CoulombFrustrated Phase Separation in a MagneticallyDoped 2DEG

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Coulomb-Frustrated Phase Separation in a
Magnetically-Doped 2DEG
Vladimir Dobrosavljevic Department of Physics
and National High Magnetic Field
Laboratory Florida State University
Funding NSF grants DMR-9974311 DMR-0234215 DM
R-0542026
Collaborators Theory
Experiment Hanna Terletska (FSU) Jan
Jaroszynski (FSU) Sergey Pankov (FSU)
Dragana Popovic (FSU)
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2D MIT driving force??
(Kravchenko, 1995)
Disorder scenario nc should decrease for
cleaner samples (not much seen in experiments?!)
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Strong correlations clean limit??
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Intermediate phase(s) phase separation in the
clean limit??
Crystal melting (Berezinskii) (weakly?) first
order transition (density jump)
? ?
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To enhance the tendency for phase separation? (J.
Jaroszynski, D. Popovic, cond-mat/0509189, to
appear in PRB)
Magnetically-doped 2DEG Mn-implanted CdTe
quantum well (Samples T. Wojtowicz, G.
Karczewski Polish Academy)

• Unique DMS system
• Mn not donnor or acceptor in CdTe
• (in GaMnAs, Mn is an acceptor)
• Low carrier density 2 electrons/Mn
• Clean due to modulation-doping

Spins of the magnetic atoms interact via a cloud
of electrons, which can be visualized using a
scanning tunneling microscope. The image is a
composite of microscopic visualization of
electron cloud together with a model of the
gallium arsenide crystal structure. (Image A.
Yazdani, Princeton University)
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Effects of Mn on 2DEG?
Moderate mobility Si-MOSFET
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Phase diagram (experiment)
MIT

Intermediate phase? (Kivelson)
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Phase diagram (theory)
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Theory perspective (Terletska, Pankov, V.D., 2007)
Competing magnetic order
A) Zener-type ferromagnetism (metal)
(Energy scale EF n)
(Anderson-Hasegawa, 1955)
B) Superexchange - antiferromagnetism (undoped
insulator)
n lt nc (Jex/t )1/2
(Energy scale Jex)
FM gain kinetic energy (broaden band), but
break AFM bonds Tc 0.1EF zJex
Uniform FM for n gt n Jex (typically n
2-3) Low density n lt n compromise by (local)
phase separation Charging limited droplet size
Droplets constant size and local carrier
density
AFM (insulator) n 0
FM (metal) n nc
Electrons confined to volume fraction x n/nc
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Low density transport
As density increases, the number of droplets
grows, but their structure does not change
Activated transport (escape from droplet) ?(T)
expEg/kT Eg Eg (B) independent of
n Magnetic field alligns Mn spins Eg (B)
decreases with B CMR!!
Strong temperature and field dependence, but weak
density dependence under CMR dome
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Experimental tests density dependence of
transport
We predict Strong T and B dependence, but weak n
dependence under CMR dome
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Phase diagram clean electron glass (theory)
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What is known about (dirty) electron glasses?
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How to detect glassiness noise spectroscopy
aging (Silicon MOSFETs D. Popovic et al. PRLs
2002-2004)
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EDMFT approach nonlinear screening theory (A. A.
Pastor and V. Dobrosavljevic, PRL 83, 4642
(1999)) also Schmalian and Wolyness, PRL 2000,
Mueller and Ioffe, PRL, 2004
Physical content environment (cavity)
treated in a Gaussian approximation. (quasiparti
clesplasmons)
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Simulation (T. Vojta, 1995)
Approaching the Coulomb Glass Pseudo-gap
Phase (S. Pankov and V.D., PRL, 2005)
Theory
At stronger disorder, the plasma dip disappears!
NO adjustable parameters!!!
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EDMFT picture of the disordered Coulomb-Hubbard
model (Dobrosavljevic, Tanaskovic, Pastor PRL
90, 016402 (2003))

• Metallic glass phase
• Hierarchical,
• correlated dynamics
• (scale invariant)
• replicon modes
• Non-Fermi liquid
• transport
• Dalidovich and
• Dobrosavljevic, PRB (2002)

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Metal
Metallic Glass
Wigner-Mott Glass (gapless)
Wigner-Mott Solid (incompressible)
Disorder
WU
Experiments by D. Popovic et al., PRL 2002
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More surprises from 2DEG

• Magnetically doped 2DEG unique system CdMnTe
• Ultra clean, very low carrier density DMS
  (2/Mn)
• Standard 2D-MIT without Mn, or at T gt T 2K,
  CMR below
• New intermediate FM cluster glass phase on
  metallic side of 2D-MIT

Open questions

• Nature of glassy behavior without disorder
  (close to percolation)?
• How generic is such Coulomb-frustrated phase
  separation?
• Role of disorder, Wigner crystalization,?