Quantum Glassines in Coulomb Systems:

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Quantum Glassines in Coulomb Systems From
MOSFETs to High Tc Cuprates
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) Christos
Panagopoulos (Cambridge)
Funding NHMFL/FSU Alfred P. Sloan Foundation NSF
grant DMR-9974311
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Contents

• Glassiness a fundamental feature of MIT-s
• Experiments InO2, MOSFETs, SiP
• 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
• Glassiness as key to High Tc superconducitvity?

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In2O3-x films (Z. Ovadyahu, A. Vaknin, M. Pollak
1997-2004)
AGING
AGING
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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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Glassy behavior of disordered electrons?
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What is known about the Coulomb glass?
Coulomb Glass Model
Efros-Shklovskii thery r(e) Cd(e-eF)d-1 (Bound
!!) NOTE in ALL dimensions!!!
T0
Simulations (finite T) (Clare Yu, 93, Vojta 95)
Glassy behavior ONLY at low T (below 5)
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• Open questions
• 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?

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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 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 cond-mat/406406)
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
• 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
• recent extension of our approach (Muller and
  Ioffe, 2004)
• explicitly show that lscr 1/T. Thus zeff ??
  MFT valid!!!

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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)

• Metallic glass phase
• Hierarchical,
• correlated dynamics
• (scale invariant)
• Experiments by
• Popovic et al., PRL 2002
• Kar et al., PRL 2003
• Replicon modes
• Non-Fermi liquid
• transport (a la Sachdev)
• Dalidovich and Dobrosavljevic, PRB (2002)

Metal
Metallic Glass
Wigner-Mott Glass (gapless)
Wigner-Mott Solid (incompressible)
Disorder
WU
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Glassy behavior as key to high-Tc
superconductors?(C. Panagopoulos,
V.Dobrosavljevic, cond-mat/0410111)
T
Pseudogapped metal
T
Antiferromagnetism
Tm
Marginal Fermi liquid
Crossover
Fermi liquid
Spin glass
x (doping)
?
Quantum critical points
Superconductivity
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Resistivity of a high Tcsuperconductor
Puzzling Marginal Fermi Liquid behavior
(Takagi, 92)
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Deviation from MFT - Crossovers

• Normal state resistivity has
• a logT upturn below optimum
• doping.
• This defined a crossover
• temperature T, which decreases
• near optimum doping
• Similar crossover between
• MFL (linear) T resistivity at high
• T and FL at low T at crossover
• temperature Tm

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Glassy behavior and superconductivity?(C.
Panagopoulos et al.)
Standard spin-glass signatures at low doping
muSR data within the superconducting
phase glassiness persists!!!
spin and charge correlation!
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The Abnormal Normal State of the High-Tc
Superconductors
Using 60 teslas ... ...to suppress the
superconducting state ...(undress the
electrons) to reveal the low-temperature
normal-state phase diagram
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Phase diagram

• STM imaging evidence of
• an inhomogeneous state!
• (Takagi, PRL 2004).
• THEORY
• Nano-scale phase separation
• Gorkov and Sokol 87, Kivelson, Dagotto et al
• Self-generated stripe glass
• Schmalian and Wolyness (EDMFT-2000)
• Charge tunneling gives logT
• Efetov, PRL 2003

SC glass
glassy insulator
inhomogeneous (glassy) metal
homogeneous metal
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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
• Possible key role in high Tc superconductors