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
Slide 2
Semiconductor FET structure WANTED : MATERIALS for devices
which can operate at REDUCED VOLTAGES with INCREASE SWITCHING
SPEEDS.
Slide 3
Memories and sensors Multiple Ground States Large Responses
[big things!] Interesting non linearities Multiple degrees of
freedom Multiple functionalities.
Slide 4
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
Slide 5
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.
Slide 6
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
Slide 7
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
Slide 8
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.
Slide 9
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 //
Slide 10
Band theory: LDA fails Monoclinic insulating phase. Rutile
Phase
Slide 11
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
Slide 12
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)
Slide 13
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)
Slide 14
Lazarovits Haule and Kotliar PRB 81, 115117 (2010) Strain
promotes metallization even though it increases the Peiersl
Splitting !!!
Slide 15
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.
Slide 16
Molecular-DMFT [ D. Jacob K. Haule Molecule with correlated
atoms
Slide 17
Experimental predictions [molecular DMFT ] for two Ni atoms
with copper contacts D. Jacob K Haule and G. Kotliar PRB 82, 195115
(2010 ) Molecular DMFT
Slide 18
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
Slide 19
More Ingredients: finite electric fields and dissipation.
Cond-mat arXiv:1105.5387. Camille Aron, Gabriel Kotliar, Cedric
Weber (2001)
Slide 20
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.
Slide 21
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
Slide 22
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 ?
Slide 23
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.
Slide 24
Thanks for your attention!
Slide 25
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)