I want to calculate the exciton spectrum for black phosphorous, like energy levels of 1s, 2s, 2p, .... I have a experimental result as comparison. My calculation is as follows,

1. Calculate the corrected band gap with GW method (yambo -F gw.in -p p -g n -r -k hartree -V qp)

2. Adding the BSE effect to calculate the exciton peak (1s) and exciton binding energy (yambo -F bse.in -r -o b -p p -y d -k sex -V all)

After these, I have obtained the band gap and exciton binding energy which are consistent with the experimental values.

However,, when I want to get the energy levels of exciton spectrum, I use the command "ypp -J bse -e s", "ypp -F ypp.in -J bse -e a" and run it, I got results that can be plotted as the attached figure. From this figure we can see, the calculated 2s and 3s levels are all higher than 2eV. But the experimental results for 2s and 3s levels are 1.68 and 1.85eV, respectively.

The setting parameters for BSE calculation are as following, hope it can be helpful.

Code: Select all

```
#
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# \ \ \ \ \\::: _ \ \\::\| \| \ \\::: _ \ \\:::_ \ \
# \:\_\ \ \\::(_) \ \\:. \ \\::(_) \/_\:\ \ \ \
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# \::\ \ \:.\ \ \ \\. \ \ \ \\::(_) \ \\:\_\ \ \
# \__\/ \__\/\__\/ \__\/ \__\/ \_______\/ \_____\/
#
#
# GPL Version 4.1.3 Revision 76
# Serial Build
# http://www.yambo-code.org
#
rim_cut # [R RIM CUT] Coulomb potential
optics # [R OPT] Optics
ppa # [R Xp] Plasmon Pole Approximation
bss # [R BSS] Bethe Salpeter Equation solver
bse # [R BSE] Bethe Salpeter Equation.
bsk # [R BSK] Bethe Salpeter Equation kernel
em1d # [R Xd] Dynamical Inverse Dielectric Matrix
StdoHash= 40 # [IO] Live-timing Hashes
Nelectro= 20.00000 # Electrons number
ElecTemp= 0.000000 eV # Electronic Temperature
BoseTemp=-1.000000 eV # Bosonic Temperature
OccTresh=0.1000E-4 # Occupation treshold (metallic bands)
DBsIOoff= "none" # [IO] Space-separated list of DB with NO I/O. DB=(DIP,X,HF,COLLs,J,GF,CARRIERs,W,SC,BS,ALL)
DBsFRAGpm= "none" # [IO] Space-separated list of +DB to be FRAG and -DB NOT to be FRAG. DB=(DIP,X,W,HF,COLLS,K,BS,QINDX,
FFTGvecs= 21149 RL # [FFT] Plane-waves
#WFbuffIO # [IO] Wave-functions buffered I/O
NonPDirs= "none" # [X/BSS] Non periodic chartesian directions (X,Y,Z,XY...)
RandQpts=1000000 # [RIM] Number of random q-points in the BZ
RandGvec= 200 RL # [RIM] Coulomb interaction RS components
#QpgFull # [F RIM] Coulomb interaction: Full matrix
% Em1Anys
0.00 | 0.00 | 0.00 | # [RIM] X Y Z Static Inverse dielectric matrix
%
IDEm1Ref=0 # [RIM] Dielectric matrix reference component 1(x)/2(y)/3(z)
CUTGeo= "none" # [CUT] Coulomb Cutoff geometry: box/cylinder/sphere X/Y/Z/XY..
% CUTBox
0.00 | 0.00 | 0.00 | # [CUT] [au] Box sides
%
CUTRadius= 0.000000 # [CUT] [au] Sphere/Cylinder radius
CUTCylLen= 0.000000 # [CUT] [au] Cylinder length
#CUTCol_test # [CUT] Perform a cutoff test in R-space
Chimod= "Hartree" # [X] IP/Hartree/ALDA/LRC/BSfxc
BSEmod= "retarded" # [BSE] resonant/retarded/coupling
BSKmod= "SEX" # [BSE] IP/Hartree/HF/ALDA/SEX
BSSmod= "d" # [BSS] (h)aydock/(d)iagonalization/(i)nversion/(t)ddft`
BSENGexx= 40 Ry # [BSK] Exchange components
#ALLGexx # [BSS] Force the use use all RL vectors for the exchange part
BSENGBlk= 8 Ry # [BSK] Screened interaction block size
#WehDiag # [BSK] diagonal (G-space) the eh interaction
#WehCpl # [BSK] eh interaction included also in coupling
KfnQPdb= "E < gw/ndb.QP" # [EXTQP BSK BSS] Database
KfnQP_N= 1 # [EXTQP BSK BSS] Interpolation neighbours
% KfnQP_E
0.000000 | 1.000000 | 1.000000 | # [EXTQP BSK BSS] E parameters (c/v) eV|adim|adim
%
KfnQP_Z= ( 1.000000 , 0.000000 ) # [EXTQP BSK BSS] Z factor (c/v)
KfnQP_Wv_E= 0.000000 eV # [EXTQP BSK BSS] W Energy reference (valence)
% KfnQP_Wv
0.00 | 0.00 | 0.00 | # [EXTQP BSK BSS] W parameters (valence) eV| eV|eV^-1
%
KfnQP_Wc_E= 0.000000 eV # [EXTQP BSK BSS] W Energy reference (conduction)
% KfnQP_Wc
0.00 | 0.00 | 0.00 | # [EXTQP BSK BSS] W parameters (conduction) eV| eV|eV^-1
%
Gauge= "length" # [BSE] Gauge (length|velocity)
#MetDamp # [BSE] Define \w+=sqrt(\w*(\w+i\eta))
DrudeWBS= ( 0.00 , 0.00 ) eV # [BSE] Drude plasmon
#Reflectivity # [BSS] Compute reflectivity at normal incidence
BoseCut= 0.10000 # [BOSE] Finite T Bose function cutoff
% BEnRange
0.00000 | 10.00000 | eV # [BSS] Energy range
%
% BDmRange
0.10000 | 0.10000 | eV # [BSS] Damping range
%
BEnSteps= 300 # [BSS] Energy steps
% BLongDir
0.000000 | 0.000000 | 1.000000 | # [BSS] [cc] Electric Field
%
% BSEBands
7 | 13 | # [BSK] Bands range
%
% BSEEhEny
-1.000000 |-1.000000 | eV # [BSK] Electron-hole energy range
%
WRbsWF # [BSS] Write to disk excitonic the WFs
#BSSPertWidth # [BSS] Include QPs lifetime in a perturbative way
XfnQPdb= "none" # [EXTQP Xd] Database
XfnQP_N= 1 # [EXTQP Xd] Interpolation neighbours
% XfnQP_E
0.000000 | 1.000000 | 1.000000 | # [EXTQP Xd] E parameters (c/v) eV|adim|adim
%
XfnQP_Z= ( 1.000000 , 0.000000 ) # [EXTQP Xd] Z factor (c/v)
XfnQP_Wv_E= 0.000000 eV # [EXTQP Xd] W Energy reference (valence)
% XfnQP_Wv
0.00 | 0.00 | 0.00 | # [EXTQP Xd] W parameters (valence) eV| eV|eV^-1
%
XfnQP_Wc_E= 0.000000 eV # [EXTQP Xd] W Energy reference (conduction)
% XfnQP_Wc
0.00 | 0.00 | 0.00 | # [EXTQP Xd] W parameters (conduction) eV| eV|eV^-1
%
% QpntsRXp
1 | 9 | # [Xp] Transferred momenta
%
% BndsRnXp
1 | 30 | # [Xp] Polarization function bands
%
NGsBlkXp= 8 Ry # [Xp] Response block size
CGrdSpXp= 100.0000 # [Xp] [o/o] Coarse grid controller
% EhEngyXp
-1.000000 |-1.000000 | eV # [Xp] Electron-hole energy range
%
% LongDrXp
0.000000 | 0.000000 | 1.000000 | # [Xp] [cc] Electric Field
%
PPAPntXp= 27.21138 eV # [Xp] PPA imaginary energy
XTermKind= "none" # [X] X terminator ("none","BG" Bruneval-Gonze)
XTermEn= 40.81708 eV # [X] X terminator energy (only for kind="BG")
```

Best regards,

Tianshu Li

Jilin University