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)