# Tutorial:Wires and slabs

Under construction

# Ground state calculation

Hexagonal boron nitride (HBN) is an insulator widely studied which have the same space group as 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 PeriodicDimensions = 2 and use a parallelepiped box of size a*a*L with 'a' the B-N bond length and 'L' large enough to describe a sheet in the vacuum. One should always converge the box length value. Here is the inp file for the GS calculation:

CalculationMode = gs

FromScratch = yes

ExperimentalFeatures = yes

PeriodicDimensions = 2

Spacing = 0.20*angstrom

BoxShape = parallelepiped

BNlength = 1.445*angstrom
a = sqrt(3)*BNlength
L=40

%LatticeParameters
a | a | L
%

%LatticeVectors
1    | 0         | 0.
-1/2 | sqrt(3)/2 | 0.
0.   | 0.        | 1.
%

%ReducedCoordinates
'B' | 0.0 | 0.0  | 0.00
'N' | 1/3 | 2/3  | 0.00
%

PseudopotentialSet=hgh_lda

LCAOStart=lcao_states

%KPointsGrid
12   | 12   | 1
%

ExtraStates = 5

UnitsOutput = 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 any computational or grid errors. That is why here the atom lays at z=0

# Band Structure

After this GS calculation, we would like to describe more precisely the band structure. Thus we will perform an unocc run:

CalculationMode = unocc

In order to plot the band structure along certain lines in the BZ, we will use the variable KPointsPath . Instead of using the KPointsGrid block of the GS calculation, we use during this unocc calculation:

%KPointsPath
12  |  7  | 12                 # Nomber of k point to sample each path
0   |  0  | 0                  # Reduced corrdinate of the 'Gamma' k point
1/3 | 1/3 | 0                  # Reduced corrdinate of the 'K' k point
1/2 |  0  | 0                  # Reduced corrdinate of the 'M' k point
0   |  0  | 0                  # Reduced corrdinate 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. Do to 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.