MetalInsulator Transitions in Strongly Correlated Systems with Disorder

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Metal-Insulator Transitions in Strongly
Correlated Systems with Disorder
Vladimir Dobrosavljevic Department of Physics
and National High Magnetic Field
Laboratory Florida State University
Collaborators Darko Tanaskovic (FSU) Maria
Carolina De Oliviera Aguiar (FSU-Brazil) Andrei
Pastor (FSU) Branislav Nikolic (Delaware) Eduardo
Miranda (Brazil) Denis Dalidovich (FSU) Sudip
Chakravarty (UCLA) Gabi Kotliar (Rutgers) Elihu
Abrahams (Rutgers)
Funding NHMFL/FSU Alfred P. Sloan Foundation NSF
grants DMR-9974311
DMR-0234215
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• Typical-Medium Theory of Anderson Localization
• Electronic Griffiths Phase non-Fermi liquid
  behavior
• The 2D-MIT as a transition to Wigner-Mott glass

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-Basis of microelectronic technology-
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Metal-insulator transition a quantum critical
point?

• Experiment
• Sharp transition at T0
• Continuous transition

• Theoretical problems
• No small parameter
• No symmetry breaking
• Order parameter??

• A way out controlled expansion around d2?
  (LCD)
• Scaling theory of localizationinteraction, sigma
  model,
• Limitations
• (disordered) Fermi liquid, low temperatures,
  small critical region (?)
• No strong correlation effects, NFL, metastability
  (glass)

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Applications Mott transition, heavy fermions
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TMT Formalism

• DMFT-like philosophy
• single site effective medium defined by
  self-energy ?(?)
• Local Greens function
• Cavity function
• Typical DOS

Results phase diagram
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Quantitative accuracy transport

• Comparison with exact numerics
• (exact diagonalization, finite size scaling, 3D
  cubic lattice)
• NOTE no adjustable parameters!

• Conductivity Mooij correlation,

?TMM
Inelastic scattering rate
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V.D.G. Kotliar, PRL 78, 3943 (1997) E.
MirandaV.D, PRL 86, 264 (2001)
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(Metal-Oxide-Semiconductor-Field-Effect-T
ransistor)
nc 1011 cm-2
FET approach for fullerine superconductors,(Scho
nBattlogg) ?!!!!!
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Insulator
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2D MIT Distinct Experimental Features
Drastic change of behavior near n nc 1011
cm-2 NOTE behavior seen up to T 0.25 TF
broad density range
Mass enhanced But not the g-factor Large
resistivity drop!
TF 10K
Metal destroyed by small parallel field near
transition Low density rs 10 Close to Wigner
crystal?
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• Experimental Puzzles
• On the metallic side
• Origin of small energy scale T TF/m (n-nc)
• Origin of small field scale H c-1 (n-nc)
• Large T-dependence of (drop) resistivity (factor
  10!!),
• but only close to transition.

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• B) On the insulating side
• Nature of the insulator origin of magnetism?
• Near transition
• Susceptibility approaches
• FREE SPIN LIMIT!!!
• Local moment magnetism???
• Origin of glassy behavior disorder dependence
• (experiments by D. Popovic)
• My claim all features approach to
  Wigner-Mott glass

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Physical picture Wigner crystal melting as Mott
transition (Analogy with He3 Spivak 2001
Dolgopolov 2002)

• Wigner crystal Mott insulator (magnet)

• Melting Vacancy-Interstitial
• pair formation
• (Phillips, Ceperley 2001)

• Model disordered Hubbard-like model

Use DMFT !!
MIT Mott transition disorder
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Global Phase Diagram
(EF/U) (W/U)-1
Physical trajectory EF n U n1/2 W const.

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Disordered Metallic Phase Correlation-Induced
Screening of Randomness (Zimanyi, Abrahams 1991
Tanaskovic, DeOliviera-Aguilar, VD, Kotliar,
Abrahams 2003)
Choose disorder W U, reduce EF (ignore
localization CPA)

• Resistivity drop at low T
• temperature-dependent screening?
• Altshuler Maslov,
• Das Sarma Hwang,
• Dolgopolov Gold,
• Herbut, Aleiner et al.

• Hartree-Fock theory
• weak T-dependence, only factor 2 drop
• (solve DMFT in H-F, similar as others)

Puzzle Hartree-Fock (RPA) screening
compressibility reduced when m large??!!
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Disordered Metallic Phase Incoherent Transport
(standard DMFT) Tanaskovic, DeOliviera-Aguilar,
Miranda, VD, Kotliar, Abrahams (PRL 91, 066603
(2003), cond-mat/0305511)

• Strong T-dependence,
• factor gt 10 drop!!!
• (solve full DMFT
• using IPT or slave bosons)
• Enhanced screening at low T
• due to correlations, even as
• compressibility is small
• (approach to Mott transition)
• Strong inelastic scattering
• at higher T

Experiment
Theory
Scattering rate 1/?
T
T/TF

• Incoherent Fermi liquid (low T TF/m
  distribution of local coherence scales)
• (microscopic origin of decoherence?)

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Glassy behavior of electrons near MIT (Pastor,
Tanaskovic, Dalidovich, V.D. 1999-2002)
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Extended DMFT of the Electron Glass (Inter-site
interactions Vij)
Glassy behavior deep in the insulator
(EfrosShklovskii, Pollak) Question when does
the glass melt?
Mobile electrons quantum
fluctuations MELT glass at T0
E-DMFT replica symmetry breaking (Parisi
scheme)
Diverges at Anderson-like transition Vanishes at
Mott transition
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Global Phase Diagram DMFT picture of the
2D-MIT Dobrosavljevic, Tanaskovic, Pastor PRL
90, 016402 (2003)

• Metallic glass phase
• Hierarchical,
• correlated dynamics
• (scale invariant)
• Experiments by
• Popovic et al., PRL 2002
• replicon modes
• Non-Fermi liquid
• transport
• Dalidovich and Dobrosavljevic, PRB (2002)

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Conclusions

• Extended DMFT order-parameter theory for
  Anderson-Mott transition
• Non-perturbative approach to correlations in
  disordered systems
• Non-Fermi liquid behavior as precursor to MIT
  two-fluid behavior
• New physical picture of MIT in correlated
  disordered systems
• Consistent with experiments in doped
  semiconductors,
• Kondo alloys, MOSFETs (freezing into a
  Wigner-Mott glass)