band unfolding for supercell calculations · 2020. 6. 10. · band unfolding for supercell...
TRANSCRIPT
![Page 1: BAND UNFOLDING FOR SUPERCELL CALCULATIONS · 2020. 6. 10. · BAND UNFOLDING FOR SUPERCELL CALCULATIONS SEPTEMBER 10th, 2019 I STEFAN ROST Peter Grünberg Institut, Forschungszentrum](https://reader034.vdocument.in/reader034/viewer/2022051811/6028e0fe33d1f60b2156c633/html5/thumbnails/1.jpg)
BAND UNFOLDING FOR SUPERCELL
CALCULATIONSSEPTEMBER 10th, 2019 I STEFAN ROST
Peter Grünberg Institut, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
![Page 2: BAND UNFOLDING FOR SUPERCELL CALCULATIONS · 2020. 6. 10. · BAND UNFOLDING FOR SUPERCELL CALCULATIONS SEPTEMBER 10th, 2019 I STEFAN ROST Peter Grünberg Institut, Forschungszentrum](https://reader034.vdocument.in/reader034/viewer/2022051811/6028e0fe33d1f60b2156c633/html5/thumbnails/2.jpg)
MOTIVATION – DEFECT STATE
phosphorus atom relaxes inwards
![Page 3: BAND UNFOLDING FOR SUPERCELL CALCULATIONS · 2020. 6. 10. · BAND UNFOLDING FOR SUPERCELL CALCULATIONS SEPTEMBER 10th, 2019 I STEFAN ROST Peter Grünberg Institut, Forschungszentrum](https://reader034.vdocument.in/reader034/viewer/2022051811/6028e0fe33d1f60b2156c633/html5/thumbnails/3.jpg)
BAND STRUCTURE 𝐌𝐨𝐒𝐞𝟐 + 𝐏
![Page 4: BAND UNFOLDING FOR SUPERCELL CALCULATIONS · 2020. 6. 10. · BAND UNFOLDING FOR SUPERCELL CALCULATIONS SEPTEMBER 10th, 2019 I STEFAN ROST Peter Grünberg Institut, Forschungszentrum](https://reader034.vdocument.in/reader034/viewer/2022051811/6028e0fe33d1f60b2156c633/html5/thumbnails/4.jpg)
MOTIVATION
Γ𝜋
2𝑎
𝜋
𝑎
E
k
supercell
![Page 5: BAND UNFOLDING FOR SUPERCELL CALCULATIONS · 2020. 6. 10. · BAND UNFOLDING FOR SUPERCELL CALCULATIONS SEPTEMBER 10th, 2019 I STEFAN ROST Peter Grünberg Institut, Forschungszentrum](https://reader034.vdocument.in/reader034/viewer/2022051811/6028e0fe33d1f60b2156c633/html5/thumbnails/5.jpg)
MOTIVATION
⇒?
Γ𝜋
2𝑎
𝜋
𝑎Γ
𝜋
𝑎
E E
k k
supercell primitive cell
![Page 6: BAND UNFOLDING FOR SUPERCELL CALCULATIONS · 2020. 6. 10. · BAND UNFOLDING FOR SUPERCELL CALCULATIONS SEPTEMBER 10th, 2019 I STEFAN ROST Peter Grünberg Institut, Forschungszentrum](https://reader034.vdocument.in/reader034/viewer/2022051811/6028e0fe33d1f60b2156c633/html5/thumbnails/6.jpg)
MOTIVATION
⇒spectral weights
Γ𝜋
2𝑎
𝜋
𝑎Γ
𝜋
𝑎
E E
k k
supercell primitive cell
1
1 0
0
![Page 7: BAND UNFOLDING FOR SUPERCELL CALCULATIONS · 2020. 6. 10. · BAND UNFOLDING FOR SUPERCELL CALCULATIONS SEPTEMBER 10th, 2019 I STEFAN ROST Peter Grünberg Institut, Forschungszentrum](https://reader034.vdocument.in/reader034/viewer/2022051811/6028e0fe33d1f60b2156c633/html5/thumbnails/7.jpg)
UNFOLDING OF A BAND STRUCTURE
EXAMPLE 2X2 SUPERCELL
Γ
g1
g2
g1, g2reciprocal lattice vectors of unit cell
![Page 8: BAND UNFOLDING FOR SUPERCELL CALCULATIONS · 2020. 6. 10. · BAND UNFOLDING FOR SUPERCELL CALCULATIONS SEPTEMBER 10th, 2019 I STEFAN ROST Peter Grünberg Institut, Forschungszentrum](https://reader034.vdocument.in/reader034/viewer/2022051811/6028e0fe33d1f60b2156c633/html5/thumbnails/8.jpg)
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
![Page 9: BAND UNFOLDING FOR SUPERCELL CALCULATIONS · 2020. 6. 10. · BAND UNFOLDING FOR SUPERCELL CALCULATIONS SEPTEMBER 10th, 2019 I STEFAN ROST Peter Grünberg Institut, Forschungszentrum](https://reader034.vdocument.in/reader034/viewer/2022051811/6028e0fe33d1f60b2156c633/html5/thumbnails/9.jpg)
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
![Page 10: BAND UNFOLDING FOR SUPERCELL CALCULATIONS · 2020. 6. 10. · BAND UNFOLDING FOR SUPERCELL CALCULATIONS SEPTEMBER 10th, 2019 I STEFAN ROST Peter Grünberg Institut, Forschungszentrum](https://reader034.vdocument.in/reader034/viewer/2022051811/6028e0fe33d1f60b2156c633/html5/thumbnails/10.jpg)
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
![Page 11: BAND UNFOLDING FOR SUPERCELL CALCULATIONS · 2020. 6. 10. · BAND UNFOLDING FOR SUPERCELL CALCULATIONS SEPTEMBER 10th, 2019 I STEFAN ROST Peter Grünberg Institut, Forschungszentrum](https://reader034.vdocument.in/reader034/viewer/2022051811/6028e0fe33d1f60b2156c633/html5/thumbnails/11.jpg)
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
![Page 12: BAND UNFOLDING FOR SUPERCELL CALCULATIONS · 2020. 6. 10. · BAND UNFOLDING FOR SUPERCELL CALCULATIONS SEPTEMBER 10th, 2019 I STEFAN ROST Peter Grünberg Institut, Forschungszentrum](https://reader034.vdocument.in/reader034/viewer/2022051811/6028e0fe33d1f60b2156c633/html5/thumbnails/12.jpg)
LAPW BASIS
D. Wortmann. “DFT in practice”. In: Computing Solids. Forschungszentrum Jülich GmbH.
![Page 13: BAND UNFOLDING FOR SUPERCELL CALCULATIONS · 2020. 6. 10. · BAND UNFOLDING FOR SUPERCELL CALCULATIONS SEPTEMBER 10th, 2019 I STEFAN ROST Peter Grünberg Institut, Forschungszentrum](https://reader034.vdocument.in/reader034/viewer/2022051811/6028e0fe33d1f60b2156c633/html5/thumbnails/13.jpg)
UNFOLDING OF BANDSTRUCTURE (2)
For the LAPW basis:
With an overlap matrix:
Spectral weight:
Test case - Si bulk
![Page 14: BAND UNFOLDING FOR SUPERCELL CALCULATIONS · 2020. 6. 10. · BAND UNFOLDING FOR SUPERCELL CALCULATIONS SEPTEMBER 10th, 2019 I STEFAN ROST Peter Grünberg Institut, Forschungszentrum](https://reader034.vdocument.in/reader034/viewer/2022051811/6028e0fe33d1f60b2156c633/html5/thumbnails/14.jpg)
UNFOLDED BANDSTRUCTURE 𝐌𝐨𝐒𝐞𝟐 + 𝐏
avoidedcrossing
spin up
Spin down
DOS [a.u.] @ Pmonolayer - relaxed
![Page 15: BAND UNFOLDING FOR SUPERCELL CALCULATIONS · 2020. 6. 10. · BAND UNFOLDING FOR SUPERCELL CALCULATIONS SEPTEMBER 10th, 2019 I STEFAN ROST Peter Grünberg Institut, Forschungszentrum](https://reader034.vdocument.in/reader034/viewer/2022051811/6028e0fe33d1f60b2156c633/html5/thumbnails/15.jpg)
UNFOLDED BANDSTRUCTURE 𝐌𝐨𝐒𝐞𝟐
spin up
Spin down
monolayer
![Page 16: BAND UNFOLDING FOR SUPERCELL CALCULATIONS · 2020. 6. 10. · BAND UNFOLDING FOR SUPERCELL CALCULATIONS SEPTEMBER 10th, 2019 I STEFAN ROST Peter Grünberg Institut, Forschungszentrum](https://reader034.vdocument.in/reader034/viewer/2022051811/6028e0fe33d1f60b2156c633/html5/thumbnails/16.jpg)
3X3 VS 5X5 - 𝐌𝐨𝐒𝟐 + 𝐂𝐫 DEFECT SYSTEM
![Page 17: BAND UNFOLDING FOR SUPERCELL CALCULATIONS · 2020. 6. 10. · BAND UNFOLDING FOR SUPERCELL CALCULATIONS SEPTEMBER 10th, 2019 I STEFAN ROST Peter Grünberg Institut, Forschungszentrum](https://reader034.vdocument.in/reader034/viewer/2022051811/6028e0fe33d1f60b2156c633/html5/thumbnails/17.jpg)
INFLUENCE OF COUPLING AND DEFECT
LEVEL ENERGIES coupling
defe
ctle
vel
![Page 18: BAND UNFOLDING FOR SUPERCELL CALCULATIONS · 2020. 6. 10. · BAND UNFOLDING FOR SUPERCELL CALCULATIONS SEPTEMBER 10th, 2019 I STEFAN ROST Peter Grünberg Institut, Forschungszentrum](https://reader034.vdocument.in/reader034/viewer/2022051811/6028e0fe33d1f60b2156c633/html5/thumbnails/18.jpg)
IMPLEMENTATION IN FLEUR
![Page 19: BAND UNFOLDING FOR SUPERCELL CALCULATIONS · 2020. 6. 10. · BAND UNFOLDING FOR SUPERCELL CALCULATIONS SEPTEMBER 10th, 2019 I STEFAN ROST Peter Grünberg Institut, Forschungszentrum](https://reader034.vdocument.in/reader034/viewer/2022051811/6028e0fe33d1f60b2156c633/html5/thumbnails/19.jpg)
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)