2DMIT as self doping the WignerMott insulator

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2D-MIT as self doping the Wigner-Mott insulator
Vladimir Dobrosavljevic Department of Physics
and National High Magnetic Field
Laboratory Florida State University
Funding NSF grants DMR-9974311 DMR-0234215 DMR
-0542026
Collaborators Sergey Pankov (FSU) Darko
Tanaskovic (FSU) Carol Aguiar (FSU,
Rutgers) Eduardo Miranda (Campinas) Gabi Kotliar
(Rutgers) Elihu Abrahams (Rutgers)
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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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What does the mass enhancement mean??

• Lessons from THERMODYNAMIC
• Assume large m (n-nc)-1 !1
• Then coherence temperaure T TF/m! 0
• (Fermi liquid destroyed above T)
• Large specific heat C mT
• Entropy per carrier
• Conclusion
• MASS ENHANCEMENT ENTROPIC INSULATOR??!!!

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• B) On the insulating side
• Nature of the insulator origin of magnetism?
• Near transition
• (Sivan et al.)
• Susceptibility approaches
• FREE SPIN LIMIT!!!
• Local moment magnetism???
• Origin of glassy behavior disorder dependence
• (experiments by D. Popovic)

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Where else is this seen ? Mott localization
transition in 2D He3 monolayer on Graphite!
Surprisingly good agreement with the
Brinkman-Rice-Anderson-Vollhardt scenario
(1987) m (nc-n)-1 g const. Why
does it work for a Hubbard model on a 2D
triangular lattice? (NOT on a square lattices
cuprates!) Odd-member any exchange
(Thouless) Effective J negligibly small!
(Saunders PRL 2003)
magnetization
specific heat
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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)
• Ignore phonons (Giamarchi, le Doussal,...)
• (lattice distortions - pinned by impurities?)

g(r)

• Low density electrons tightly bound to lattice
  sites (electrostatic repulsion)
• Model (disordered) Hubbard-like
• charge-transfer model (oxides)

QMC simulations Tanatar, Ceperley 89
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Charge-transfer (vacancy-interstitial)
model (Sergey Pankov V.D. 2006)
Guztwiller-slave boson solution (self-consistent
lattice parameters)
Energy
increasing density
d
Fermi liquid
0
nc
density
QP weight (charge transferred) Z m/m (n-nc)
Instability to self-doping precedes Mott
transition at half-filling!!! (analogy with
supersolid He??)
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Finite temperature trasport
Experiment
DMFT theory no disorder
incoherent transport
Ioffe-Regel-Mott limit s kFl e2/h
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Effects of disorder??
Friend or Foe???
Sir Neville Mott
P. W. Anderson
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Disordered metallic phase incoherent transport
Tanaskovic, DeOliviera-Aguilar, Miranda, VD,
Kotliar, Abrahams (PRL (2003), EPL (2003)))

• 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 0.1TF/m
  distribution of local coherence scales)

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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)

Carrier density
(EF/U) (W/U)-1
Physical trajectory EF n U n1/2 W const.

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Summary

• 2D-MIT as interaction-driven Wigner-Mott
  transition (self-doping)
• Explains mass enhancement, large resistivity
  drop, field dependence
• (ballistic regime)
• Effects of disorder strong disorder screening
  and glassiness

Open questions

• Relation to diffusion-mode physics (Punnoose and
  Finkelstein)
• Nature of insulating state (Anderson or
  Wigner-Mott insulator)?
• Coulomb-frustrated phase separation (Kivelson
  and Spivak)

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Metal Insulator Transitions long vs. short
length scales??
Most experimental features seen over very broad
parameter range (n-nc)/nc O(1) (e.g. doped
semiconductors effects of compensation, magnetic
field) This includes striking scaling collapse
of data Question is this mean-field (e.g.
Landau) scaling or asymptotic (critical) scaling?
Data of Dragana Popovic, IBM MOSFETs, PRL 1997
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Proposed physical pictures of 2D-MIT
Diffusion modes within a Fermi liquid
Fermi liquid to Wigner-Mott insulator
Anderson insulator
resistance
Key question nature of insulating state?
interactions
Picture Wigner-Mott Diffusion-mode
density
metal
insulator
Magnetic ? 1/T (Curie) QP die
Fermi liquid ? 1/m (Pauli) QP live
Almost magnetic metal (??!) ? ?8 ? ?8 ? ?0 QP
die (agonizingly slowly)
Anderson ? ?o (Pauli) QP live
Faraday rotation (Kapitulnik)!!
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MIT vs. Local Quantum Criticality
Two general scenarios for magnetic quantum
critical points
Hertz-Millis (preformed quasiparticles)
Deconfined (local) quantum criticality
(quasiparticles die at QCP) (Coleman, Si,
Fisher, Balents, Senthil...)
Metal-insulator transitions
Wigner-Mott scenario Destruction of
quasiparticles at MIT incoherent transport
Diffusion-mode theory analogue of
Hertz-Millis coherent transport