How to treat low dimensional systems

In this tutorial you will learn how to:

• generate a truncated coulomb potential with a box-like cutoff
• visualize this truncated coulomb potential
• use this truncated coulomb in the HF, GW and BSE calculation
• analyze the difference with similar calculations without using this cutoff

Prerequisites

• Complete the Generating the Yambo databases tutorial
• SAVE folder for 2D hBN.
• yambo executable
• ypp executable
• Run Initialization

Generate the cutoff databases (yambo -r)

To simulate an isolated nano-material a convergence with cell vacuum size is in principle required, like in the DFT runs. The use of a truncated Coulomb potential allows to achieve faster convergence eliminating the interaction between the repeated images along the non-periodic direction (see i.e. D. Varsano et al Phys. Rev. B and .. ) In this tutorial we learn how to generate a box-like cutoff for a 2D system with the non-periodic direction along z.

In YAMBO you can use :

spherical   cutoff (for 0D systems)  
cylindrical cutoff (for 1D systems) 
box-like    cutoff (for 0D, 1D and 2D systems)

The Coulomb potential with a box-like cutoff is defined as

Then the FT component is

where

For a 2D-system with non period direction along z-axis we have

Important remarks:

• the Random Integration Method (RIM) is required to perform the Q-space integration
• choose L_i sligthly smaller than the cell size in the i-direction

Create the input

Creation of the input file:

$ yambo -F yambo_cut2D.in  -r

Open the input file yambo_cut2D.in

Change the variables inside as:

RandQpts= 1000000          # [RIM] Number of random q-points in the BZ
RandGvec= 100        RL    # [RIM] Coulomb interaction RS components

CUTGeo= "box z"            # [CUT] Coulomb Cutoff geometry: box/cylinder/sphere X/Y/Z/XY..
% CUTBox
 0.00     | 0.00     | 32.0    |        # [CUT] [au] Box sides

Close the input file

run yambo

$ yambo -F  yambo_cut2D.in  -J 2D

in the directory 2D you will find the two new databases

ndb.RIM		ndb.cutoff

==Visualize the coulomb potential

Generate again the input with an higher level of verbosity $ yambo -r -V RL -F yambo_cut2D.in

Open the input file and uncomment

1. CUTCol_test # [CUT] Perform a cutoff test in R-space

Close the input and run again yambo

At the end you will find some new files

o-2D.RL_components o-2D.xy_plane o-2D.xz_plane o-2D.yz_plane

and you can use gnuplot to plot them

$ gnuplot
gnuplot> plot 'o-2D.RL_components' u 1:2,'o-2D.RL_components' u 1:3 

gnuplot> splot 'o-2D.xy_plane' u 1:2:3,'o-2D.xy_plane' u 1:2:4

gnuplot> splot 'o-2D.xz_plane' u 1:2:3,'o-2D.xz_plane' u 1:2:4