Tutorial:Wires and slabs
Ground state calculation
Hexagonal boron nitride (HBN) is an insulator widely studied which has a similar structure to graphene. Here we will describe how to get the band structure of an HBN monolayer. A sheet of HBN is periodic in the x-y directions, but not in the z. Thus we will set= 2
here BN lenght= 1.445*angstrom '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 % = 5 = ev_angstrom
Remark: If the system has a z-translation symmetry, one should always centre its system with respect to the z-direction in order to avoid any asymmetric effect in the z direction due to some computational or grid errors. Here the box is centred at z=0 (with 20 bohr extension in +z and -z direction): that is why the atom lays at z=0.
After this GS calculation, we would like to describe more precisely the band structure. Thus we will perform an unocc run:
In order to plot the band structure along certain lines in 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 line. The next row are the coordinate of k points from which each line start and stop. In this particular example, we describe the lines 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.
One should also make sure that the calculation is converged with respect to the spacing. To do so, we have converged the band gap. Figure 2 shows the band gap for several spacing values. Here we can see that a spacing of 0.14 Angstrom is needed in order to converge the band gap up to 0.01 eV.