Tutorial:Wires and slabs

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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 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

 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



  12   | 12   | 1

ExtraStates = 2

UnitsOutput = ev_angstrom

Band Structure

Convergence of the band gap with respect to the spacing for a HBN monolayer.

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

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 KPointsPath . Instead of using the KPointsGrid 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.