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Kerr Effect Tutorials

Posted: Mon Oct 17, 2016 2:00 pm
by pereng7180
Hello,

I have a problem with first part of Kerr Effect Tutorials.
I downloaded the tutorial files and followed up the steps without any modification of files.
However, in terms of dielectric function, there is a huge difference around the region of low energy part.

Here is my result figure of first tutorial part.
https://drive.google.com/file/d/0Bz9z8k ... sp=sharing

I use yambo 3.4.2 which is suggested version.
Input file is like following which is provided from website.

Code: Select all

#  __  __   ________   ___ __ __    _______   ______        
# /_/\/_/\ /_______/\ /__//_//_/\ /_______/\ /_____/\       
# \ \ \ \ \\::: _  \ \\::\| \| \ \\::: _  \ \\:::_ \ \      
#  \:\_\ \ \\::(_)  \ \\:.      \ \\::(_)  \/_\:\ \ \ \     
#   \::::_\/ \:: __  \ \\:.\-/\  \ \\::  _  \ \\:\ \ \ \    
#     \::\ \  \:.\ \  \ \\. \  \  \ \\::(_)  \ \\:\_\ \ \   
#      \__\/   \__\/\__\/ \__\/ \__\/ \_______\/ \_____\/   
#                                                           
#               Version 3.3.1 Revision 2085                 
#                http://www.yambo-code.org                  
#
optics                       # [R OPT] Optics
bse                          # [R BSE] Bethe Salpeter Equation.
BSEmod= "causal"             # [BSE] resonant/causal/coupling
BSKmod= "IP"                 # [BSE] IP/Hartree/HF/ALDA/SEX/BSfxc
Gauge= "velocity"            # [BSE] Gauge (length|velocity). In metals length misses An-Hall
DrudeWBS= ( 4.800000 , 5.650000 )  eV  # [BSE] Drude plasmon
% BEnRange
 0.000000 | 8.000000 | eV    # [BSS] Energy range
%
% BDmRange
 0.300000 | 0.500000 | eV    # [BSS] Damping range
%
BEnSteps=  400               # [BSS] Energy steps
% BLongDir
 1.000000 | 0.000000 | 0.000000 |        # [BSS] [cc] Electric Field
%
% BSEBands
  1 | 20 |                   # [BSK] Bands range
%
The results is

Code: Select all

#  ____  ____     _       ____    ____  ______      ___     
# |_  _||_  _|   / \     |_   \  /   _||_   _ \   ."   `.   
#   \ \  / /    / _ \      |   \/   |    | |_) | /  .-.  \  
#    \ \/ /    / ___ \     | |\  /| |    |  __". | |   | |  
#    _|  |_  _/ /   \ \_  _| |_\/_| |_  _| |__) |\  `-"  /  
#   |______||____| |____||_____||_____||_______/  `.___."   
#                                                           
#              GPL Version 3.4.2 Revision 93                
#                http://www.yambo-code.org                  
#
# Absorption @ Q(1) [q->0 direction] : 1.000000  0.000000  0.000000
#
#
#
# - The Green`s function is causal -
# - Using the Velocity Gauge -
# - [r,Vnl] *is* included -
#
#
#  E/ev[1]    eps /Im[2] eps /Re[3]
#
  0.000000   0.000000   1.000000
 0.2005E-1   1540.     -16.05   
 0.4010E-1   892.7     -9.350   
 0.6015E-1   615.3     0.7542E-2
 0.8020E-1   468.8      3.795   
 0.1003      379.3      5.365   
 0.1203      319.3      5.387   
 0.1404      276.5      5.400   
 0.1604      244.5      5.510   
 0.1805      219.7      4.663   
    0.2005   199.8804     3.7639
    0.2206   183.7056     2.7739
    0.2406   170.1920     1.2663
 0.2607      158.7     0.9143E-1
    0.2807   148.6616    -1.2722
    0.3008   139.8044    -2.9538
    0.3208   131.8161    -4.4217
    0.3409   124.4958    -6.1356
    0.3609   117.6856    -7.4896
    0.3810   111.2762    -9.0157
    0.4010   105.1925   -10.2342
   0.42105   99.39152  -11.33695
   0.44110   93.85189  -12.22295
   0.46115   88.57468  -12.81132
   0.48120   83.57115  -13.16398
   0.50125   78.85963  -13.14044
   0.52130   74.45914  -12.96109
   0.54135   70.38425  -12.60153
   0.56140   66.64371  -12.10725
   0.58145   63.23386  -11.39925
   0.60150   60.14822  -10.61833
   0.62155   57.36956   -9.75511
   0.64160   54.87816   -8.92220
   0.66165   52.64769   -8.09894
   0.68170   50.65144   -7.30885
   0.70175   48.85941   -6.53428
   0.72180   47.24635   -5.80607
   0.74185   45.78427   -5.14785
   0.76190   44.45052   -4.58812
   0.78195   43.22358   -4.04444
   0.80201   42.08517   -3.57405
   0.82206   41.01907   -3.17506
   0.84211   40.01144   -2.80780
   0.86216   39.05117   -2.46019
   0.88221   38.13116   -2.16187
   0.90226   37.24529   -1.88012
   0.92231   36.39024   -1.63259
   0.94236   35.56479   -1.37611
   0.96241   34.76795   -1.12881
   0.98246   34.00313   -0.89657
   1.00251   33.27282   -0.63439
   1.02256   32.57973   -0.37442
   1.04261   31.92846   -0.09998
   1.06266   31.32154    0.16306
   1.08271   30.76028    0.44516
   1.10276   30.24651    0.70368
   1.12281   29.77881    0.95027
   1.14286   29.35625    1.20651
   1.16291   28.97477    1.42862
   1.18296   28.63178    1.63022
   1.20301   28.32182    1.80767
   1.22306   28.04060    1.93993
   1.24311   27.78287    2.06193
   1.26316   27.54277    2.13946
   1.28321   27.31438    2.18438
   1.30326   27.09272    2.21906
   1.32331   26.87278    2.21012
   1.34336   26.64911    2.17738
   1.36341   26.41742    2.12745
   1.38346   26.17376    2.04836
   1.40351   25.91503    1.95797
   1.42356   25.63899    1.85744
   1.44361   25.34449    1.74990
   1.46366   25.03094    1.64232
   1.48371   24.69873    1.54668
   1.50376   24.34986    1.46018
   1.52381   23.98606    1.36837
   1.54386   23.60967    1.30708
   1.56391   23.22465    1.26316
   1.58396   22.83337    1.24550
   1.60401   22.43998    1.25690
   1.62406   22.04820    1.28299
   1.64411   21.66208    1.34330
   1.66416   21.28407    1.42459
   1.68421   20.91846    1.53029
   1.70426   20.56767    1.65586
   1.72431   20.23605    1.80327
   1.74436   19.92482    1.97184
   1.76441   19.63735    2.16601
   1.78446   19.37575    2.36956
   1.80451   19.14132    2.58504
   1.82456   18.93600    2.81337
   1.84461   18.76025    3.04704
   1.86466   18.61559    3.28873
   1.88471   18.50196    3.52484
   1.90476   18.41939    3.76026
   1.92481   18.36699    3.99227
   1.94486   18.34539    4.21097
   1.96491   18.35281    4.42100
   1.98496   18.38762    4.61738
   2.00501   18.44921    4.79541
   2.02506   18.53423    4.95476
   2.04511   18.64048    5.09105
   2.06516   18.76534    5.19870
   2.08521   18.90594    5.28284
   2.10526   19.05797    5.34332
   2.12531   19.21853    5.36961
   2.14536   19.38467    5.37035
   2.16541   19.55248    5.34625
   2.18546   19.71825    5.28783
   2.20551   19.87996    5.20879
   2.22556   20.03416    5.10559
   2.24561   20.17966    4.97619
   2.26566   20.31406    4.82944
   2.28571   20.43576    4.66211
   2.30576   20.54395    4.48107
   2.32581   20.63788    4.28456
   2.34586   20.71656    4.07249
   2.36591   20.77957    3.85537
   2.38597   20.82583    3.62165
   2.40602   20.85600    3.38255
   2.42607   20.86949    3.13762
   2.44612   20.86601    2.89195
   2.46617   20.84545    2.64033
   2.48622   20.80825    2.38878
   2.50627   20.75409    2.13251
   2.52632   20.68292    1.88185
   2.54637   20.59526    1.63364
   2.56642   20.49085    1.39096
   2.58647   20.37126    1.15367
   2.60652   20.23684    0.92572
   2.62657   20.08854    0.70749
   2.64662   19.92793    0.50171
   2.66667   19.75680    0.31049
   2.68672   19.57631    0.13153
   2.70677   19.38968   -0.03166
   2.72682   19.19861   -0.17887
   2.74687   19.00519   -0.30713
   2.76692   18.81194   -0.42207
   2.78697   18.62049   -0.51946
   2.80702   18.43364   -0.60395
   2.82707   18.25240   -0.67455
   2.84712   18.07834   -0.73381
   2.86717   17.91307   -0.78043
   2.88722   17.75755   -0.81484
   2.90727   17.61294   -0.84575
   2.92732   17.47929   -0.86905
   2.94737   17.35756   -0.88720
   2.96742   17.24822   -0.90338
   2.98747   17.15105   -0.91710
   3.00752   17.06627   -0.92946
   3.02757   16.99359   -0.94464
   3.04762   16.93229   -0.96321
   3.06767   16.88205   -0.98711
   3.08772   16.84202   -1.01712
   3.10777   16.81131   -1.05467
   3.12782   16.78848   -1.10047
   3.14787   16.77252   -1.15844
   3.16792   16.76183   -1.22477
   3.18797   16.75501   -1.30311
   3.20802   16.75033   -1.39452
   3.22807   16.74696   -1.49607
   3.24812   16.74239   -1.61230
   3.26817   16.73547   -1.73791
   3.28822   16.72460   -1.87660
   3.30827   16.70842   -2.02831
   3.32832   16.68525   -2.18994
   3.34837   16.65344   -2.36103
   3.36842   16.61200   -2.54360
   3.38847   16.55900   -2.73335
   3.40852   16.49396   -2.93173
   3.42857   16.41474   -3.13444
   3.44862   16.32144   -3.34005
   3.46867   16.21284   -3.55052
   3.48872   16.08882   -3.75885
   3.50877   15.94901   -3.96688
   3.52882   15.79395   -4.16999
   3.54887   15.62455   -4.36899
   3.56892   15.44160   -4.55674
   3.58897   15.24639   -4.73811
   3.60902   15.04059   -4.90722
   3.62907   14.82534   -5.06591
   3.64912   14.60261   -5.21323
   3.66917   14.37426   -5.34760
   3.68922   14.14157   -5.46918
   3.70927   13.90558   -5.57959
   3.72932   13.66782   -5.67988
   3.74937   13.42902   -5.76774
   3.76942   13.19013   -5.84540
   3.78947   12.95176   -5.91402
   3.80952   12.71433   -5.97215
   3.82957   12.47769   -6.02140
   3.84962   12.24260   -6.06259
   3.86967   12.00911   -6.09537
   3.88972   11.77778   -6.12008
   3.90977   11.54867   -6.13646
   3.92982   11.32223   -6.14527
   3.94987   11.09875   -6.14614
   3.96993   10.87900   -6.13909
   3.98997   10.66352   -6.12458
   4.01003   10.45270   -6.10408
   4.03008   10.24700   -6.07752
   4.05013   10.04690   -6.04566
  4.070176   9.852642  -6.008393
  4.090226   9.664184  -5.966389
  4.110276   9.482124  -5.919865
  4.130326   9.305793  -5.872016
  4.150376   9.135288  -5.822252
  4.170426   8.970190  -5.770442
  4.190476   8.810174  -5.717053
  4.210526   8.654967  -5.663412
  4.230577   8.503894  -5.608531
  4.250627   8.356589  -5.554471
  4.270677   8.212382  -5.500478
  4.290727   8.071138  -5.445133
  4.310777   7.932533  -5.390213
  4.330827   7.796114  -5.335196
  4.350877   7.661733  -5.279264
  4.370927   7.529159  -5.223117
  4.390977   7.398514  -5.164741
  4.411028   7.269466  -5.105393
  4.431077   7.142107  -5.045683
  4.451128   7.016504  -4.985182
  4.471178   6.892456  -4.922864
  4.491229   6.770291  -4.859434
  4.511278   6.649757  -4.793148
  4.531328   6.531056  -4.726810
  4.551379   6.414088  -4.657661
  4.571429   6.298958  -4.588098
  4.591479   6.185766  -4.516157
  4.611529   6.074500  -4.441288
  4.631579   5.965330  -4.365067
  4.651629   5.858472  -4.286068
  4.671679   5.753985  -4.205474
  4.691730   5.652201  -4.122398
  4.711780   5.553363  -4.036829
  4.731830   5.457700  -3.948644
  4.751880   5.365557  -3.859730
  4.771930   5.277273  -3.767590
  4.791980   5.193048  -3.672740
  4.812030   5.113018  -3.577892
  4.832080   5.037496  -3.481562
  4.852130   4.966666  -3.383767
  4.872181   4.900475  -3.285921
  4.892231   4.839078  -3.187839
  4.912281   4.782417  -3.090225
  4.932331   4.730490  -2.992206
  4.952381   4.682962  -2.896308
  4.972431   4.639783  -2.801450
  4.992481   4.600628  -2.708393
  5.012532   4.565269  -2.616964
  5.032581   4.533409  -2.527020
  5.052632   4.504703  -2.440652
  5.072682   4.478875  -2.355149
  5.092732   4.455595  -2.272259
  5.112782   4.434600  -2.191875
  5.132832   4.415693  -2.113316
  5.152883   4.398668  -2.037561
  5.172932   4.383300  -1.963182
  5.192983   4.369555  -1.890800
  5.213033   4.357237  -1.820462
  5.233083   4.346369  -1.752156
  5.253133   4.336795  -1.685081
  5.273183   4.328555  -1.619407
  5.293233   4.321489  -1.555109
  5.313283   4.315628  -1.493010
  5.333333   4.310960  -1.432471
  5.353384   4.307352  -1.372422
  5.373434   4.304822  -1.314237
  5.393484   4.303395  -1.256898
  5.413534   4.303038  -1.201022
  5.433584   4.303833  -1.146121
  5.453634   4.305863  -1.092021
  5.473684   4.309071  -1.038670
  5.493734   4.313641  -0.986758
  5.513785   4.319726  -0.936010
  5.533835   4.327364  -0.886308
  5.553885   4.336601  -0.838575
  5.573935   4.347578  -0.791504
  5.593985   4.360328  -0.745628
  5.614036   4.374966  -0.702549
  5.634085   4.391310  -0.660679
  5.654136   4.409463  -0.621618
  5.674186   4.429101  -0.585054
  5.694236   4.450108  -0.551004
  5.714286   4.472275  -0.520306
  5.734336   4.495239  -0.492300
  5.754386   4.518754  -0.468336
  5.774436   4.542330  -0.447438
  5.794487   4.565560  -0.429884
  5.814537   4.588335  -0.415566
  5.834587   4.610065  -0.404246
  5.854637   4.630506  -0.396319
  5.874687   4.649234  -0.390480
  5.894737   4.666068  -0.387864
  5.914787   4.680696  -0.387748
  5.934837   4.693181  -0.388645
  5.954887   4.703219  -0.391225
  5.974937   4.710837  -0.394570
  5.994987   4.716012  -0.399360
  6.015038   4.718820  -0.403956
  6.035088   4.719376  -0.409162
  6.055138   4.717727  -0.414023
  6.075188   4.714070  -0.418250
  6.095238   4.708573  -0.422714
  6.115288   4.701476  -0.426033
  6.135339   4.692958  -0.427742
  6.155388   4.683094  -0.429004
  6.175439   4.672203  -0.428967
  6.195489   4.660599  -0.428146
  6.215539   4.648347  -0.425361
  6.235589   4.635658  -0.421520
  6.255640   4.622753  -0.416171
  6.275690   4.609876  -0.409638
  6.295739   4.597290  -0.402114
  6.315790   4.585056  -0.393242
  6.335840   4.573558  -0.383161
  6.355890   4.562787  -0.372325
  6.375940   4.552920  -0.360962
  6.395990   4.544191  -0.347839
  6.416040   4.536597  -0.334721
  6.436090   4.530326  -0.320889
  6.456141   4.525442  -0.306182
  6.476191   4.521989  -0.292163
  6.496241   4.520009  -0.277701
  6.516291   4.519528  -0.263505
  6.536341   4.520777  -0.249898
  6.556391   4.523542  -0.236513
  6.576441   4.527951  -0.224217
  6.596491   4.533873  -0.213075
  6.616541   4.541406  -0.202810
  6.636592   4.550474  -0.193952
  6.656642   4.560884  -0.186800
  6.676692   4.572550  -0.181592
  6.696742   4.585377  -0.178275
  6.716792   4.599009  -0.177532
  6.736842   4.613225  -0.179761
  6.756892   4.627772  -0.184480
  6.776943   4.642087  -0.192143
  6.796993   4.655947  -0.202569
  6.817043   4.668826  -0.215897
  6.837093   4.680259  -0.232519
  6.857143   4.689848  -0.251873
  6.877193   4.697185  -0.273166
  6.897243   4.701949  -0.296418
  6.917294   4.703878  -0.321739
  6.937343   4.702598  -0.348041
  6.957394   4.698070  -0.375273
  6.977444   4.690367  -0.402536
  6.997494   4.679535  -0.429421
  7.017544   4.665673  -0.455729
  7.037594   4.649117  -0.480862
  7.057645   4.630008  -0.504468
  7.077694   4.608942  -0.526268
  7.097744   4.586187  -0.546616
  7.117795   4.562181  -0.564231
  7.137845   4.537261  -0.580466
  7.157895   4.511705  -0.594777
  7.177945   4.485868  -0.607270
  7.197996   4.459954  -0.618105
  7.218045   4.434109  -0.627517
  7.238095   4.408422  -0.635824
  7.258145   4.383030  -0.643194
  7.278196   4.357776  -0.649750
  7.298246   4.332726  -0.655370
  7.318296   4.307726  -0.660714
  7.338346   4.282792  -0.665601
  7.358397   4.257746  -0.669650
  7.378446   4.232566  -0.672886
  7.398496   4.207239  -0.675817
  7.418547   4.181742  -0.678043
  7.438597   4.156178  -0.679582
  7.458647   4.130512  -0.679446
  7.478697   4.104861  -0.679451
  7.498747   4.079335  -0.677834
  7.518797   4.054143  -0.675279
  7.538847   4.029355  -0.671789
  7.558897   4.005237  -0.667562
  7.578948   3.981756  -0.662403
  7.598998   3.959095  -0.656638
  7.619048   3.937295  -0.650300
  7.639098   3.916458  -0.643704
  7.659149   3.896471  -0.637027
  7.679198   3.877364  -0.630511
  7.699248   3.859009  -0.623478
  7.719298   3.841362  -0.617285
  7.739348   3.824242  -0.611498
  7.759399   3.807557  -0.606149
  7.779449   3.791126  -0.601048
  7.799500   3.774728  -0.596825
  7.819549   3.758225  -0.592985
  7.839599   3.741515  -0.589439
  7.859649   3.724412  -0.586749
  7.879699   3.706813  -0.583876
  7.899750   3.688681  -0.581225
  7.919800   3.669890  -0.578366
  7.939850   3.650458  -0.575567
  7.959899   3.630379  -0.572124
  7.979950   3.609651  -0.568474
  8.000000   3.588325  -0.564212
# 
# YAMBO@golubh1 x 001 CPUs * 10/14/2016  19:06 [start]
#                            10/14/2016  19:06 [end]
# 
# Cpu Timing [Min/Max/Average]: 06s/06s/06s
#
# .-Input file : Inputs/02_IP-RPA_vel
# | optics                       # [R OPT] Optics
# | bse                          # [R BSE] Bethe Salpeter Equation.
# | ElecTemp=0.1000E-3     eV    # Electronic Temperature
# | BoseTemp=0.1000E-3     eV    # Bosonic Temperature
# | FFTGvecs= 1865         RL    # [FFT] Plane-waves
# | BSEmod= "causal"             # [BSE] resonant/causal/coupling
# | BSKmod= "IP"                 # [BSE] IP/Hartree/HF/ALDA/SEX
# | Gauge= "velocity"            # [BSE] Gauge (length|velocity). In metals length misses An-Hall
# | DrudeWBS= ( 4.800000 , 5.650000 )  eV  # [BSE] Drude plasmon
# | % BEnRange
# |  0.000000 | 8.000000 | eV    # [BSS] Energy range
# | %
# | % BDmRange
# |  0.300000 | 0.500000 | eV    # [BSS] Damping range
# | %
# | BEnSteps=  400               # [BSS] Energy steps
# | % BLongDir
# |  1.000000 | 0.000000 | 0.000000 |        # [BSS] [cc] Electric Field
# | %
# | % BSEBands
# |   1 | 20 |                   # [BSK] Bands range
# | %
Very first part always show the 0.0000 value in imaginary part.
For the other parts, the shape shows similar to figure presented on the website.

In order to test the SAVE file, I also generated and tested the SAVE files from the abinit input files which is provided.
From those generated SAVE files, yambo shows same results.
What can be the problem?
Thank you!

Best regards,
KISUNG KANG

Re: Kerr Effect Tutorials

Posted: Tue Oct 18, 2016 1:29 am
by Davide Sangalli
Dear KISUNG KANG,
thank you for using yambo. Please remember to add the signature in your profile.
It is a rule of the forum.

Coming to your question, I checked the code, and indeed it seems there is a problem in the inclusion of the Drude term.

You should replace the source file src/bse/K_eh_setup.F with the one attached here (remove the .txt extension) and then recompile the code
This should solve your problem.

Best,
D.

Re: Kerr Effect Tutorials

Posted: Tue Oct 18, 2016 7:23 pm
by pereng7180
Hello,

Thank you for help. I finally got similar dielectric function results from yambo 3.4.2.
During the next step with SO effect, I face another problem.

https://drive.google.com/open?id=0Bz9z8 ... zktXzh4cFk

My off-diagonal calculation shows similar results from tutorial.
However, diagonal calculation does not show difference between 'with SO' and 'without SO' as much as tutorial does.

How can I deal with this?
My INPUT option is here. But, I did not change any thing from provided INPUT.

Code: Select all

#  __  __   ________   ___ __ __    _______   ______        
# /_/\/_/\ /_______/\ /__//_//_/\ /_______/\ /_____/\       
# \ \ \ \ \\::: _  \ \\::\| \| \ \\::: _  \ \\:::_ \ \      
#  \:\_\ \ \\::(_)  \ \\:.      \ \\::(_)  \/_\:\ \ \ \     
#   \::::_\/ \:: __  \ \\:.\-/\  \ \\::  _  \ \\:\ \ \ \    
#     \::\ \  \:.\ \  \ \\. \  \  \ \\::(_)  \ \\:\_\ \ \   
#      \__\/   \__\/\__\/ \__\/ \__\/ \_______\/ \_____\/   
#                                                           
#               Version 3.3.1 Revision 2085                 
#                http://www.yambo-code.org                  
#
optics                       # [R OPT] Optics
bse                          # [R BSE] Bethe Salpeter Equation.
BSEmod= "causal"             # [BSE] resonant/causal/coupling
BSKmod= "IP"                 # [BSE] IP/Hartree/HF/ALDA/SEX/BSfxc
Gauge= "velocity"            # [BSE] Gauge (length|velocity). In metals length misses An-Hall
EvalKerr                     # [BSE] Compute the Kerr effect
DrudeWBS= ( 4.800000 , 5.650000 )  eV  # [BSE] Drude plasmon
% BEnRange
 0.000000 | 8.000000 | eV    # [BSS] Energy range
%
% BDmRange
 0.300000 | 0.500000 | eV    # [BSS] Damping range
%
BEnSteps=  400               # [BSS] Energy steps
% BLongDir
 1.000000 | 0.000000 | 0.000000 |        # [BSS] [cc] Electric Field
%
% BSEBands
  1 | 30 |                   # [BSK] Bands range
%
Thank you!

Best regards,
KISUNG KANG

Re: Kerr Effect Tutorials

Posted: Tue Oct 18, 2016 7:44 pm
by Davide Sangalli
Dear Kisung Kang,
I think your new calculation is correct.
Indeed SOC in bulk Iron is small enough and one does not expect to see its effect using such high smearing.

We should update the image on the yambo-website.
I do not remember why previously we were obtaining the slightly different image.
With your permission I'd be glad to use the image you just sent up and upload it in the website.

Best,
D.

Re: Kerr Effect Tutorials

Posted: Tue Oct 18, 2016 8:03 pm
by pereng7180
Dear Davide Sangalli,

Thank you for reply.
If it is helpful to use my figures, don't hesitate use them.
Hope there is no error with my calculation and plotting.

Here are other figures with replaced K_eh_setup.F code on YAMBO 3.4.2.
I also correct some typos and thus you can use these figures.
https://drive.google.com/open?id=0Bz9z8 ... UtlWkxpQkk
https://drive.google.com/open?id=0Bz9z8 ... zktXzh4cFk
https://drive.google.com/open?id=0Bz9z8 ... GxGcFRLZDQ

Please check any problem or typo on them.
Thank you!

Best regards,
KISUNG KANG