Tutorial:Wires and slabs

Under construction

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 PeriodicDimensions = 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:

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

Band Structure

After this GS calculation we will perform an unocc run. This non-self consistent calculation which needs the density from the previous GS calculation.

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                 # 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.