New Perspectives in ab initio Calculations. Semiconducting Oxides

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1 for Semiconducting Oxides Volker Eyert Center for Electronic Correlations and Magnetism Institute of Physics, University of Augsburg October 28, 21

2 Outline LAOSTO 1 LAOSTO 2

3 Outline LAOSTO 1 LAOSTO 2

4 Calculated Electronic Properties Moruzzi, Janak, Williams (IBM, 1978) E/Ryd E/Ryd K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Cohesive Energies ˆ= Stability WSR/au WSR/au K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga 2 Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Wigner-Seitz-Rad. ˆ= Volume Bulk modulus/kbar Bulk modulus/kbar K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Compressibility ˆ= Hardness

5 Energy band structures from screened HF exchange Si, AlP, AlAs, GaP, and GaAs Experimental and theoretical bandgap properties Shimazaki, Asai JCP 132, (21)

6 Outline LAOSTO 1 LAOSTO 2

7 2D Electron Gas at LaAlO 3 -SrTiO 3 Interface

8 2D Electron Gas at LaAlO 3 -SrTiO 3 Interface Issues Role of electronic correlations? SrTiO 3, LaAlO 3 : band insulators SrTiO 3 /LaAlO 3 interface: MIT (# LaAlO 3 layers) magnetic properties of the interface superconductivity below 2 mk What is the origin of the 2-DEG? intrinsic mechanism? defect-doping?

9 Slab Calculations for the LaAlO 3 -SrTiO 3 Interface Structural setup of calculations central region: 5 layers SrTiO 3, TiO 2 -terminated sandwiches: 2 to 5 layers LaAlO 3, AlO 2 surface vacuum region 2 Å inversion symmetry lattice constant of SrTiO 3 from GGA (3.944 Å)

10 Slab Calculations for the LaAlO 3 -SrTiO 3 Interface Calculational method Vienna Ab Initio Simulation Package (VASP) GGA-PBE Steps: 1 optimization of SrTiO 3 lattice constant 2 slab calculations full relaxation of all atomic positions k-points Γ-centered k-mesh Methfessel-Paxton BZ-integration

11 Slab Calculations for the LaAlO 3 -SrTiO 3 Interface Ideal Structural relaxation AlO 2 surface layers strong inward relaxation weak buckling LaO layers strong buckling AlO 2 subsurface layers buckling TiO 2 interface layers small outward relaxation Optimized

12 Slab Calculations for the LaAlO 3 -SrTiO 3 Interface DOS (1/eV) L 3L 4L 5L (E - E F ) (ev)

13 Tunneling Spectroscopy of LaAlO 3 -SrTiO 3 Interface What is the origin of the 2-DEG? Intrinsic mechanism or defect-doping? I t V s STM tip z x Ti 4 unit cells LaAlO 3 interface electron system SrTiO 3 M. Breitschaft et al., PRB 81, (21)

14 Tunneling Spectroscopy of LaAlO 3 -SrTiO 3 Interface VS (V) 4uc LaAlO 3 on SrTiO 3, tunneling data NDC (arb. units) (a) exp. 4uc LaAlO 3 on SrTiO 3, LDA calculations, DOS of interface Ti (b) LDA E - EF (ev) 4uc LaAlO 3 on SrTiO 3, LDA+U calculations, DOS of interface Ti (c) LDA+U E - EF (ev)

15 Tunneling Spectroscopy of LaAlO 3 -SrTiO 3 Interface VS (V) bulk SrTiO 3, LDA calculations, conduction band DOS NDC (arb. units) (a) (b) exp. LDA DOS (1/eV) (c) E - EF (ev) LDA+U (E - E V ) (ev) E - EF (ev)

16 2D Electron Liquid State at LaAlO 3 -SrTiO 3 Interface Al x Ga 1-x As GaAs CB LaAlO 3 SrTiO 3 E F VB (a) s E F (b) Ti 3d M. Breitschaft et al., PRB 81, (21)

17 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 v Hartree + v x violated repair using exact Hartree-Fock exchange functional hybrid functionals (PBE, HSE3, HSE6)

18 Critical review of the Local Density Approximation 1 W L G X W K 1 1 W L G X W K Limitations and Beyond Self-interaction cancellation in v Hartree + v x violated repair using exact Hartree-Fock exchange functional hybrid functionals (PBE, HSE3, HSE6) GGA Energy (ev) Si bandgap exp: 1.11 ev GGA:.57 ev HSE: 1.15 ev HSE Energy (ev)

19 Critical review of the Local Density Approximation 1 W L G X W K 1 1 W L G X W K Limitations and Beyond Self-interaction cancellation in v Hartree + v x violated repair using exact Hartree-Fock exchange functional hybrid functionals (PBE, HSE3, HSE6) GGA Energy (ev) Ge bandgap exp:.67 ev GGA:.9 ev HSE:.66 ev HSE Energy (ev)

20 Critical review of the Local Density Approximation Calculated vs. experimental bandgaps

21 SrTiO 3 GGA 1 8 DOS (1/eV) (E - E V ) (ev) Bandgap GGA: 1.6 ev, exp.: 3.2 ev

22 SrTiO 3 GGA 1 HSE DOS (1/eV) 6 4 DOS (1/eV) (E - E V ) (ev) (E - E V ) (ev) Bandgap GGA: 1.6 ev, HSE: 3.1 ev, exp.: 3.2 ev

23 LaAlO 3 GGA 25 2 DOS (1/eV) (E - E V ) (ev) Bandgap GGA: 3.5 ev, exp.: 5.6 ev

24 LaAlO 3 GGA 25 HSE DOS (1/eV) 15 1 DOS (1/eV) (E - E V ) (ev) (E - E V ) (ev) Bandgap GGA: 3.5 ev, HSE: 5. ev, exp.: 5.6 ev

25 Outline LAOSTO 1 LAOSTO 2

26 Metal-Insulator Transition of Morin, PRL 1959 Metal-Insulator Transitions (MIT) (d 1 ) 1st order, 34 K, σ 1 4 rutile M 1 (monoclinic) V 2 O 3 (d 2 ) 1st order, 17 K, σ 1 6 corundum monoclinic paramagn. AF order Origin of the MIT??? Structural Changes? Electron Correlations?

27 Metal-Insulator Transition of Octahedral Coordination V 3d e σ g V 3d t 2g E F σ π Rutile Structure simple tetragonal P4 2 /mnm (D 14 4h ) O 2p π σ V 3d-O 2p hybridization σ, σ (p-de σ g ) π, π (p-dt 2g )

28 Metal-Insulator Transition of Octahedral Coordination e σ g Orbitals V 3d e σ g σ V 3d t 2g O 2p E F π π σ t 2g Orbitals V 3d-O 2p hybridization σ, σ (p-de σ g ) π, π (p-dt 2g )

29 Metal-Insulator Transition of Octahedral Chains Rutile Structure simple tetragonal P4 2 /mnm (D 14 4h )

30 Metal-Insulator Transition of Octahedral Coordination t 2g Orbitals V 3d e σ g σ V 3d t 2g E F π e π g = π a 1g = d O 2p π σ

31 Metal-Insulator Transition of Rutile Structure M 1 -Structure Structural Changes V-V dimerization c R antiferroelectric displacement c R

32 Metal-Insulator Transition of Rutile M 1 π π d d E F d Goodenough, metal-metal dimerization c R splitting into d, d antiferroelectric displacement c R upshift of π Zylbersztejn and Mott, 1975 splitting of d by electronic correlations upshift of π unscreenes d electrons

33 Metal-Insulator Transition of Other Compounds d d 1 d 2 d 3 d 4 d 5 d 6 3d TiO 2 VO 2 CrO 2 MnO 2 (S) (M S) (F M) (AF S) 4d NbO 2 MoO 2 TcO 2 RuO 2 RhO 2 (M S) (M) (M) (M) (M) 5d TaO 2 WO 2 ReO 2 OsO 2 IrO 2 PtO 2 (?) (M) (M) (M) (M) (M) deviations from rutile, M = metal, S = semiconductor F/AF = ferro-/antiferromagnet

34 Metal-Insulator Transition of Other Phases Ì Ãµ Ù Ù Ä Ù ¼¼ ÄÄ Ä ÄÄ Ù Ù Ù Ù Ù Ù Ä Ì ¾¼¼ ÄÄ Å ½ Ä Ù ÄÄ Ù Ù Ù ÙÄ ½¼¼ Ù Ù Ù ÄÄ Ù Ù Ù Ù Ù Ä Ù Ù ÄÄ Ù Ä ¹ ¼º¼½ ¼º¼¾ ¼º¼ ¼º¼ ¼º¼ Ü Å ¾ Ê doping with Cr, Al, Fe, Ga uniaxial pressure 11 Cr x V 1 x O 2 Pouget, Launois, 1976

35 Electronic Structure in Detail Rutile Structure molecular-orbital picture octahedral crystal field = V 3d t 2g /e g V 3d O 2p hybridization DOS (1/eV) V 3d t 2g V 3d e g O 2p (E - E F ) (ev) VE, Ann. Phys. (Leipzig) 11, 65 (22)

36 Electronic Structure in Detail Rutile Structure molecular-orbital picture V 3d x 2 -y 2 V 3d yz V 3d xz octahedral crystal field = V 3d t 2g /e g V 3d O 2p hybridization t 2g at E F : d x 2 y 2, d yz, d xz n(d x 2 y 2) n(d yz) n(d xz ) DOS (1/eV) (E - E F ) (ev) VE, Ann. Phys. (Leipzig) 11, 65 (22)

37 Electronic Structure in Detail Rutile Structure M 1 Structure V 3d x 2 -y 2 V 3d yz V 3d xz V 3d x 2 -y 2 V 3d yz V 3d xz DOS (1/eV) DOS (1/eV) (E - E F ) (ev) (E - E F ) (ev) bonding-antibonding splitting of d bands energetical upshift of π bands = orbital ordering optical band gap on the verge of opening

38 Further investigations Cluster-DMFT Calculations Rutile- moderately correlated metal M 1 - correlations strong/weak on d /π optical band gap of.6 ev Phase Transition correlation-assisted Peierls transition S. Biermann, A. Poteryaev, A. I. Lichtenstein, A. Georges PRL 94, 2644 (25)

39 New Calculations: GGA vs. HSE Rutile Structure GGA Rutile Structure HSE 5 4 V 3d O 2p 5 4 V 3d O 2p DOS (1/eV) 3 2 DOS (1/eV) (E - E F ) (ev) (E - E F ) (ev) Rutile Structure: GGA = HSE broadening of O 2p and V 3d t 2g (!) bands splitting within V 3d t 2g bands

40 New Calculations: GGA vs. HSE M 1 Structure GGA M 1 Structure HSE 5 4 V 3d O 1 2p O 2 2p 5 4 V 3d O 1 2p O 2 2p DOS (1/eV) 3 2 DOS (1/eV) (E - E F ) (ev) (E - E F ) (ev) M 1 Structure: GGA = HSE splitting of d bands, upshift of π bands optical bandgap of 1 ev

41 New Calculations: GGA vs. HSE M 1 Structure GGA M 1 Structure HSE Energy (ev) Energy (ev) C Y G B A E Z C Y G B A E Z M 1 Structure: GGA = HSE splitting of d bands, upshift of π bands optical bandgap of 1 ev

42 New Calculations: GGA vs. HSE Total and Summed Density of States (1/eV) Partial Density of States (1/eV) Total and Summed Density of States (1/eV) Partial Density of States (1/eV) M 2 Structure GGA M 2 Structure HSE Energy (ev) Energy (ev) M 2 Structure: GGA = HSE localized magnetic moment of 1 µ B optical bandgap of 1.6 ev

43 Unified Picture LAOSTO Rutile-Related Transition-Metal Dioxides (3d 1 ), NbO 2 (4d 1 ), MoO 2 (4d 2 ) (WO 2 (5d 2 ), TcO 2 (4d 3 ), ReO 2 (5d 3 )) instability against similar local distortions metal-metal dimerization c R antiferroelectric displacement c R ( accidental ) metal-insulator transition of the d 1 -members VE et al., J. Phys.: CM 12, 4923 (2) VE, Ann. Phys. 11, 65 (22) VE, EPL 58, 851 (22) J. Moosburger-Will et al., PRB 79, (29)

44 Success Stories LAOSTO LaAlO 3 /SrTiO 3 DOS (1/eV) L 3L 4L 5L (E - E F ) (ev) Metal-Insulator Transitions in 5 4 V 3d O 1 2p O 2 2p 5 4 V 3d O 1 2p O 2 2p DOS (1/eV) 3 2 DOS (1/eV) (E - E F ) (ev) (E - E F ) (ev)

45 Acknowledgments LAOSTO 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

46 Acknowledgments LAOSTO 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!

Metal-Insulator Transitions of the Vanadates. New Perspectives of an Old Mystery

Metal-Insulator Transitions of the Vanadates. New Perspectives of an Old Mystery : New Perspectives of an Old Mystery Volker Eyert Center for Electronic Correlations and Magnetism Institute of Physics, University of Augsburg November 15, 21 Outline Basic Theories 1 Basic Theories Density