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Mon, 6 Jun 2011 Modeling of Strongly Correlated Materials Gabriel Kotliar Physics Department and Center for Materials Theory Rutgers University Virtual Teleconference Presentation for the International Technology Roadmap for Semiconductors (ITRS) to generate a chapter on the Theory of Correlated Electrons

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Semiconductor FET structure WANTED : MATERIALS for devices which can operate at REDUCED VOLTAGES with INCREASE SWITCHING SPEEDS.

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Memories and sensors Multiple Ground States Large Responses [big things!] Interesting non linearities Multiple degrees of freedom Multiple functionalities.

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Outline Role of theory, semiconductors, correlated electron, DMFT (dynamical mean field theory) VO2 Mott-Peierls or Peierls-Mott system. [room T MIT, ultrafast response] Electronic phase transition under strain. Molecular DMFT for nano-electronics. Materials landscape organization and design. Questions/discussion

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The role of theory: semiconductors Theory provides the concepts needed to describe the carriers of electricity. Theory provides computational tools to describe quantiatively the energy wave vector dispersion in different materials. Extensions to inhomogeneous situations: impurity states, junctions, interfaces. Boltzman theory for device modeling.

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The role of theory: correlated materials The excitations in correlated materials are not in one to one correspondence to those in band theory. The computational tools of band theory fail for correlated materials. A new framework is needed, has to treat atomic excitations (multiplets) on the same footing as quasiparticle exciations. System specific implementations LDA+DMFT treat successfully numerous materials. LOCALITY OF IRREDUCIBLE QUANTITIES. Extensions to inhomogeneous and non equilibrium situation. Simple models (to develop concepts) + Computational tools (for realistic description of materials. ) Long wavelength theories to describe domain scale physics

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Phase diagram :frustrated Hubbard model, integer filling M. Rozenberg G. Kotliar H. Kajuter G. Thomas PRL75, 105 (1995) T/W 16 Quasiparticles +Hubbard bands Transfer of spectral weight Mott transition Coherence Incoherence Crossover Spectral functions

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Outline Role of theory, semiconductors, correlated electron, DMFT (dynamical mean field theory) VO2 Mott-Peierls or Peierls-Mott system. [room T, MIT, ultrafast response] Electronic phase transition under strain. Molecular DMFT for nano-electronics. Materials landscape organization and design.

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The Metal to Insulator Transition in VO 2 MIT discovered long ago 50 years, yet is still proving challenging to explain. Debate about whether the transition is driven by the lattice (Peierls physics) or electron correlation effects (Mott- Hubbard physics). Importance of correlations ? Dramatic change of optical properties (even in visible) and ultra-fast transition (~ 100 fs), may find applications as eg. optical switch, smart windows. Tunable MIT near room temperature. Many applications. Recent focus of optical experiments as well as GW and LDA+DMFT studies, Biermann Tomczak, Georges,Lichtenstein. Role of strain ? Morin, Phys. Rev. Lett. 3, 34 (1959) Eyert, Ann. Phys. 11, 650 (2002) high-temperature rutile (R) phase low-temperature monoclinic (M 1 ) phase d //

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Band theory: LDA fails Monoclinic insulating phase. Rutile Phase

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Correlations Matter :Anomalous transfer of spectral weight. Optical conductivity of VO2.Sum rule is not recovered up to 4 ev. Expts quazilbash et. al. LDA+DMFT theory

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Electronic structure LDA cannot account for insulating phase (always metallic), and V 3d O 2p are predicted to be well-separated in energy. Eyert, Ann. Phys. 11, 650 (2002) LDA+U correctly accounts for insulating phase, but cannot reproduce metallic phase (always insulating). Williams et al., J. Appl. Phys. 105 07E510 (2009) More recent cluster DMFT calculations describe both phases well. Biermann et al., Phys Rev. Lett. 94, 026404 (2005); Lazarovits Haule and Kotliar PRB 81, 115117 (2010) Lazarovits Haule and Kotliar PRB 81, 115117 (2010)

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July 2010 Strain Compressive strain along c-axis (of rutile structure) is found to lower transition temperature (to approximately room temperature). Obvious technological benefits for such tunability of MIT temperature. However, this behavior goes against a Peierls-type picture: compressive strain increases the overlap of d // orbitals, increasing the splitting of the d // bands in the insulating phase, thus stabilising it. Instead, we see the metallic phase is stabilised. Muraoka and Hiroi, Appl. Phys. Lett. 80, 583 (2002)

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Lazarovits Haule and Kotliar PRB 81, 115117 (2010) Strain promotes metallization even though it increases the Peiersl Splitting !!!

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Outline Role of theory, semiconductors, correlated electron, DMFT (dynamical mean field theory) VO2 Mott-Peierls or Peierls-Mott system. [room T, MIT, ultrafast response] Electronic phase transition under strain. Molecular DMFT for nano-electronics. Materials landscape organization and design.

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Molecular-DMFT [ D. Jacob K. Haule Molecule with correlated atoms

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Experimental predictions [molecular DMFT ] for two Ni atoms with copper contacts D. Jacob K Haule and G. Kotliar PRB 82, 195115 (2010 ) Molecular DMFT

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Theory D. Jacob K Haule and G Kotliar. PRL 103, 016803 (2009)Co atom / gold contacts PDOS Conductance Expts Nel et al PRL 98 016801 '07 T K ~ 200 K Quite good Agreement! T K ~ 150 K

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More Ingredients: finite electric fields and dissipation. Cond-mat arXiv:1105.5387. Camille Aron, Gabriel Kotliar, Cedric Weber (2001)

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Outline Role of theory, semiconductors, correlated electron, DMFT (dynamical mean field theory) VO2 Mott-Peierls or Peierls-Mott system. [room T, MIT, ultrafast response] Electronic phase transition under strain. Molecular DMFT for nano-electronics. Materials landscape organization and design.

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Paglione and Greene Nature Physics 6, 645(2010) The space of materials The families The phase diagram 4 K 1-x Fe 2-2x Se 2

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Max T SC (K) 60 50 40 30 20 10 0 Moment ( B /Fe) 2.0 1.0 0.0 m*/m band 7 5 3 1 Yin,Haule, and Kotliar 2011 Correlations in Fe-based superconductors LDA+DMFT RESULTS Cond-mat arXiv:1104.3454 Searching for new superconductors. Can Mn superconduct ?

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Wrap up Role of theory, semiconductors, correlated electron, DMFT (dynamical mean field theory) VO2 Mott-Peierls or Peierls-Mott system. [room T, MIT, ultrafast response] Electronic phase transition under strain. Molecular DMFT for nano-electronics. Materials landscape organization and design.

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Thanks for your attention!

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If you want to know more. Some General References on Dynamical Mean FieldTheory (DMFT) D. Vollhardt and G. Kotliar Physics Today Physics Today 57, No. 3 (March), 53 (2004). A.Georges, G. Kotliar., W. Krauth and M. J. Rozenberg, Reviews of. Modern Physics 68, 13 (1996). G. Kotliar, S. Y. Savrasov, K. Haule, V. S. Oudovenko, O. Parcollet, C.A. Marianetti, RMP 78, 865-951, (2006). K. Held Advances in Physics 56 829 (2007)