Sasha Kuntsevich Nimrod Teneh Vladimir Pudalov Spin-droplet state of an interacting 2D electron...
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Sasha Kuntsevich Nimrod Teneh Vladimir Pudalov Spin-droplet state of an interacting 2D electron system M. Reznikov Magnetic order in clean low- density
Sasha Kuntsevich Nimrod Teneh Vladimir Pudalov Spin-droplet
state of an interacting 2D electron system M. Reznikov Magnetic
order in clean low- density systems Methods of magnetization
measurements Recharging Technique Experimental results Implications
Technion
Slide 2
Electron gas with interactions Short range repulsive
interaction 2nd order phase transition into ferromagnetic ordered
state For a single-valley system Stoner (1947) Stoner
instability
Slide 3
Ferromagnetic Bloch Instability Decreasing density Energy
Slide 4
Phase diagram Attaccalite et al. (2001) First order transition
at r s ~20: Senatore et al. (2001) r s ~26
Slide 5
Clean system B. Tanatar and D.C. Ceperley (1989)
ferromagnetic
Slide 6
Clean system Very small energy difference! antiferromagnetic
ferromagnetic B. Tanatar and D.C. Ceperley (1989)
Slide 7
Methods: Shubnikov - de Haas beatings F. Fang and P. Stiles
(1968), T. Okamoto at al., (1999), S. Vitkalov at al. (2000), V.
Pudalov at.al., (2001) 2 4 6 7 rsrs
Slide 8
V. Pudalov at al, (2001) Metal-Insulator Transition in a
Silicon Inversion Layer gg
Slide 9
In-plane magnetoresistance S. Vitkalov et al. PRL 2001A.
Shashkin et al. PLR, 2001
Slide 10
In-plane magnetoresistance A. Shashkin et al. PLR, 2001
Possible FM transition ??
Slide 11
Samples: Si Field effect transistors Russian samples, beginning
of 80 th, Holland samples, mid 80 th Typical parameters 3.4 x10 4
cm 2 /Vs @1.7K
Slide 12
The Principle of the Recharging Technique Maxwell relation:
Small correction
Slide 13
Diamagnetic contribution Capacitance contribution
Slide 14
Recharging Technique _ + VGVG Out Modulated magnetic field B+
Current Amplifier Ohmic contact Gate SiO 2 Si 2D electron gas
Slide 15
Expected behavior T=0, finite magnetic field gg Interactions M
n No interactions n Interactions Prus et al,2003 B>T
Slide 16
B (T) g B B~2E F kT/4
Slide 17
Raw data, low fields Compare with single spins M/n= B tanh(b),
b=g B B/2T
Slide 18
1
Slide 19
Slide 20
The same characteristic magnetic field
Slide 21
Interactions n n No interactions Interactions d /dn(n),
expectations
Slide 22
d /dn(n), T=1.7-13K
Slide 23
d /dn(n), T=0.6-4K
Slide 24
vs. Temperature
Slide 25
Slide 26
Slide 27
(n), T=1.7-13K
Slide 28
Magnetic moment at B=2T
Slide 29
Comparison with Transport Measurements
Slide 30
Main observations Possible scenario: few electron droplets
Slide 31
Droplet scenario vs theory Fermi-liquid expectations:
Spontaneous large spin droplets in disordered metal Diffusion
enhanced interactions in quantum dots Mean Field treatment:
Andreev, Kamenev (1998) Numerics: Shepelyansky (2001) Narozhny, B.
N. and Aleiner, I. L. and Larkin, A. I. (2000)
Slide 32
Conclusion: Problems :
Slide 33
Problem O. Prus, Y. Yaish, M. Reznikov, U. Sivan, and V.
Pudalov, PRB 2003 : Assumption: at large density the susceptibility
is the renormalized Pauli one This assumption happened to be
wrong!
Slide 34
Old results (Prus et al, 2003)
Slide 35
Field dependence of the magnetic moment
Slide 36
In-plane magnetoresistance A. Shashkin et al. PLR, 2001Fleury,
Weintal, 2010.
Slide 37
Raw data
Slide 38
Susceptibility in at B=2T
Slide 39
d /dn(n), Holland sample
Slide 40
Stoner Ferromagnetic Instability Stoner (1947) Finkelstein
(1983) For a short range repulsive interaction Diffusion enhanced
interactions in quantum dots Mean Field treatment: Andreev, Kamenev
(1998) Numerics: Shepelyansky (2001)
Slide 41
Clean system Very small energy difference! antiferromagnetic
ferromagnetic A. Finkelstein (1983), Castellani at al.,(1984)
Shekhter, A. and Finkel'stein, A. M (2005) B. Tanatar and D.C.
Ceperley (1989)
Slide 42
Real system S=0 Bhatt and Lee (1982)
Slide 43
Real system S=0 Bhatt and Lee (1982)
Slide 44
Real system S=0 Bhatt and Lee (1982) Andreev, A. V. &
Kamenev, A. (1998) Kurland, I. L. and Aleiner, I. L. and Altshuler,
B. L. (2000)