StrongCoupling Approach to Anderson Localization

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Strong-Coupling Approach to Anderson Localization
Vladimir Dobrosavljevic Department of Physics
and National High Magnetic Field
Laboratory Florida State University
Collaborators Darko Tanaskovic (FSU) Maria
Carolina De Oliviera Aguiar (FSU-Brazil) Andrei
Pastor (FSU) Branislav Nikolic (Delaware) Eduardo
Miranda (Brazil) Sudip Chakravarty (UCLA) Gabi
Kotliar (Rutgers) Elihu Abrahams (Rutgers)
Funding NHMFL/FSU Alfred P. Sloan Foundation NSF
grants DMR-9974311
DMR-0234215
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Contents

• Experimental puzzles 2D-MIT
• Duality and phenomenological scaling
• Strong coupling approach to Anderson
  localization
• Typical-Medium Theory (TMT)
• Future TMTDMFT localizationinteraction

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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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Insulator
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What can we learn from (phenomenological)
scaling? Dobrosavljevic, Abrahams, Miranda,
Chakravarty, PRL 79, 455 (1997)

• Scaling theory of localization (Abrahams et al.,
  1979)
• conductance g as a scaling variable
• Beta function
• D2 scenario for MIT?
• Metallic behavior perfect conductor!!
• Scaling does not seem to apply at the
• lowest temperatures

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Scaling in the quantum critical region and
duality

• Strong coupling form
  
• 
  
• 
  from
  
• Quantum critical behavior
• Duality
  ONLY for
• LESSON QC behavior dominated physics of the
  INSULATOR!

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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 model

Use DMFT !!
MIT Mott transition disorder
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Conventional critical points spontaneous
symmetry breaking
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Applications Mott transition, heavy fermions
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Disordered Metallic Phase Incoherent Transport
(standard DMFT) Tanaskovic, DeOliviera-Aguilar,
Miranda, VD, Kotliar, Abrahams (cond-mat/03003145,
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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Typical medium theory a local order-parameter
picture of localization Dobrosavljevic , Pastor,
Nikolic Europhys. Lett. 62, 76 (2003)

• So far mean-field treatment of interactions,
  numerical (Bethe lattice) of localization
• Goal mean-field (order-parameter) treatment of
  both interactions localization
• Idea local picture of localization (Anderson,
  1958 Abou-Chacra, Anderson, Thouless, 1971)
• Problem with CPA wrong order parameter (average
  DOS noncritical)
• Order parameter typical DOS, self-consistently
  calculated in DMFT-like fashion
• CLAIM reproduces most expected features of
  Anderson transition
• Can easily add interactions using DMFT

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TMT Formalism

• DMFT-like philosophy
• single site effective medium defined by
  self-energy ?(?)
• Local Greens function
• Cavity function
• Typical DOS

Results phase diagram
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Quantitative accuracy transport

• Comparison with exact numerics
• (exact diagonalization, finite size scaling, 3D
  cubic lattice)
• NOTE no adjustable parameters!

• Conductivity Mooij correlation,

?TMM
Inelastic scattering rate
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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)