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Sveta Anissimova Ananth Venkatesan (now at UBC) Mohammed Sakr (now at UCLA) Mariam Rahimi (now at UC Berkeley) Sergey Kravchenko Alexander Shashkin Valeri.

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Presentation on theme: "Sveta Anissimova Ananth Venkatesan (now at UBC) Mohammed Sakr (now at UCLA) Mariam Rahimi (now at UC Berkeley) Sergey Kravchenko Alexander Shashkin Valeri."— Presentation transcript:

1 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

2  Silicon MOSFETs  GaAs/AlGaAs heterostructures  SiGe heterostructures  Surface of a material (liquid helium, graphene sheets)

3 At low densities, n s ~ 10 11 cm -2, Coulomb energy exceeds Fermi energy: E C >> E F electron density decreases strength of interactions increases r s = E C / E F >10 – strongly interacting regime can easily be reached  large m* = 0.19 m 0  average  = 7.7  two valleys n v = 2

4 Hanein, Shahar, Tsui et al., PRL 1998 Kravchenko, Mason, Bowker, Furneaux, Pudalov, and D’Iorio, PRB 1995 Similar transition is also observed in other 2D structures: p-Si:Ge (Coleridge’s group) p-GaAs/AlGaAs (Tsui’s group, Boebinger’s group) n-GaAs/AlGaAs (Tsui’s group, Stormer’s group, Eisenstein’s group) n-Si:Ge (Okamoto’s group, Tsui’s group) p-AlAs (Shayegan’s group)

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9 Such a dramatic reaction on parallel magnetic field suggests unusual spin properties

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11 - Diagonal resistance - Hall resistance Rotator equipped Oxford dilution refrigerator Base temperature ~ 30 mK High mobility (100)-Si MOSFET μ=3 m 2 /Vs at T=0.1 K Excitation current 0.1 – 0.2 nA f = 0.4 Hz

12 (Okamoto et al., PRL 1999; Vitkalov et al., PRL 2000) Shashkin, Kravchenko, Dolgopolov, Klapwijk, PRL 2001 BcBc BcBc BcBc

13 Shashkin et al, 2001 Vitkalov, Sarachik et al, 2001 Pudalov et al, 2002 nn Vanishing B c at a finite n   n c indicates a ferromagnetic transition in this electron system The fact that n  is sample independent and n   n c indicates that the MIT in clean samples is driven by interactions Extrapolated polarization field, B c, vanishes at a finite electron density, n 

14  gm as a function of electron density calculated using Shashkin et al., PRL 2001 nn

15 Effective Mass Measurements: amplitude of the weak-field Shubnikov-de Haas oscillations vs. temperature Rahimi, Anissimova, Sakr, Kravchenko, and Klapwijk, PRL 2003 high density:low density: n s = 5x10 11 cm -2 n s = 1.2x10 11 cm -2

16 dots – ν = 10 squares – ν = 14 solid line – fit by L-K formula 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. Shashkin, Rahimi, Anissimova, Kravchenko, Dolgopolov, and Klapwijk, PRL 2003 n s = 1.2x10 11 cm -2

17 Comparison of the effective masses determined by two independent experimental methods: Shashkin, Rahimi, Anissimova, Kravchenko, Dolgopolov, and Klapwijk, PRL 2003 Therefore, the sharp increase of the spin susceptibility near the critical density is due to the enhancement of the effective mass rather then g-factor, unlike in the Stoner scenario *

18 2D electron layer Ohmic contact SiO 2 Si Gate Modulated magnetic field B + B mod Current-to-Voltage converter VgVg + - Measurements of thermodynamic magnetization suggested by B. Halperin (1998); first implemented by Prus et al. (2003) C – capacitance  - chemical potential Maxwell relation: R=10 10  Lock-in amplifier LVC6044 CMOS Quad Micropower Operational Amplifier with noise level: 0.2 fA/(Hz) 1/2 f = 0.45 Hz B mod = 0.01 – 0.03 tesla

19 Magnetic field of the full spin polarization B c vs. n s BcBc nsns 0 B c =  h 2 n s /2  B m b nsns 0 dMdM dnsdns M =  B  n s =  B n s B/B c for B < B c  B n s for B > B c B > B c B < B c B B c =  h 2 n s /  B g*m* nn non-interacting system spontaneous spin polarization at n  

20 1 fA!! Raw magnetization data: induced current vs. gate voltage d  /dB = - dM/dn B || = 5 tesla the onset of complete spin polarization d  /dB = 0 Shashkin, Anissimova, Sakr, Kravchenko, Dolgopolov, and Klapwijk, cond-mat/0409100

21 Raw magnetization data: induced current vs. gate voltageIntegral of the previous slide gives M (n s ): complete spin polarization B || = 5 tesla at n s =1.5x10 11 cm -2

22 d  /dB vs. n s in different parallel magnetic fields: Shashkin, Anissimova, Sakr, Kravchenko, Dolgopolov, and Klapwijk, cond-mat/0409100

23 Spontaneous spin polarization at n  ? Magnetic field of full spin polarization vs. electron density from magnetization measurements

24 2D electron layer Ohmic contact SiO 2 Si Gate Modulated gate voltage Vg +  Vg Current-to-Voltage converter VgVg + - Measurements of thermodynamic density of states C 0 – geometric capacitance A – sample area R=10 10  Lock-in amplifier LVC6044 CMOS Quad Micropower Operational Amplifier with noise level: 0.2 fA/(Hz) 1/2 f = 0.3 Hz  V g = 0.09V C 0 = 624 pF

25 Jump in the density of states signals the onset of full spin polarization D -1 nsns fully spin-polarized electrons spin-unpolarized electrons Polarization field from capacitance measurements: Shashkin, Anissimova, Sakr, Kravchenko, Dolgopolov, and Klapwijk, cond-mat/0409100

26 Magnetic field of full spin polarization vs. electron density: electron density (10 11 cm -2 ) data become T-dependent, possibly due to localized band-tail Shashkin, Anissimova, Sakr, Kravchenko, Dolgopolov, and Klapwijk, cond-mat/0409100

27 Spin susceptibility exhibits critical behavior near the metal-insulator transition:  ~ n s /(n s – n  ) insulator cannot measure Shashkin, Anissimova, Sakr, Kravchenko, Dolgopolov, and Klapwijk, cond-mat/0409100

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29 d  /dB vs. n s in perpendicular magnetic field

30 g-factor measurements in perpendicular fields: Anissimova, Venkatesan, Shashkin, Sakr, Kravchenko, and Klapwijk, cond-mat/0503123

31 g-factor:g-factor and effective mass: Anissimova, Venkatesan, Shashkin, Sakr, Kravchenko, and Klapwijk, cond-mat/0503123

32 Summary of the results obtained by four (or five) independent methods

33  spin susceptibility critically grows near the metal-insulator transition  the enhancement of the g-factor is weak and practically density independent  the effective mass becomes strongly enhanced as the density is decreased 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)

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35 Zeitschrift fur Physik B (Condensed Matter) -- 1984 -- vol.56, no.3, pp. 189-96 Weak localization and Coulomb interaction in disordered systems Finkel'stein, A.M. L.D. Landau Inst. for Theoretical Phys., Acad. of Sci., Moscow, USSR  Insulating behavior when interactions are weak  Metallic behavior when interactions are strong  Magnetic field destroys metal

36  Insulating behavior when interactions are weak  Metallic behavior when interactions are strong  Magnetic field destroys metal

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38 …the point of the metal to insulator transition correlates with the appearance of the divergence in the spin susceptibility… note that at the fixed point the g-factor remains finite These conclusions are in agreement with experiments Punnoose and Finkelstein, Science, Vol. 310. no. 5746, pp. 289 - 291

39 Punnoose and Finkelstein, Science Vol. 310. no. 5746, pp. 289 - 291

40 Pauli spin susceptibility critically grows with a tendency to diverge near the critical electron density We find no sign of increasing g-factor, but the effective mass is strongly (×3) enhanced near the metal-insulator transition and… Punnoose-Finkelstein theory gives a quantitatively correct description of the metal-insulator transition in 2D


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