MetalInsulator Transition in 2D Electron Systems. Sveta Anissimova Ananth Venkatesan (now at UBC) Mohammed Sakr (now at UCLA) Mariam Rahimi (now at UC Berkeley) Sergey Kravchenko Alexander Shashkin Valeri Dolgopolov Teun Klapwijk.
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MetalInsulator Transition in 2D Electron Systems
Sveta Anissimova
Ananth Venkatesan (now at UBC)
Mohammed Sakr (now at UCLA)
Mariam Rahimi (now at UC Berkeley)
Sergey Kravchenko
Alexander Shashkin
Valeri Dolgopolov
Teun Klapwijk
Si MOSFET: Silicon MetalOxideSemiconductor FieldEffect Transistor
2D QUANTUM SYSTEMS:
Why Si MOSFET?
At low densities,
ns ~ 1011 cm2,
Coulomb energy exceeds Fermi energy: EC >> EF
electron density decreases
strength of interactions increases
rs = EC / EF >10 – strongly interacting
regimecan easily be reached
MetalInsulator Transition in 2D
HighMobility Si MOSFETs
B = 0
Kravchenko, Mason, Bowker, Furneaux, Pudalov, and D’Iorio, PRB 1995
Hanein, Shahar, Tsui et al., PRL 1998
In very clean samples, the transition is practically universal:
Klapwijk’s sample:
Pudalov’s sample:
(Note: samples from
different sources,
measured in different labs)
… in contrast to strongly disordered samples:
disordered sample:
clean sample:
The effect of magnetic field
Magnetic field, by aligning spins, changes metallic R(T) to insulating:
(spins aligned)
Such a dramatic reaction on parallel magnetic field suggests unusual spin properties
How to study magnetic properties of
2D electrons?
Transport measurements: standard fourterminal technique
 Diagonal resistance
 Hall resistance
Magnetoresistance in a parallel magnetic field:
T = 30 mK
Bc
Bc
Bc
Spins become fully polarized
Shashkin, Kravchenko, Dolgopolov, Klapwijk, PRL 2001
(Okamoto et al., PRL 1999;
Vitkalov et al., PRL 2000)
Extrapolated polarization field, Bc,
vanishes at a finite electron density, nc
Vanishing Bc at a
finite n ncindicates aferromagnetic transition
in this electron system
The fact that n is sample independent and n nc indicates that the MIT in clean samplesis drivenby interactions
Shashkin et al, 2001
Pudalov et al, 2002
Vitkalov, Sarachik et al, 2001
nc
Shashkin et al., PRL 2001
nc
Effective Mass Measurements: amplitude of the weakfield Shubnikovde Haas oscillations vs. temperature
high density:
ns= 5x1011 cm2
low density:
ns = 1.2x1011 cm2
Rahimi, Anissimova, Sakr,
Kravchenko, and Klapwijk, PRL 2003
dots – ν = 10
squares – ν = 14
solid line – fit by LK formula
ns = 1.2x1011 cm2
Shashkin, Rahimi, Anissimova, Kravchenko, Dolgopolov, and Klapwijk, PRL 2003
The amplitude of the SdH oscillations follows the calculated curve down to the lowest achieved temperature: the electrons are in a good thermal contact with the bath.
*
Therefore, the sharp increase
of the spin susceptibility near
the critical density is due to the
enhancement of the effective massrather then gfactor, unlike in the Stoner scenario
Shashkin, Rahimi, Anissimova, Kravchenko, Dolgopolov, and Klapwijk, PRL 2003
Measurements of thermodynamic magnetization
suggested by B. Halperin (1998); first implemented by Prus et al. (2003)
LVC6044 CMOS Quad Micropower Operational
Amplifier with noise level: 0.2 fA/(Hz)1/2
f = 0.45 Hz
Bmod = 0.01 – 0.03 tesla
R=1010

Lockin
amplifier
+
Vg
Gate
CurrenttoVoltage converter
SiO2
Modulated magnetic field
B + Bmod
Si
2D electron layer
Ohmic contact
Maxwell relation:
C – capacitance
 chemical potential
spontaneous spin polarization at nc:
noninteracting system
mBns B/Bc forB < Bc
Bc = ph2ns/mB g*m*
Bc = ph2ns/2mBmb
M = mBx ns =
mBns forB > Bc
dM
Bc
dns
B > Bc
0
B
ns
nc
B < Bc
0
ns
Raw magnetization data: induced current vs. gate voltage
dm/dB =  dM/dn
B = 5 tesla
1 fA!!
the onset of complete
spin polarization
d/dB = 0
Shashkin, Anissimova, Sakr, Kravchenko,
Dolgopolov, and Klapwijk, condmat/0409100
Raw magnetization data: induced current vs. gate voltage
Integral of the previous slide gives M (ns):
complete spin polarization
at ns=1.5x1011 cm2
B = 5 tesla
dm/dB vs. ns in different parallel magnetic fields:
Shashkin, Anissimova, Sakr, Kravchenko,
Dolgopolov, and Klapwijk, condmat/0409100
Magnetic field of full spin polarization vs.electron density from magnetization measurements
Spontaneous spin polarization at nc?
Measurements of thermodynamic density of states
LVC6044 CMOS Quad Micropower Operational
Amplifier with noise level: 0.2 fA/(Hz)1/2
f = 0.3 Hz
Vg = 0.09V
C0 = 624 pF
R=1010

Lockin
amplifier
+
Vg
Gate
CurrenttoVoltage converter
SiO2
Si
2D electron layer
Ohmic contact
Modulated gate voltage
Vg + dVg
C0– geometric capacitance
A – sample area
Polarization field from capacitance measurements:
Jump in the density of states signals the onset of full spin polarization
D1
fully spinpolarized electrons
ns
spinunpolarized electrons
Shashkin, Anissimova, Sakr, Kravchenko,
Dolgopolov, and Klapwijk, condmat/0409100
Magnetic field of full spin polarization vs. electron density:
data become Tdependent, possibly due to localized bandtail
electron density (1011 cm2)
Shashkin, Anissimova, Sakr, Kravchenko,
Dolgopolov, and Klapwijk, condmat/0409100
Spin susceptibility exhibits critical behavior near the
metalinsulator transition: c ~ ns/(ns – nc)
insulator
cannot measure
Shashkin, Anissimova, Sakr, Kravchenko,
Dolgopolov, and Klapwijk, condmat/0409100
gfactor or effective mass?
Anissimova, Venkatesan, Shashkin, Sakr,
Kravchenko, and Klapwijk, condmat/0503123
gfactor and effective mass:
Anissimova, Venkatesan, Shashkin, Sakr,
Kravchenko, and Klapwijk, condmat/0503123
Summary of the results obtained by four (or five) independent methods
Shashkin, Anissimova, Sakr, Kravchenko, Dolgopolov, and Klapwijk, Phys. Rev. Lett. 96, 036403 (2006);
Anissimova, Venkatesan, Shashkin, Sakr, Kravchenko, and Klapwijk, Phys. Rev. Lett. 96, 046409 (2006)
Shashkin, Rahimi, Anissimova, Kravchenko, Dolgopolov, and Klapwijk, Phys. Rev. Lett. 91, 046403 (2003)
Temperaturedependent corrections to conductivity due to
electronelectron interactions
Low temperatures, Diffusive regime
(Tt<<1)
(always “insulating” behavior)
Same corrections persist to ballistic regime
(Higher temperatures; Tt>>1)
Theory of the metalinsulator transition
(diffusive regime)
…the point of the metal to insulator transition correlates with the appearance of the divergence in the spinsusceptibility… note that at the fixed point the gfactor remains finite
Punnoose and Finkelstein, Science,
Vol. 310. no. 5746, pp. 289  291
These conclusions are in agreement with experiments
Punnoose and Finkelstein, Science
Vol. 310. no. 5746, pp. 289  291
SUMMARY:
and…
PunnooseFinkelstein theory gives a quantitatively correct description of the metalinsulator transition in 2D