Glassy Behavior of Electrons Near MetalInsulator Transitions

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Glassy Behavior of Electrons Near Metal-Insulator
Transitions (Is Mayonnaise a Metal or an
Insulator?)
Vladimir Dobrosavljevic Department of Physics
and National High Magnetic Field
Laboratory Florida State University
Collaborators Darko Tanaskovic (FSU) Andrei
Pastor (FSU) Sergey Pankov (Paris) Denis
Dalidovich (FSU) Marcelo Rozenberg
(Paris) Liliana Arachea (Trieste)
Funding NHMFL/FSU Alfred P. Sloan Foundation NSF
grant DMR-9974311
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Contents

• Glassiness a fundamental feature of MIT-s
• What is known Coulomb gap, glassiness, no
  screening?
• EDMFT formulation for electron glasses
• Classical model for electron glass
  self-organized criticality
• Long-range Coulomb interactions correlated
  plasma vs. glass
• Quantum melting of electron glass Anderson vs.
  Mott localization

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Evidence of Glassy Behavior near MIT-s noise
spectroscopy in MOSFETs (Dragana Popovic, FSU
PRL, 2002)
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What is known about the Coulomb glass?
Coulomb Gap

• Open questions (unknown unknowns)
• Why is the bound saturated?
• Why universal prefactor and exponent?
• Relation to possible glassy freezing
• ES assumed no screening. Why?
• Role of quantum fluctuations, MIT?

Efros-Shklovskii theory r(e)
Cd(e-eF)d-1 (Bound !!) NOTE in ALL dimensions!!!
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Glassy behavior of disordered electrons?
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EDMFT approach controlled theory in large d A.
A. Pastor and V. Dobrosavljevic, PRL 83, 4642
(1999)
Physical content environment (cavity)
treated in a Gaussian approximation. (quasiparti
clesplasmons)
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Results short-range repulsion

• Uniform ordering (Wigner crystal)
• at small disorder
• Glassy phase (RSB) at strong disorder
• TG 1/W at large disorder (Why?)
• ( AT line for SK model TG exp-W/V )

cool
Nothing interesting at T gt TG
GAP!!! at T 0
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Exotic Features of the Electron Glass Phase
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Long Range Coulomb Interactions (S. Pankov, V.
Dobrosavljevic 2003, unpublished)
d5 cubic lattice

• Coulomb interactions are
• strongly frustrating
• Ordering temperature only
• few percent of Coulomb energy U!!!
• Strongly correlated Coulomb liquid
• survives down to T ltlt Ue2/a
• Small disorder (WltltU) destroys the
• Wigner crystal
• Disorder increases TG(W) at small W.

T/U
Disorder W/U
NOTE consistent with large critical rsU/EF (100
for clean d3 40 for clean d2 Ceperley
QMC) (10 for disordered d2 ChuiTanatar, 1995)
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No Disorder Coulomb Plasma Correlation Gap
This gap is nonuniversal and similar in all
dimensions
MC simulations A. Efros, PRL 1992
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Approaching the Coulomb Glass Pseudogap Phase
Simulation (T. Vojta, 1995)
At stronger disorder, the plasma dip disappears!
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What about the Efros-Shklovskii gap?
Efros-Sklovskii theory r(e)
Cd(e-eF)d-1 Gap EG W-1/(d-1)
EG

• Our analytical results give TG W-1/(d-1) (at W
  large)
• This suggests that the universal Coulomb gap
• is a feature of the glassy phase.
• Consistent with vanishing ZFC compressibility
• at T0 in the glass phase, thus no screening

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Quantum Melting of the Electron Glass
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-like
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 (a la Sachdev)
• Dalidovich and Dobrosavljevic, PRB (2002)

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Conclusions What have we learned from the EDMFT
approach to the Coulomb glass?

• Simple analytical approach, has nonlinear
  screening, glassiness,...
• Coulomb repulsion disorder glassiness
• Strongly correlated plasma in the fluid phase
• Absence of screening (at T0) in the glassy
  phase
• Self-organized criticality, marginal stability ?
  universal Coulomb gap
• Quantum fluctuations due to mobility of
  electrons
• Anderson localization singular perturbation,
  stabilizes glass
• Intermediate metallic glass phase as seen in
  MOSFETs