Electronic correlations in models and materials. Jan Kuneš

Transcription

1 Electronic correlations in models and materials Jan Kuneš

2 Outline Dynamical-mean field theory Implementation (impurity problem) Single-band Hubbard model MnO under pressure moment collapse metal-insulator transition volume collapse Fe 2 O 3 AFM long-range order

3 Interacting electrons in periodic solid Hamiltonian = Kinetic energy + Crystal potential + Interaction

4 Hubbard model Hamiltonian = Hopping + Local interaction t U

5 Large dimension limit - classical Heisenberg model Cavity construction: Expansion in hybridization : Cumulant expansion: Scaling:

6 Hubbard model in d= How to construct non-trivial d= limit? E kin E int How to scale hopping? Metzner and Vollhardt, PRL 62, 324 (1998)

7 Dynamical mean-field theory Weak coupling expansion In d= limit only local contributions to the self-energy survive! Cumulant expansion (cavity construction) In d= limit tha action reduces to interacting site subject to time dependent external field equivalent to fermionic bath Georges and Kotliar, PRB 45, 6479 (1992)

8 DMFT Weiss molecular field

9 Dynamical Mean-Field Theory (DMFT) Single out a site from the lattice Replace the rest of the lattice by an effective medium Solve the impurity many-body problem Reconstruct lattice quantities A. Georges et al. RMP 68, 13 (1996) Physics Today (March 2004) Kotliar, Vollhardt

10 Hamiltonian formulation Impurity problem Action formulation

11 Impurity solver In U, Δ(ω) U Out Σ(ω) analytic (IPT, NCA) - diagrammatic expansions diagonalization (ED, NRG, DMRG) - Hamiltonian based QMC (Hirsch-Fye, CT-QMC) - action based

12 LDA Wannier projection: H LDA (k) constrained LDA: double counting : H = Σ k H 0 (k) + Σ R U ij n Ri n Rj DMFT G dd (iω n ) U ij H 0 (k)= H LDA (k)-e dc n d Find chem. potential Compute local propagator FP-LMTO, PW paramagnetic solution 8x8 (MnO), 38x38 (Fe ) matrices on 3375 k-points Σ(iω n ) Construct impurity problem FT: ω n τ invft: τ ω n Compute Σ G(τ), U ij Solve impurity problem G dd (τ) Hirsch-Fye QMC CT-QMC hybridization expansion MaxEnt One- and two-particle quantities on real axis

13 DMFT (QMC) implementation QMC

14 Hubbard model: DMFT results crossover I critical point M 1st order transition Bulla et al. PRB 64, (2001)

15 Hubbard model: DMFT results I M Bulla et al. PRB 64, (2001)

16 Hubbard model: DMFT results I M Bulla et al. PRB 64, (2001)

17 Hubbard model: metal-insulator transition T=0 (NRG solver) Increasing U/W Bulla, PRL 83, 136 (1999)

18 Hubbard model: metal-insulator transition self-energy: with increasing U quasiparticles become heavier (m * ) in Mott insulator Σ(ω) develops pole inside the band in DMFT the gaps opens due to self-consistency Bulla et al. PRB 64, (2001)

19 Hubbard model: metal-insulator transition self-energy: with increasing U quasiparticles become heavier (m * ) in Mott insulator Σ(ω) develops pole inside the band in DMFT the gaps opens due to self-consistency Bulla et al. PRB 64, (2001)

20 Hubbard model: metal-insulator transition self-energy: with increasing U quasiparticles become heavier (m * ) in Mott insulator Σ(ω) develops pole inside the band in DMFT the gaps opens due to self-consistency Bulla et al. PRB 64, (2001)

21 Materials Models t U I M

22 MnO MnO FeO CoO Pressure NiO Mattila et al. PRL 98, (2007)

23 MnO experimental summary Mn 2+ O 2- => d 5 local configuration Conceptual phase diagram of MnO moment collapse insulator -> metal transition volume collapse structural transition C. S. Yoo et al., Phys. Rev. Lett. 94, (2005)

24 MnO - magnetic moment vs volume No change down to v c =0.68 Fluctuations increase dramatically in metallic phase at/below p c Orbital occupations follow the atomic scenario of J vs Δ cf competition M s2 = m z2 instantaneous moment M eff2 =T dτ m z (τ)m z (0) screened moment

25 MnO - magnetic moment vs volume No change down to v c =0.68 Fluctuations increase dramatically in metallic phase at/below p c Orbital occupations follow the atomic scenario of J vs Δ cf competition M s2 = m z2 instantaneous moment M eff2 =T dτ m z (τ)m z (0) screened moment

26 MnO - magnetic moment vs volume No change down to v c =0.68 At v c : t 2g gap closes Fluctuations increase dramatically in metallic phase at/below p c Orbital occupations follow the atomic scenario of J vs Δ cf competition Increasing J => shifts the transition

27 MnO - spectral density at ambient pressure PES/BIS (van Elp et al. PRB 44, 1530 (1991) ) vs Mn-3d spectral density: (U=6.9 ev, J=0.86 ev)

28 Pressure induced metallization

29 Pressure induced metallization

30 Pressure induced metallization

31 Pressure induced metallization

32 Pressure induced metallization

33 Pressure induced metallization Correlation effects weaker in LS

34 MnO - volume collapse E tot =E LDA +(E DMFT - E HF ) p=-de/dv

35 MnO - volume collapse E tot =E LDA +(E DMFT - E HF ) p=-de/dv p c

36 AFM order Fe 2 O K Fe-d total Fe-d spin resolved

37 AFM order Fe 2 O K Fe-d total Fe-d spin resolved

38 AFM order Fe 2 O K Fe-d total Fe-d spin resolved

39 AFM order Fe 2 O K Fe-d total Fe-d spin resolved

40 Conclusions DMFT allows a systematic treatment of Hubbard model in the whole parameter range. LDA+DMFT has proved to be very useful for real materials, multi-band character leads to new physics JK, A. L. Lukoyanov, V. I. Anisimov, R. T. Scalettar, and W. E. Pickett, Nature Materials 7, 198 (2008) JK, Dm. M. Korotin, M. A. Korotin, V. I. Anisimov, P. Werner, Phys. Rev. Lett. 102, (2009)

41 Outlook Computation of susceptibilities: spin, charge, orbital, - investigation of ordering phenomena - dynamic susceptibilities for comparison with ineleastic spectroscopies 2 PhD positions available at Instutite of Physics, AS CR 1 PhD position available at Uni.. Augsburg

42 insulator -> metal transition resistance Patterson et al., Phys. Rev. B 69, R (2004)