Quantum Fluctuations and Glassy Behavior of Electrons

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Quantum Fluctuations and Glassy Behavior of
Electrons Near Metal-Insulator Transitions
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 2D (MOSFETs) and 3D
(SiP) (Dragana Popovic, FSU 3 PRLs, 2002, 2004
Kar et al. PRL 2003)
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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Dobrosavljevic 2003, unpublished)
Entropy vanishes along this line!
d3 cubic lattice

• Coulomb interactions are
• strongly frustrating
• Ordering temperature only
• 10 of Coulomb energy eo!!!
• Strongly correlated Coulomb liquid
• survives down to T ltlt eoe2/a
• Small disorder (W/eo3) destroys the
• Wigner crystal
• TG(W) weakly depends on disorder.

NOTE consistent with large critical
rseo/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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Simulation (T. Vojta, 1995)
Approaching the Coulomb Glass Pseudogap Phase
Theory
At stronger disorder, the plasma dip disappears!
NO adjustable parameters!!!
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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
Metal-Insulator Transition Dobrosavljevic,
Tanaskovic, Pastor PRL 90, 016402 (2003)
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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