How to analyse excitons
In this tutorial you will learn (for a 2D-hBN) how to:
- analyze a BSE optical spectrum in terms of excitonic eigenvectors and eigenvalues
- look at the spatial distribution of the exciton
- You must have completed the How to treat low dimensional systems tutorial
You will need:
gnuplot or xmgraceexecutable
If you have completed the tutorials of 2D hBN you should have all the databases required to do this tutorial in your SAVE and 2D_WR_WC (databases generated with RIM and cutoff) directories
$ ls ./SAVE ndb.gops ndb.kindx ns.db1 ns.kb_pp_pwscf_fragment_1 .... $ ls ./2D_WR_WC ndb.BS_Q1_CPU_0 ndb.cutoff ndb.dip_iR_and_P_fragment_1 ndb.pp_fragment_1 ...
Sort the excitonic eigenvalues
$ ypp -J 2D_WR_WC -e s
The new generated file o-2D_WR_WC.exc_E_sorted (o-2D_WR_WC.exc_I_sorted) reports the energies of the excitons and their Dipole Oscillator Strenghts sorted by energy (Index).
Open the first file and look inside. The first exciton is at 4.83 eV and the second one has the highest strenght (normalized to 1)
Or you can make a plot
$ gnuplot gnuplot> plot 'o-2D_WR_WC.eps_q1_diago_bse' w l title 'BSE2D' ,'o-2D_WR_WC.exc_E_sorted' u 1:($2*10) title 'Strenght2D'
Attention the convergence of these results with different k-points grids is mandatory!
Calculate the exciton oscillator strenght and amplitude
We can now analyze the excitons in terms of single-particle states, to do that create the appropriate input
$ ypp -F ypp_AMPL.in -J 2D_WR_WC -e a
Suppose you wish to analyze the first 5 excitons then change this line as:
States= "1 - 5" # Index of the BS state(s)
Close the input and run ypp
$ ypp -F ypp_AMPL.in -J 2D_WR_WC
$ls ls o*exc*at* o-2D_WR_WC.exc_amplitude_at_1 o-2D_WR_WC.exc_weights_at_1 ...
For an exciton [math]|\lambda\gt [/math] , o-2D_WR_WC.exc_weights_at_* report the Weights
and o-2D_WR_WC.exc_amplitudes_at_* report the amplitudes
Open the file o-2D_WR_WC.exc_weights_at_1
# Band_V Band_C K ibz Symm. Weight Energy # 4.000000 5.000000 7.000000 2.000000 0.922095 4.401093 4.000000 5.000000 7.000000 1.000000 0.922086 4.401093 The first exciton is essentially done of only single particle transitions from VBM to CBM at K (last k-point of the grid).
Plot the exciton spatial distribution
To see the spatial character of the exciton YPP writes the exciton spatial distribution, in other words the probability to find the electron somewhere in the space when the hole is fixed in a give position. Different output formats can be selected and 1D,2D,3D plots done. Create the input and change the size of the cell where to see the exciton. Note that If the k-grid of the BSE simulation is a NxNx1 the exciton has an induced fictitious periodicity every Nx Nx1 Cell of the simulation. For hBN-2D this is not a problem because the exciton is strongly localized but in other systems with more delocalized excitons to look at the real exciton size it is necessary to use very large k-grids in the BSE
$ ypp -F ypp_WF.in -J 2D_WR_WC -e w
excitons # [R] Excitons wavefunction # [R] Wavefunction Format= "x" # Output format [(c)ube/(g)nuplot/(x)crysden] Direction= "12" # [rlu] [1/2/3] for 1d or [12/13/23] for 2d  for 3D FFTGvecs= 3951 RL # [FFT] Plane-waves States= "1 - 1" # Index of the BS state(s) Degen_Step= 0.0100 eV # Maximum energy separation of two degenerate states % Cells 5 | 5 | 1 | # Number of cell repetitions in each direction (odd or 1) % % Hole 2.4 | 1.400 | 0.00 | # [cc] Hole position in unit cell
Close the input and run ypp
$ ypp -F ypp_WF.in -J 2D_WR_WC
$ xcrysden --xsf o-2D_WR_WC.exc_2d_1.xsf
$ xcrysden --sushi