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LDA band structures of transition-metal oxides

Lecture 2.2, XV Training Course in the Physics of Strongly Correlated Systems, IASS Vietri sul Mare. LDA band structures of transition-metal oxides. and what electronic correlations may do to them. The metal-insulator transition in V 2 O 3. Is it really the prototype Mott transition?.

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LDA band structures of transition-metal oxides

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  1. Lecture 2.2, XV Training Course in the Physics of Strongly Correlated Systems, IASS Vietri sul Mare LDA band structures of transition-metal oxides and what electronic correlations may do to them The metal-insulator transition in V2O3 Is it really the prototype Mott transition?

  2. [1] T. Saha-Dasgupta, O.K. Andersen, J. Nuss, A.I. Poteryaev, A. Georges, A.I. Lichtenstein; arXiv: 0907.2841. [2] A.I. Poteryaev, J.M. Tomczak, S. Biermann, A. Georges, A.I. Lichtenstein, A.N. Rubtsov, T. Saha-Dasgupta, O.K. Andersen; Phys. Rev. B76, 085127 (2007) [3] F. Rodolakis, P. Hansmann, J.-P. Rueff, A. Toschi, M.W. Haverkort, G. Sangiovanni, A. Tanaka, T. Saha-Dasgupta, O.K. Andersen, K. Held, M. Sikora, I. Alliot, J.-P. Itié, F. Baudelet, P.Wzietek, P. Metcalf, M. Marsi; Phys. Rev. Lett.104, 047401 (2010). [4] S. Lupi, L. Baldassarre, B. Mansart, A. Perucchi, A. Barinov, P. Dudin, E. Papalazarou, F. Rodolakis, J.-P. Rueff, J.-P. Itié, S. Ravy, D. Nicoletti, P. Postorino, G. Sangiovanni, A. Toschi, P. Hansmann, N. Parragh, T. Saha-Dasgupta, O.K. Andersen, K. Held, M. Marsi; (accepted)

  3. Doped Mott Insulators have rich physical properties and controlling them is one of the major challenges for developing Advanced Materials High-Temperature Superconductors Colossal Magneto-Resistance Materials Intelligent Windows, Field-effect Transistors

  4. Hubbard model LDA+DMFT 1/2 filling T=2000K, U =2.1 eV U = 3.0 eV Mott transition in cuprate HTSCs Wannier orbital Conduction band (LDA) T. Saha-Dasgupta and OKA 2002

  5. A. Georges et al, Rev Mod Phys 1996: Georges and Kotliar 1992: The single-band Hubbard Model in the d=∞ limit can be mapped exactly onto the Anderson impurity model supplemented by a CPA-like self-consistency condition for the dynamical coupling to the non-interacting medium. Hence, the Kondo-resonance may develop into a quasi-particle peak. For general hopping, the Georges-Kotliar mapping leads to the dynamical mean-field approximation(DMFT). U/W = 1 LDA O.K. W = 1 DMFT needed U/W = 2 DMFT needed U/W = 2.5 QP DMFT needed U/W = 3 Mott transition LDA+U O.K. U/W = 4 LHB UHB Gap

  6. Electronic-structure calculations for materials with strong correlations Current approximations to ab inito Density-Functional Theory (LDA) are insufficient for conduction bands with strong electronic correlations, e.g. they do not account for the Mott metal-insulator transition. On the other hand, LDA Fermi surfaces are accurate for most metals, including overdoped high-temperature superconductors. Presently, we therefore start with the LDA. For the few correlated bands, we then construct localized Wannier orbitals (NMTOs) and a corresponding low-energy Hubbard Hamiltonian:HLDA + Uon-site. This is solved in the dynamical mean-field approximation (DMFT).

  7. M AFI I AFI I M M LDA+U: Ezhov, Anisimov, Khomskii, Sawatzky 1999 AFI monoclinic Paramagnetic Mand I corundum str V 3d2

  8. LDA band structure of V2O3 projected onto various orbital characters: EF EF Blow up the energy scale and split the panels: Pick various sub-bands by generating the corresponding minimal NMTO basis set: EF For the low-energy Hamiltonian we just need the t2g set EF N=2 N=2 N=2 N=1

  9. (V1-xMx)2O3 V2O3 3d (t2g)2 a1g-egπ crystal-field splitting = 0.3 eV Hund's-rule coupling J=0.7 eV

  10. LDA t2gNMTO Wannier Hamiltonian LDA+DMFT U = 4.25 eV, J = 0.7 eV a1g PM PM PM 2.0 a1g-egπcrystal-field splitting = 0.3 eV U-enhancement = 1.85 eV ~ 3J egπ Crystal-field enhanced and mass-renormalized QP bands Undo hybridization LDA 390 K

  11. Comparison with PES (Mo et al. PRL 2004):

  12. PM eg electronsare "localized" and only coherent below ~250K a1g electronsare "itinerant" and coherent below ~400K More important for the temperature dependence of the conductivity is, however, that internal structural parameters of V2O3 change with temperature, as we shall see later.

  13. LDA t2gNMTO Wannier Hamiltonian LDA+DMFT U = 4.25 eV, J = 0.7 eV = −0.41 a1g PM PM PI a1g PM 2.0 1.7 a1g a1g-egπcrystal-field splitting = 0.3 eV U-enhancement = 1.85 eV ~ 3J egπ egπ egπ Crystal-field enhanced and mass-renormalized QP bands Undohybridization Undo hybridization LDA 390 K

  14. PM PI U=4.2 eV, 0 % Cr, T=390 K U=4.2 eV, 3.8% Cr, T=580 K

  15. t = -0.72 eV

  16. t = -0.49 eV

  17. t = -0.72 eV t = -0.49 eV

  18. T=300K V2O3 (V0.96Cr0.04)2 O3 undo a1g-egπ undo a1g-egπ LDA LDA 1.7 2.0 eV Robinson, Acta Cryst. 1975: (V0.99Cr0.01)2 O3 ~ V2O3 at 900K V2O3 at 300K ~ undo a1g-egπ undo a1g-egπ LDA LDA 1.9 1.6

  19. V2O33d (t2g)2 Hund's-rule coupling

  20. This metal-insulator transition in V2O3 isnot, like in the case of a single band, e.g. a HTSC: Wannier orbital and LDA conduction band Hubbard model, LDA+DMFT Band 1/2 full T=2000K U =2.1 eV U = 3.0 eV T. Saha-Dasgupta and OKA 2002 caused by disappearance of the quasi-particle peak and driven by the Coulomb repulsion (U), i.e. it is not really a Mott transition.

  21. Conclusion In the (t2g)2system V2O3, described by an LDA t2g Hubbard model, the metal-insulator transition calculated in the DMFT is caused by quasi-particle bands being separated bycorrelation-enhanced a1g-egπ crystal-field splitting and lattice distortion. The driving mechanism is multiplet splitting (nJ) rather than direct Coulomb repulsion (U). The a1gelectrons stay coherent to higher temperatures (~450K) than the egπelectrons (~250K).

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