Graphene band structure¶

This example plots the band structure of graphene, a 2D material. 2D band structures are not supported natively (yet), so we manually build a custom path in reciprocal space.

In [1]:
using DFTK
using Unitful
using UnitfulAtomic
using LinearAlgebra

# Define the convergence parameters (these should be increased in production)
L = 20  # height of the simulation box
kgrid = [6, 6, 1]
Ecut = 15
temperature = 1e-3

# Define the geometry and pseudopotential
a = 4.66  # lattice constant
a1 = a*[1/2,-sqrt(3)/2, 0]
a2 = a*[1/2, sqrt(3)/2, 0]
a3 = L*[0  , 0        , 1]
lattice = [a1 a2 a3]
C1 = [1/3,-1/3,0.0]  # in reduced coordinates
C2 = -C1
positions = [C1, C2]
atoms = [C, C]

# Run SCF
model = model_PBE(lattice, atoms, positions; temperature)
basis = PlaneWaveBasis(model; Ecut, kgrid)
scfres = self_consistent_field(basis)

# Construct 2D path through Brillouin zone
sgnum = 13  # Graphene space group number
kpath = irrfbz_path(model; dim=2, sgnum)
plot_bandstructure(scfres, kpath; kline_density=20)

n     Energy            log10(ΔE)   log10(Δρ)   Diag
---   ---------------   ---------   ---------   ----
1   -11.15663652643                   -0.60    5.9
2   -11.16017635789       -2.45       -1.30    1.0
3   -11.16040527607       -3.64       -2.29    3.1
4   -11.16041638521       -4.95       -2.94    3.3
5   -11.16041688914       -6.30       -3.24    3.1
Computing bands along kpath:
Γ -> M -> K -> Γ
Diagonalising Hamiltonian kblocks: 100%|████████████████| Time: 0:00:03

Out[1]: