New Perspectives in ab initio Calculations for ...
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LAOSTO VO 2 New Perspectives in ab initio Calculations for Semiconducting Oxides Volker Eyert Center for Electronic Correlations and Magnetism Institute of Physics, University of Augsburg October 28, 2010 Volker@Eyert.de New Perspectives in ab initio Calculations
Transcript of New Perspectives in ab initio Calculations for ...
LAOSTOVO2
New Perspectives in ab initio Calculations forSemiconducting Oxides
Volker Eyert
Center for Electronic Correlations and MagnetismInstitute of Physics, University of Augsburg
October 28, 2010
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Calculated Electronic Properties
Moruzzi, Janak, Williams (IBM, 1978)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga
E/R
yd
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In
E/R
yd
Cohesive Energies=̂ Stability
2
2.5
3
3.5
4
4.5
5
5.5
K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga
WSR
/au
2
2.5
3
3.5
4
4.5
5
5.5
Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In
WSR
/au
Wigner-Seitz-Rad.=̂ Volume
0
500
1000
1500
2000
2500
3000
3500
4000
K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga
Bul
k m
odul
us/k
bar
0
500
1000
1500
2000
2500
3000
3500
4000
Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In
Bul
k m
odul
us/k
bar
Compressibility=̂ Hardness
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Energy band structures from screened HF exchange
Si, AlP, AlAs, GaP, and GaAs
Experimental andtheoretical bandgapproperties
Shimazaki, AsaiJCP 132, 224105 (2010)
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2D Electron Gas at LaAlO3-SrTiO3 Interface
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2D Electron Gas at LaAlO3-SrTiO3 Interface
Issues
Role of electronic correlations?SrTiO3, LaAlO3: band insulatorsSrTiO3/LaAlO3 interface: MIT (# LaAlO3 layers)magnetic properties of the interfacesuperconductivity below ≈ 200 mK
What is the origin of the 2-DEG?intrinsic mechanism?defect-doping?
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Slab Calculations for the LaAlO3-SrTiO3 Interface
Structural setup of calculations
central region: 5 layers SrTiO3, TiO2-terminated
sandwiches: 2 to 5 layers LaAlO3, AlO2 surface
vacuum region ≈ 20 Å
inversion symmetry
lattice constant of SrTiO3 from GGA (3.944 Å)
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Slab Calculations for the LaAlO3-SrTiO3 Interface
Calculational method
Vienna Ab Initio Simulation Package (VASP)
GGA-PBESteps:
1 optimization of SrTiO3 lattice constant2 slab calculations
full relaxation of all atomic positions5× 5× 1 k-pointsΓ-centered k-meshMethfessel-Paxton BZ-integration
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Slab Calculations for the LaAlO3-SrTiO3 Interface
Ideal
Structural relaxation
AlO2 surface layersstrong inward relaxationweak buckling
LaO layersstrong buckling
AlO2 subsurface layersbuckling
TiO2 interface layerssmall outward relaxation
Optimized
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Slab Calculations for the LaAlO3-SrTiO3 Interface
0
20
40
60
80
100
120
-10 -8 -6 -4 -2 0 2 4 6
DO
S (
1/eV
)
(E - EF) (eV)
2L3L4L5L
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Tunneling Spectroscopy of LaAlO3-SrTiO3 Interface
What is the origin of the 2-DEG?Intrinsic mechanism or defect-doping?
Vs
It
interface electron system
4 unit cells LaAlO3
SrTiO3
Ti
STM
tipz
x
M. Breitschaft et al., PRB 81, 153414 (2010)
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Tunneling Spectroscopy of LaAlO3-SrTiO3 Interface
4uc LaAlO3 on SrTiO3,tunneling data
4uc LaAlO3 on SrTiO3,LDA calculations,DOS of interface Ti
4uc LaAlO3 on SrTiO3,LDA+U calculations,DOS of interface Ti
(a)
(b)
(c)
LDA+U
LDA
exp.
VS (V)
E - EF (eV)
E - EF (eV)
ND
C (
arb
. u
nits)
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Tunneling Spectroscopy of LaAlO3-SrTiO3 Interface
bulk SrTiO3,LDA calculations,conduction band DOS
0
2
4
6
8
10
12
14
2 2.5 3 3.5 4 4.5 5
DO
S (
1/eV
)
(E - EV) (eV)
(a)
(b)
(c)
LDA+U
LDA
exp.
VS (V)
E - EF (eV)
E - EF (eV)
ND
C (
arb
. u
nits)
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“2D Electron Liquid State” at LaAlO3-SrTiO3 Interface
SrTiO3LaAlO3AlxGa1-xAs GaAs
CB
VBEF
EF Ti 3d
(a) (b)s
M. Breitschaft et al., PRB 81, 153414 (2010)
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Critical review of the Local Density Approximation
Limitations and Beyond
LDA exact for homogeneous electron gas (within QMC)Spatial variation of ρ ignored→ include ∇ρ(r), . . .→ Generalized Gradient Approximation (GGA)
Self-interaction cancellation in vHartree + vx violated→ repair using exact Hartree-Fock exchange functional→ hybrid functionals (PBE0, HSE03, HSE06)
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Critical review of the Local Density Approximation
Limitations and Beyond
Self-interaction cancellation in vHartree + vx violated→ repair using exact Hartree-Fock exchange functional→ hybrid functionals (PBE0, HSE03, HSE06)
GGA
W L G X W K
En
er
gy
(e
V)
− 1 0
0
Si bandgap
exp: 1.11 eV
GGA: 0.57 eV
HSE: 1.15 eV
HSE
W L G X W K
En
er
gy
(e
V)
− 1 0
0
1 0
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Critical review of the Local Density Approximation
Limitations and Beyond
Self-interaction cancellation in vHartree + vx violated→ repair using exact Hartree-Fock exchange functional→ hybrid functionals (PBE0, HSE03, HSE06)
GGA
W L G X W K
En
er
gy
(e
V)
− 1 0
0
Ge bandgap
exp: 0.67 eV
GGA: 0.09 eV
HSE: 0.66 eV
HSE
W L G X W K
En
er
gy
(e
V)
− 1 0
0
1 0
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Critical review of the Local Density Approximation
Calculated vs. experimental bandgaps
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SrTiO3
GGA
0
2
4
6
8
10
-8 -6 -4 -2 0 2 4 6 8 10
DO
S (
1/eV
)
(E - EV) (eV)
Bandgap
GGA: ≈ 1.6 eV, exp.: 3.2 eV
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SrTiO3
GGA
0
2
4
6
8
10
-8 -6 -4 -2 0 2 4 6 8 10
DO
S (
1/eV
)
(E - EV) (eV)
HSE
0
2
4
6
8
10
-8 -6 -4 -2 0 2 4 6 8 10
DO
S (
1/eV
)
(E - EV) (eV)
Bandgap
GGA: ≈ 1.6 eV, HSE: ≈ 3.1 eV, exp.: 3.2 eV
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LaAlO3
GGA
0
5
10
15
20
25
-8 -6 -4 -2 0 2 4 6 8 10
DO
S (
1/eV
)
(E - EV) (eV)
Bandgap
GGA: ≈ 3.5 eV, exp.: 5.6 eV
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LaAlO3
GGA
0
5
10
15
20
25
-8 -6 -4 -2 0 2 4 6 8 10
DO
S (
1/eV
)
(E - EV) (eV)
HSE
0
5
10
15
20
25
-8 -6 -4 -2 0 2 4 6 8 10
DO
S (
1/eV
)
(E - EV) (eV)
Bandgap
GGA: ≈ 3.5 eV, HSE: ≈ 5.0 eV, exp.: 5.6 eV
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Metal-Insulator Transition of VO2
Morin, PRL 1959 Metal-Insulator Transitions (MIT)
VO2 (d1)1st order, 340 K, ∆σ ≈ 104
rutile → M1 (monoclinic)
V2O3 (d2)1st order, 170 K, ∆σ ≈ 106
corundum → monoclinicparamagn. → AF order
Origin of the MIT???
Structural Changes?
Electron Correlations?
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Metal-Insulator Transition of VO2
Octahedral Coordination
O 2p
V 3d t2g
V 3d eσ
g
EF
σ
π
π∗
σ∗
V 3d -O 2p hybridizationσ, σ∗ (p-deσ
g )π, π∗ (p-dt2g)
Rutile Structure
simple tetragonal
P42/mnm (D144h)
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Metal-Insulator Transition of VO2
Octahedral Coordination
O 2p
V 3d t2g
V 3d eσ
g
EF
σ
π
π∗
σ∗
V 3d -O 2p hybridizationσ, σ∗ (p-deσ
g )π, π∗ (p-dt2g)
eσ
g Orbitals
t2g Orbitals
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Metal-Insulator Transition of VO2
Octahedral Chains Rutile Structuresimple tetragonal
P42/mnm (D144h)
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Metal-Insulator Transition of VO2
Octahedral Coordination
O 2p
V 3d t2g
V 3d eσ
g
EF
σ
π
π∗
σ∗
t2g Orbitals
��
AA a1g = “d‖”
eπ
g = “π∗”
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Metal-Insulator Transition of VO2
Rutile Structure
Structural Changes
V-V dimerization ‖ cR
antiferroelectricdisplacement ⊥ cR
M1-Structure
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Metal-Insulator Transition of VO2
Rutile M1
EF
π∗π∗
d‖d‖
d∗‖
Goodenough, 1960-1972metal-metal dimerization ‖ cR → splitting into d‖, d∗
‖
antiferroelectric displacement ⊥ cR → upshift of π∗
Zylbersztejn and Mott, 1975splitting of d‖ by electronic correlationsupshift of π∗ unscreenes d‖ electrons
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Metal-Insulator Transition of VO2
Other Compounds
d0 d1 d2 d3 d4 d5 d6
3d TiO2 VO∗2 CrO2 MnO2
(S) (M–S) (F–M) (AF–S)
4d NbO∗2 MoO∗
2 TcO∗2 RuO2 RhO2
(M–S) (M) (M) (M) (M)
5d TaO2 WO∗2 ReO∗
2 OsO2 IrO2 PtO∗2
(?) (M) (M) (M) (M) (M)∗ deviations from rutile, M = metal, S = semiconductorF/AF = ferro-/antiferromagnet
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Metal-Insulator Transition of VO2
Other Phases
-0.01 0.02 0.03 0.04 0.05 x
6
100200300T(K) LLLLLLLLLLLLLLLLLLL
XXXXXXXXXXXXXXXXXXXXXXXXXXXuu uu A u uu u####B eeeeuuuuA e ee eu uu u����B
uuuuA uu uu u\\��\\��BM1 T M2R doping withCr, Al, Fe, Ga
uniaxial pressure‖ 〈110〉
CrxV1−xO2
Pouget, Launois, 1976
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Electronic Structure in Detail
Rutile Structuremolecular-orbital picture X
octahedral crystal field=⇒ V 3d t2g /eg
V 3d–O 2p hybridization
0
1
2
3
4
5
-8 -6 -4 -2 0 2 4 6 8
DO
S (1
/eV
)(E - EF) (eV)
V 3d t2gV 3d eg
O 2p
VE, Ann. Phys. (Leipzig) 11, 650 (2002)
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Electronic Structure in Detail
Rutile Structuremolecular-orbital picture X
octahedral crystal field=⇒ V 3d t2g /eg
V 3d–O 2p hybridization
t2g at EF: dx2−y2 , dyz , dxz
n(dx2−y2) ≈ n(dyz) ≈n(dxz)
0
0.5
1
1.5
2
2.5
3
3.5
-1 0 1 2 3 4 5
DO
S (1
/eV
)(E - EF) (eV)
V 3dx2-y2
V 3dyzV 3dxz
VE, Ann. Phys. (Leipzig) 11, 650 (2002)
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Electronic Structure in Detail
Rutile Structure
0
0.5
1
1.5
2
2.5
3
3.5
-1 0 1 2 3 4 5
DO
S (1
/eV
)
(E - EF) (eV)
V 3dx2-y2
V 3dyzV 3dxz
M1 Structure
0
0.5
1
1.5
2
2.5
3
-1 0 1 2 3 4 5
DO
S (1
/eV
)
(E - EF) (eV)
V 3dx2-y2
V 3dyzV 3dxz
bonding-antibonding splitting of d‖ bands
energetical upshift of π∗ bands =⇒ orbital ordering
optical band gap on the verge of opening
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Further investigations
Cluster-DMFT Calculations
Rutile-VO2
moderately correlated metal
M1-VO2
correlations strong/weak on d‖/π∗
optical band gap of 0.6 eV
Phase Transition“correlation-assisted Peierls transition”
S. Biermann, A. Poteryaev, A. I. Lichtenstein, A. GeorgesPRL 94, 026404 (2005)
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New Calculations: GGA vs. HSE
Rutile Structure GGA
0
1
2
3
4
5
-10 -8 -6 -4 -2 0 2 4
DO
S (
1/eV
)
(E - EF) (eV)
V 3dO 2p
Rutile Structure HSE
0
1
2
3
4
5
-10 -8 -6 -4 -2 0 2 4
DO
S (
1/eV
)
(E - EF) (eV)
V 3dO 2p
Rutile Structure: GGA =⇒ HSE
broadening of O 2p and V 3d t2g(!) bands
splitting within V 3d t2g bands
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New Calculations: GGA vs. HSE
M1 Structure GGA
0
1
2
3
4
5
-10 -8 -6 -4 -2 0 2 4
DO
S (
1/eV
)
(E - EF) (eV)
V 3dO1 2pO2 2p
M1 Structure HSE
0
1
2
3
4
5
-10 -8 -6 -4 -2 0 2 4
DO
S (
1/eV
)
(E - EF) (eV)
V 3dO1 2pO2 2p
M1 Structure: GGA =⇒ HSE
splitting of d‖ bands, upshift of π∗ bands
optical bandgap of ≈ 1 eV
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New Calculations: GGA vs. HSE
M1 Structure GGA
C Y G B A E Z
En
er
gy
(e
V)
−1
0
1
M1 Structure HSE
C Y G B A E Z
En
er
gy
(e
V)
−1
0
1
2
3
M1 Structure: GGA =⇒ HSE
splitting of d‖ bands, upshift of π∗ bands
optical bandgap of ≈ 1 eV
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New Calculations: GGA vs. HSE
M2 Structure GGA
P a r t i a l D e n s i t y o f S t a t e s ( 1 / e V )
−4 −2 0 2 4
En
er
gy
(e
V)
− 1 0
−5
0
5
T o t a l a n d S u m m e d D e n s i t y o f S t a t e s ( 1 / e V )
− 1 0 0 1 0
M2 Structure HSE
P a r t i a l D e n s i t y o f S t a t e s ( 1 / e V )
−4 −2 0 2 4
En
er
gy
(e
V)
− 1 0
−5
0
5
T o t a l a n d S u m m e d D e n s i t y o f S t a t e s ( 1 / e V )
− 2 0 − 1 0 0 1 0 2 0
M2 Structure: GGA =⇒ HSE
localized magnetic moment of 1 µB
optical bandgap of ≈ 1.6 eV
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Unified Picture
Rutile-Related Transition-Metal Dioxides
VO2 (3d1), NbO2 (4d1), MoO2 (4d2)(WO2 (5d2), TcO2 (4d3), ReO2 (5d3))
instability against similar local distortionsmetal-metal dimerization ‖ cR
antiferroelectric displacement ⊥ cR
(„accidental“) metal-insulator transition of the d1-members
VE et al., J. Phys.: CM 12, 4923 (2000)VE, Ann. Phys. 11, 650 (2002)VE, EPL 58, 851 (2002)J. Moosburger-Will et al., PRB 79, 115113 (2009)
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Success Stories
LaAlO3/SrTiO3
0
20
40
60
80
100
120
-10 -8 -6 -4 -2 0 2 4 6
DO
S (
1/eV
)
(E - EF) (eV)
2L3L4L5L
Metal-Insulator Transitions in VO2
0
1
2
3
4
5
-10 -8 -6 -4 -2 0 2 4
DO
S (
1/eV
)
(E - EF) (eV)
V 3dO1 2pO2 2p
0
1
2
3
4
5
-10 -8 -6 -4 -2 0 2 4
DO
S (
1/eV
)
(E - EF) (eV)
V 3dO1 2pO2 2p
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Acknowledgments
Augsburg
M. Breitschaft, U. Eckern,K.-H. Höck, S. Horn, R. Horny,T. Kopp, J. Kündel, J. Mannhart,J. Moosburger-Will, N. Pavlenko
Darmstadt/Jülich
P. C. Schmidt, M. Stephan,J. Sticht †
Europe/USA
M. Christensen, C. Freeman,M. Halls, A. Mavromaras, P. Saxe,E. Wimmer, R. Windiks, W. Wolf
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Acknowledgments
Augsburg
M. Breitschaft, U. Eckern,K.-H. Höck, S. Horn, R. Horny,T. Kopp, J. Kündel, J. Mannhart,J. Moosburger-Will, N. Pavlenko
Darmstadt/Jülich
P. C. Schmidt, M. Stephan,J. Sticht †
Europe/USA
M. Christensen, C. Freeman,M. Halls, A. Mavromaras, P. Saxe,E. Wimmer, R. Windiks, W. Wolf
San Diego
Thank You for Your Attention!
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