Tutorial:Wires and slabs
Hexagonal boron nitride (h-BN) is an insulator widely studied which has a similar structure to graphene. Here we will describe how to get the band structure of an h-BN monolayer.
Ground state calculation
A layer of h-BN is periodic in the x-y directions, but not in the z. Thus we will set= 2 . Here we set the bond length to 1.445*angstrom. The box size in the z direction is 2*L with 'L' large enough to describe a monolayer in the vacuum. One should always converge the box length value. Here is the inp file for the GS calculation:
= gs = yes = yes = 2 = 0.20*angstrom = parallelepiped BNlength = 1.445*angstrom a = sqrt(3)*BNlength L=40 % a | a | L % % 1 | 0 | 0. -1/2 | sqrt(3)/2 | 0. 0. | 0. | 1. % % 'B' | 0.0 | 0.0 | 0.00 'N' | 1/3 | 2/3 | 0.00 % =hgh_lda =lcao_states % 12 | 12 | 1 % = 2 = ev_angstrom
After this GS calculation we will perform an unocc run. This non-self consistent calculation which needs the density from the previous GS calculation.
= unocc ExtraStates = 5
expliquer pk le nbr d extra strate
Mettre warning du log: mode de caclule en BS: pas d reecriture des fonction du GS.
In order to calculate the band structure along a certain path along the BZ, we will use the variable . Instead of using the block of the GS calculation, we use during this unocc calculation:
%12 | 7 | 12 # Number of k point to sample each path 0 | 0 | 0 # Reduced coordinate of the 'Gamma' k point 1/3 | 1/3 | 0 # Reduced coordinate of the 'K' k point 1/2 | 0 | 0 # Reduced coordinate of the 'M' k point 0 | 0 | 0 # Reduced coordinate of the 'Gamma' k point %
The first row describes how many k points will be used to sample each segment. The next rows are the coordinate of k points from which each segment start and stop. In this particular example, we chose the path: Gamma-K, K-M, M-Gamma using 12-7-12 k points. In Figure 1 is plotted the output band structure where blue lines represent the occupied states and the reds one the unoccupied ones.
Info: The code will run in band structure mode. No restart information will be printed.
One should also make sure that the calculation is converged with respect to the spacing. Figure 2 shows the band gap for several spacing values. We find that a spacing of 0.14 Angstrom is needed in order to converge the band gap up to 0.01 eV.