10th Hopping and Related Phenomena Conference

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10-th Hopping and Related Phenomena
Conference Trieste, Italy
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2D-MIT Transition to a Wigner-Mott Glass
Vladimir Dobrosavljevic Department of Physics
and National High Magnetic Field
Laboratory Florida State University
Collaborators Darko Tanaskovic (FSU) Maria
Carolina de Oliveira Aguiar (FSU, Brazil) Andrei
Pastor (FSU) Denis Dalidovich (FSU) Branislav
Nikolic (Georgetown? Delaware) Eduardo Miranda
(Brazil) Gabi Kotliar (Rutgers) Elihu Abrahams
(Rutgers)
Funding NHMFL/FSU Alfred P. Sloan Foundation NSF
grant DMR-9974311 DMR-0234215
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Contents

• Experimental puzzles strong correlation physics?
• Physical picture Wigner crystal melting as Mott
  transition
• 2D-MIT as a transition to a Wigner-Mott glass
• Extended DMFT results
• Correlation-enhanced disorder screening,
  resistivity drop!!
• Mott-Anderson transition Mott physics survives
  disorder
• Insulator local-moment magnetism
• Electron glass behavior in the vicinity of the
  (disordered) MIT

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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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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, 1130 talk)
• 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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Insulator
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Conventional critical points spontaneous
symmetry breaking
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Applications Mott transition, heavy fermions
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(VD, Pastor, Nikolic, 2002)
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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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Global Phase Diagram
(EF/U) (W/U)-1
Physical trajectory EF n U n1/2 W const.

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DMFT Picture of the Anderson-Mott
Transition (DMFT localization V.D. G.
Kotliar, PRL 1997 in progress)
Mott-like order parameter Typical quasiparticle
weight Z 1/m
Fraction of electrons turn into local moments
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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
• replocon modes
• Non-Fermi liquid
• transport
• Dalidovich and Dobrosavljevic, PRB (2002)

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Conclusions

• New physical picture of 2D MIT
• Wigner crystal melting disorder transition
  to Wigner-Mott glass
• Extended DMFT order-parameter theory for
  metal-insulator transition
• Non-perturbative approach to strong correlations
  in disordered systems
• Metallic phase enhanced disorder screening (low
  T) inelastic scattering (high T)
• Microscopic origin of small energy (field) scales
  near MIT
• Predicts glassy behaviors of electrons close to
  MIT (as seen by exp. of D. Popovic)