BAND UNFOLDING FOR SUPERCELL
CALCULATIONSSEPTEMBER 10th, 2019 I STEFAN ROST
Peter Grünberg Institut, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
MOTIVATION – DEFECT STATE
phosphorus atom relaxes inwards
BAND STRUCTURE 𝐌𝐨𝐒𝐞𝟐 + 𝐏
MOTIVATION
Γ𝜋
2𝑎
𝜋
𝑎
E
k
supercell
MOTIVATION
⇒?
Γ𝜋
2𝑎
𝜋
𝑎Γ
𝜋
𝑎
E E
k k
supercell primitive cell
MOTIVATION
⇒spectral weights
Γ𝜋
2𝑎
𝜋
𝑎Γ
𝜋
𝑎
E E
k k
supercell primitive cell
1
1 0
0
UNFOLDING OF A BAND STRUCTURE
EXAMPLE 2X2 SUPERCELL
Γ
g1
g2
g1, g2reciprocal lattice vectors of unit cell
UNFOLDING OF A BAND STRUCTURE
EXAMPLE 2X2 SUPERCELL
Γ
g1
g2
G2
G1K
g1, g2 reciprocal lattice vectors of unit cell
G1, G2reciprocal lattice vectors of 2x2 super cell
K wave vector in 2x2 super cell
UNFOLDING OF A BAND STRUCTURE
EXAMPLE 2X2 SUPERCELL
Γ
g1
g2
G2
G1K
g1, g2reciprocal lattice vectors of unit cell
G1, G2reciprocal lattice vectors of 2x2 supercell
K wave vector in 2x2 super cell
UNFOLDING OF BAND STRUCTURE
Γ
g1
g2
G2
G1
k
K
using plane waves:
spectral weight
Subset of Gmatching to one k and its multiples in the unit cell
UNFOLDING OF BAND STRUCTURE
Γ
g1
g2
G2
G1
k
K
using plane waves:
spectral weight
Subset of Gmatching to one k and its multiples in the unit cell
LAPW BASIS
D. Wortmann. “DFT in practice”. In: Computing Solids. Forschungszentrum Jülich GmbH.
UNFOLDING OF BANDSTRUCTURE (2)
For the LAPW basis:
With an overlap matrix:
Spectral weight:
Test case - Si bulk
UNFOLDED BANDSTRUCTURE 𝐌𝐨𝐒𝐞𝟐 + 𝐏
avoidedcrossing
spin up
Spin down
DOS [a.u.] @ Pmonolayer - relaxed
UNFOLDED BANDSTRUCTURE 𝐌𝐨𝐒𝐞𝟐
spin up
Spin down
monolayer
3X3 VS 5X5 - 𝐌𝐨𝐒𝟐 + 𝐂𝐫 DEFECT SYSTEM
INFLUENCE OF COUPLING AND DEFECT
LEVEL ENERGIES coupling
defe
ctle
vel
IMPLEMENTATION IN FLEUR
SUMMARY- Unfolding of supercell band structures helps to understand the
material properties- Unfolded band structures represent the defect as a
perturbation to the pristine system (like in ARPES experiments)