064389     1.856153
0.400000 0.000000 0.514493 0.754321 0.391577 0.955750 1.069400
  0.564346 0.374508 0.000000 0.514493 0.754321 0.391577
  0.955750 1.069400 0.564346 0.374508 0.000000 0.514493
  0.754321 0.391577 0.955750 1.069400 0.564346 0.374508

In the excerpt above the first value 0.400000 is the energy in Rydbergs, the next 8 numbers correspond to the 8 irreducible k-points and the electric field orientated along x, while the next 8 correspond to electric field orientated along y followed by the z counterpart. To identify the order of the k points it is necessery to invoke the lm program with an additional command line switch:

lm pbte -voptmod=0 -vnit=1 –pr81 –rs=1,0

here the switch “- -pr81” increases the verbosity setting of the program to print out the required information. With such high verbosity setting a large amount of data is printed, however we are looking for the brillouin zone q-point mapping shown, a complete list of reducible k-points is also provided in this output.

 BZMESH: qp mapping   
  i1..i3                          qp                    iq   ig  g  
 (1,1,1)           0.000000    0.000000    0.000000     1    1 i*i   
 (2,1,1)          -0.250000    0.250000    0.250000     2    1 i*i   
 (4,1,1)           0.250000   -0.250000   -0.250000     2    2 i   
 (1,2,1)           0.250000   -0.250000    0.250000     2    3 r3(1,1,-1)   
 (1,4,1)          -0.250000    0.250000   -0.250000     2    4 i*r3(1,1,-1)   
 (4,4,4)          -0.250000   -0.250000   -0.250000     2    5 r3(-1,-1,1)   
 (2,2,2)           0.250000    0.250000    0.250000     2    6 i*r3(-1,-1,1)   
 (1,1,2)           0.250000    0.250000   -0.250000     2    9 r3(-1,-1,-1)   
 (1,1,4)          -0.250000   -0.250000    0.250000     2   10 i*r3(-1,-1,-1)   
 (3,1,1)          -0.500000    0.500000    0.500000     3    1 i*i   
 (1,3,1)           0.500000   -0.500000    0.500000     3    3 r3(1,1,-1)   
 (3,3,3)          -0.500000   -0.500000   -0.500000     3    5 r3(-1,-1,1)   
 (1,1,3)           0.500000    0.500000   -0.500000     3    9 r3(-1,-1,-1)   
 (2,2,1)           0.000000    0.000000    0.500000     4    1 i*i   
 (4,4,1)           0.000000    0.000000   -0.500000     4    2 i   
 (4,1,4)           0.000000   -0.500000    0.000000     4    3 r3(1,1,-1)   
 (2,1,2)           0.000000    0.500000    0.000000     4    4 i*r3(1,1,-1)   
 (1,4,4)          -0.500000    0.000000    0.000000     4    5 r3(-1,-1,1)   
 (1,2,2)           0.500000    0.000000    0.000000     4    6 i*r3(-1,-1,1)   
 (3,2,1)          -0.250000    0.250000    0.750000     5    1 i*i   
 (3,4,1)           0.250000   -0.250000   -0.750000     5    2 i   
 (4,2,4)           0.250000   -0.750000    0.250000     5    3 r3(1,1,-1)   
 (2,4,2)          -0.250000    0.750000   -0.250000     5    4 i*r3(1,1,-1)   
 (4,3,3)          -0.750000   -0.250000   -0.250000     5    5 r3(-1,-1,1)    
 (2,3,3)           0.750000    0.250000    0.250000     5    6 i*r3(-1,-1,1)   
 (1,3,2)           0.750000   -0.250000    0.250000     5    7 r3d   
 (1,3,4)          -0.750000    0.250000   -0.250000     5    8 i*r3d   
 (2,1,3)           0.250000    0.750000   -0.250000     5    9 r3(-1,-1,-1)   
 (4,1,3)          -0.250000   -0.750000    0.250000     5   10 i*r3(-1,-1,-1)   
 (3,3,4)          -0.250000   -0.250000   -0.750000     5   11 r2x   
 (3,3,2)           0.250000    0.250000    0.750000     5   12 mx   
 (2,4,4)          -0.750000    0.250000    0.250000     5   17 r3(1,-1,-1)   
 (4,2,2)           0.750000   -0.250000   -0.250000     5   18 i*r3(1,-1,-1)   
 (3,1,2)          -0.250000    0.750000    0.250000     5   19 r3(-1,1,1)    
 (3,1,4)           0.250000   -0.750000   -0.250000     5   20 i*r3(-1,1,1)   
 (1,4,3)          -0.750000   -0.250000    0.250000     5   23 r2(1,0,-1)   
 (1,2,3)           0.750000    0.250000   -0.250000     5   24 m(1,0,-1)   
 (4,4,2)           0.250000    0.250000   -0.750000     5   25 r2y    
 (2,2,4)          -0.250000   -0.250000    0.750000     5   26 my   
 (2,3,1)           0.250000   -0.250000    0.750000     5   33 r2z   
 (4,3,1)          -0.250000    0.250000   -0.750000     5   34 mz   
 (3,4,3)          -0.250000   -0.750000   -0.250000     5   41 r3(1,-1,1)   
 (3,2,3)           0.250000    0.750000    0.250000     5   42 i*r3(1,-1,1)   
 (4,2,1)          -0.500000    0.500000    1.000000     6    1 i*i   
 (2,4,1)           0.500000   -0.500000   -1.000000     6    2 i   
 (4,3,4)           0.500000   -1.000000    0.500000     6    3 r3(1,1,-1)   
 (2,3,2)          -0.500000    1.000000   -0.500000     6    4 i*r3(1,1,-1)   
 (3,2,2)          -1.000000   -0.500000   -0.500000     6    5 r3(-1,-1,1)   
 (3,4,4)           1.000000    0.500000    0.500000     6    6 i*r3(-1,-1,1)   
 (1,4,2)           1.000000   -0.500000    0.500000     6    7 r3d   
 (1,2,4)          -1.000000    0.500000   -0.500000     6    8 i*r3d   
 (2,1,4)           0.500000    1.000000   -0.500000     6    9 r3(-1,-1,-1)   
 (4,1,2)          -0.500000   -1.000000    0.500000     6   10 i*r3(-1,-1,-1)   
 (2,2,3)          -0.500000   -0.500000   -1.000000     6   11 r2x   
 (4,4,3)           0.500000    0.500000    1.000000     6   12 mx   
 (3,3,1)           0.000000    0.000000    1.000000     7    1 i*i   
 (3,1,3)           0.000000   -1.000000    0.000000     7    3 r3(1,1,-1)   
 (1,3,3)          -1.000000    0.000000    0.000000     7    5 r3(-1,-1,1)   
 (4,3,2)           0.000000    0.500000    1.000000     8    1 i*i   
 (2,3,4)           0.000000   -0.500000   -1.000000     8    2 i   
 (3,2,4)           0.500000   -1.000000    0.000000     8    3 r3(1,1,-1)   
 (3,4,2)          -0.500000    1.000000    0.000000     8    4 i*r3(1,1,-1)   
 (4,2,3)          -1.000000    0.000000   -0.500000     8    5 r3(-1,-1,1)   
 (2,4,3)           1.000000    0.000000    0.500000     8    6 i*r3(-1,-1,1)

 {::nomarkdown}</div>{:/nomarkdown}

Resolving by k-points and band to band contributions

To resolve the optics and density data by both k-points and band to band contributions option OPTICS_PART=3 is used. In this case the popt.ext file has a similar format to the two previous showed, however here the bands are resolved by band to band contribution first and followed by contributions of each k-point within that band-to-band transitions. that is for the case below

  OPTICS  MODE=1 NPTS=1001 WINDOW=0 1 LTET=3
          FILBND=4,5 EMPBND=6,7
          PART=3

with 8 irreducible k-pointsthere will be 96 values for each energy point. these values are the contributions of the transitions resolved by band to band first ( as described for OPTICS_PART=1 ) and k-points second (as described for OPTICS_PART=2.


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