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

[email protected] New Perspectives in ab initio Calculations

LAOSTOVO2

Outline

1 LAOSTO

2 VO2


LAOSTOVO2

Outline

1 LAOSTO

2 VO2


LAOSTOVO2

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


WSR

/au

2

2.5

3

3.5

4

4.5

5

5.5


WSR

/au

Wigner-Seitz-Rad.=̂ Volume

0

500

1000

1500

2000

2500

3000

3500

4000


Bul

k m

odul

us/k

bar

0

500

1000

1500

2000

2500

3000

3500

4000


Bul

k m

odul

us/k

bar

Compressibility=̂ Hardness


LAOSTOVO2

Energy band structures from screened HF exchange

Si, AlP, AlAs, GaP, and GaAs

Experimental andtheoretical bandgapproperties

Shimazaki, AsaiJCP 132, 224105 (2010)


LAOSTOVO2

Outline

1 LAOSTO

2 VO2


LAOSTOVO2

2D Electron Gas at LaAlO3-SrTiO3 Interface


LAOSTOVO2

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?


LAOSTOVO2

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)


LAOSTOVO2


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


LAOSTOVO2


Ideal

Structural relaxation

AlO2 surface layersstrong inward relaxationweak buckling

LaO layersstrong buckling

AlO2 subsurface layersbuckling

TiO2 interface layerssmall outward relaxation

Optimized


LAOSTOVO2


0

20

40

60

80

100

120

-10 -8 -6 -4 -2 0 2 4 6

DO

S (

1/eV

)

(E - EF) (eV)

2L3L4L5L


LAOSTOVO2

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)


LAOSTOVO2


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)


LAOSTOVO2


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)


LAOSTOVO2

“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)


LAOSTOVO2

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)


LAOSTOVO2




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


LAOSTOVO2




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


LAOSTOVO2


Calculated vs. experimental bandgaps


LAOSTOVO2

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


LAOSTOVO2

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


LAOSTOVO2

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


LAOSTOVO2

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


LAOSTOVO2

Outline

1 LAOSTO

2 VO2


LAOSTOVO2

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?


LAOSTOVO2


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)


LAOSTOVO2



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


LAOSTOVO2


Octahedral Chains Rutile Structuresimple tetragonal

P42/mnm (D144h)


LAOSTOVO2



O 2p

V 3d t2g

V 3d eσ

g

EF

σ

π

π∗

σ∗

t2g Orbitals

��

AA a1g = “d‖”

eπ

g = “π∗”


LAOSTOVO2


Rutile Structure

Structural Changes

V-V dimerization ‖ cR

antiferroelectricdisplacement ⊥ cR

M1-Structure


LAOSTOVO2


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


LAOSTOVO2


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


LAOSTOVO2


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


LAOSTOVO2

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)


LAOSTOVO2


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)


LAOSTOVO2


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


LAOSTOVO2

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)


LAOSTOVO2

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


LAOSTOVO2


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


LAOSTOVO2


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


splitting of d‖ bands, upshift of π∗ bands

optical bandgap of ≈ 1 eV


LAOSTOVO2


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


localized magnetic moment of 1 µB

optical bandgap of ≈ 1.6 eV


LAOSTOVO2

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)


LAOSTOVO2

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


LAOSTOVO2

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


LAOSTOVO2

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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