Quantum Melting of the Wigner Solid and the 2DMIT

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Quantum Melting of the Wigner Solid and the
2D-MIT
Vladimir Dobrosavljevic Department of Physics
and National High Magnetic Field
Laboratory Florida State University
Collaborators John Janik (FSU) Ben Thayer
(FSU) Darko Tanaskovic (FSU) Carol Aguiar (FSU,
Rutgers) Gabi Kotliar (Rutgers) Elihu Abrahams
(Rutgers)
Funding NHMFL/FSU Alfred P. Sloan Foundation NSF
grant DMR-0234215
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Contents

• Experimental puzzles strong correlation physics?
• 2D-MIT as a transition to a melting of Wigner
  glass
• Physical picture Wigner glass melting as Mott
  transition
• Mapping a 2D electron fluid to a Hubbard-like
  model
• DMFT results
• Large mass enhancement near MIT
• Correlation-enhanced disorder screening,
  resistivity drop!!

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What is known about the 2D-MIT?
...There are known knowns, there are things we
know we know. We also know there are known
unknowns, that is to say we know there are some
things we do not know. But there are also unknown
unknowns the ones we dont know we dont
know... ...the latter tend to be the difficult
ones...
Donald Rumsfeld, US Secretary of Defense
winner of the 2003 Foot in Mouth Award
(The Economist, Dec. 6, 2003)
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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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• B) On the insulating side
• Nature of the insulator origin of magnetism?
• Near transition
• Susceptibility approaches
• FREE SPIN LIMIT!!!
• Local moment magnetism???
• Origin of glassy behavior disorder dependence
• (experiments by D. Popovic, Friday 1025 talk)
• My claim all features approach to
  Wigner-Mott glass

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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?)

• Low density electrons tightly bound to lattice
  sites (electrostatic repulsion)
• Model disordered Hubbard-like (charge-transfer)
  model.
• Microscopic modelling (density-dependent
  parameters)?

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Charge-transfer (vacancy-interstitial) model
(similar model as in oxides, cuprates)
Interstitial orbital
Coulomb potential (side view)
Quantum Fluctuations
Lattice orbital

• Virtual process hopping in and out of
  interstitial site
• (similar as superexchange through the oxygen
  p-orbital in oxides)
• Correlations single-occupation (Uinf.)
  constraint
• in the lattice orbitals
• Remains at half-filling at any density, bands
  broaden
• bandwith-driven Mott transition

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Density-dependent band structure results (J.
Janik, B. Thayer, V.D., 2005)
Bands cross around rs 10
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Applications Mott transition, heavy fermions
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Phase diagram density-driven Wigner-Mott
transition

• Large effective mass
• enhancement near
• transition
• m (n nc)-1
• Correlated metallic
• state wiped out by
• Zeeman effects
• (parallel field)
• First-order finite T
• transition, but only
• BELOW T 0.03

Wigner-Mott insulator
Correlated metal
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Phase diagram with disorder
(EF/U) (W/U)-1
Physical trajectory EF n U n1/2 W const.

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Disordered metallic phase correlation-induced
screening of randomness (Zimanyi, Abrahams 1991
Tanaskovic, DeOliviera-Aguilar, VD, Kotliar,
Abrahams) Phys. Rev. Lett. 91, 066603 (2003)
Europhys. Lett. 67, 226 (2004)
Choose disorder W U, reduce EF (ignore
localization CPA)

• Resistivity drop at low T
• temperature-dependent screening?
• Altshuler Maslov,
• Das Sarma Hwang,
• Dolgopolov Gold,
• Herbut, Aleiner et al.

• Hartree-Fock theory
• weak T-dependence, only factor 2 drop
• (solve DMFT in H-F, similar as others)

Puzzle Hartree-Fock (RPA) screening
compressibility reduced when m large??!!
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Disordered metallic phase incoherent transport
Tanaskovic, DeOliviera-Aguilar, Miranda, VD,
Kotliar, Abrahams (PRL 91, 066603 (2003),
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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Conclusions

• New physical picture of 2D MIT
• Wigner crystal melting disorder transition
  to Wigner-Mott glass
• Extended DMFT order-parameter theory for
  metal-insulator transition
• Non-perturbative approach to strong correlations
  in disordered systems
• Microscopic origin of small energy (field) scales
  near MIT
• Metallic phase enhanced disorder screening (low
  T) inelastic scattering (high T)
• Predicts glassy behaviors of electrons close to
  MIT (as seen by exp. of D. Popovic)