OUTLINE. II - The temperature dependence:- an apparent metal-insulator transition in 2D

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2 OUTLINE I - Brief History II - The temperature dependence:- an apparent metal-insulator transition in 2D Partial list of theoretical suggestions Important question: Mundane? e. g. oxide traps Profound? e. g. new ground state III - The effect of magnetic field applied parallel to the plane IV - Scaling of the magnetoconductance - Evidence for a divergence in the susceptibility χ, g*m*, m* Quantum phase transition; to what new ground state??

3 No metallic state is possible in non-interacting 2D electron systems Abrahams, Anderson, Licciardello and Ramakishnana, 1979 Weak disorder: σ = ne 2 τ/m*+ A(e 2 /h) ln (T/T 0 ) Strong disorder: σ ~ exp [-(T/T 0 ) 1/p ] p=1,2,3 No metallic state is possible in weakly interacting 2D electron systems stronger localization Altshuler, Aronov, Lee 1980

4 Uren, Davies and Pepper, J. Phys. C 13, L985 (1980)

5 Dolan and Osheroff, PRL 43, 721 (1979) Bishop, Tsui and Dynes, PRL 44, 1153 (1980) 2.03x10 12 cm x10 12 cm -2

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8 OUTLINE I - Brief History II - The temperature dependence:- an apparent metal-insulator transition in 2D -

9 Kravchenko, Mason, Bowker, Furneaux, Pudalov, D Iorio PRB 52, 7038 (1995)

10 Kravchenko, Mason, Bowker, Furneaux, Pudalov, D Iorio PRB 52, 7038 (1995)

11 Temperature scaling Kravchenko, Mason, Bowker, Furneaux, Pudalov, D Iorio PRB 51, 7038 (1995)

12 Electric field scaling Kravchenko, Simonian, Sarachik, Mason, Furneaux, PRL 77, 4938 (1996)

13 Kravchenko, Simonian, Sarachik, Mason, Furneaux, PRL 77, 4938 (1996) (Z+1)ν = 2.7 Zν = 1.2 z= 0.8 ν = 1.5

14 QUESTION: Why had this transition not been seen in Earlier experiments in silicon MOSFET s? Why had this not been seen in 2D systems in other materials?

15 Hanein, Meirav, Shahar, Li, Tsui, Shtrikman, PRL 80, 1288 (1998)

16 In silicon MOSFET s Fermi energy: E F = n s πh 2 /2m = 0.63 mev Electron-electron interaction energy: E ee ~ e 2 /εa ~ e 2 (πn s ) 1/2 /ε ~ 10 mev E ee / E F > 1 E ee / E F ~ n -1/2

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18 No metallic state is possible in non-interacting 2D electron systems Abrahams, Anderson, Licciardello and Ramakishnana, 1979 Weak disorder: σ = ne 2 τ/m*+ A(e 2 /h) ln (T/T 0 ) Strong disorder: σ ~ exp [-(T/T 0 ) 1/p ] p=1, 2, 3 No metallic state is possible in weakly interacting 2D electron systems stronger localization Altshuler, Aronov, Lee 1980 Can strong electron-electron interactions cause delocalization? Finkelstein, 1983 Castellani, DiCastro, Lee and Ma, 1984 Efros and Pikus, 1995

19 OUTLINE I - Brief History II - The temperature dependence:- an apparent metal-insulator transition in 2D Partial list of theoretical suggestions Important question: Mundane? e. g. oxide traps Profound? e. g. new ground state

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22 OUTLINE I - Brief History II - The temperature dependence:- an apparent metal-insulator transition in 2D III - The effect of magnetic field applied parallel to the plane

23 Simonian, Kravchenko, Sarachik, Pudalov, PRL 79, 2304 (1997)

24 Simonian, Kravchenko, Sarachik, Pudalov, PRL 79, 2304 (1997)

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26 Sarachik and Kravchenko, Proc Natl. Acad. Sci. USA 96, 5900 (1999)

27 Pudalov, Brunthaler, Prinz, Bauer, JETP Lett. 65, 932 (1997)

28 Yoon, Li, Shahar, Tsui, Shayegan, PRL 84, 4421 (2000)

29 Shubnikov-de Haas measurement 2DEG V dc silicon φ H I dc

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32 SCALING OF THE MAGNETOCONDUCTANCE

33 Vitkalov, Zheng, Mertes, Sarachik, Klapwijk, PRL 87, (2001)

34 Vitkalov, Zheng, Mertes, Sarachik, Klapwijk, PRL 87, (2001) SCALING: [σ (0) - σ (H)] / [σ (0) - σ ( )] = φ (H/H σ )

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36 (σ(0)-σ(h))/(σ(0)-σ(inf)) K 0.50 K 1.0 K 1.5 K 2.0 K 3.1 K Conductivity (e 2 /h) n = cm K 0.25 K 1.0 K 1.5 K 2.0 K Field (T) H/H σ

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40 SCALING OF THE MAGNETOCONDUCTANCE Spin susceptibility diverges at finite density g*m* at n o ~ n c Quantum phase transition to a new ground state?

41 Pudalov, Gershenson, Kojima, Butch, Dizhur, Brunthaler, Prinz, Bauer, PRL 88, (2002)

42 Shashkin, Kravchenko, Dolgopolov and Klapwijk, PRL 87, (2001). Shashkin, Kravchenko, Dolgopolov and Klapwijk, PRB 66, (2002).

43 Vitkalov, Sarachik, Klapwijk, PRB 65, (2002)

44 SUMMARY II - The temperature dependence:- an apparent metal-insulator transition in 2D III - The effect of magnetic field applied parallel to the plane IV - Scaling of the magnetoconductance - Evidence for a divergence in the susceptibility χ, g*m*, m* Important question: Mundane? e. g. oxide traps Profound? e. g. new ground state

45 Sarachik and Kravchenko, Proc Natl. Acad. Sci. USA 96, 5900 (1999)

46 Sarachik and Kravchenko, Proc Natl. Acad. Sci. USA 96, 5900 (1999)

47 Vitkalov, Sarachik, Klapwijk, PRB 65, (2002)

48 Vitkalov, Sarachik, Klapwijk, PRB 65, (2002)

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51 τ = µm*c/e Sarachik, Europhys. Lett. 57, 546 (2002)

52 Sarachik and Kravchenko, Proc Natl. Acad. Sci. USA 96, 5900 (1999)

53 Bogdanovich and Popovic, PRL 88, (2001) Noise power µ 1/f α

54 Kravchenko and Klapwijk, PRL 84, 2909 (2000)

55 Shashkin, Kravchenko, Dolgopolov and Klapwijk, PRL 87, (2001).

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57 Sarachik and Kravchenko, Proc Natl. Acad. Sci. USA 96, 5900 (1999)

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61 Vitkalov and Sarachik, J. Phys. Soc. Jap. (2003)