Sergey Kravchenko in collaboration with: S. Anissimova, A. M. Finkelstein, T. M. Klapwijk, and A. Punnoose

1. Flow diagram of the metal-insulator transition in 2D Sergey Kravchenko in collaboration with: S. Anissimova, A. M. Finkelstein, T. M. Klapwijk, and A. Punnoose OSU 2008

2. One-parameter scaling theory for non-interacting electrons: the origin of the common wisdom “all states are localized in 2D” Abrahams, Anderson, Licciardello, and Ramakrishnan, PRL 42, 673 (1979) However, this conclusion was reached for non-interacting electrons. Does it change in the presence of the interactions? OSU 2008

3. Samples • What do experiments show? • What do theorists have to say? • Experimental test of the Punnoose-Finkelstein theory • Summary OSU 2008

4. Al silicon MOSFET SiO2 p-Si conductance band 2D electrons chemical potential energy valence band _ + distance into the sample (perpendicular to the surface) OSU 2008

5. WhySi MOSFETs? • large m*=0.19 m0 • twovalleys • low average dielectric constant e=7.7 As a result, at low electron densities, Coulomb energy strongly exceeds Fermi energy: EC >> EF rs = EC / EF >10 can easily be reached in clean samples OSU 2008

6. Samples • What do experiments show? • What do theorists have to say? • Experimental test of the Punnoose-Finkelstein theory • Summary OSU 2008

7. Strongly disordered Si MOSFET (Pudalov et al.) • Consistent (more or less) with the one-parameter scaling theory OSU 2008

8. Clean sample, much lower electron densities Kravchenko, Mason, Bowker, Furneaux, Pudalov, and D’Iorio, PRB 1995 OSU 2008

9. In very clean samples, the transition is practically universal: Klapwijk’s sample: Pudalov’s sample: (Note: samples from different sources, measured in different labs) OSU 2008

10. The effect of the parallel magnetic field: T = 30 mK Shashkin, Kravchenko, Dolgopolov, and Klapwijk, PRL 2001 OSU 2008

11. Magnetic field, by aligning spins, changes metallic R(T) to insulating: (spins aligned) OSU 2008

12. Samples • What do experiments show? • What do theorists have to say? • Experimental test of the Punnoose-Finkelstein theory • Summary OSU 2008

13. Corrections to conductivity due to electron-electron interactions in the diffusive regime (Tt < 1) • always insulating behavior However, later this prediction was shown to be incorrect OSU 2008

14. 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 • Effective strength of interactions grows as the temperature decreases Altshuler-Aronov-Lee’s result Finkelstein’s & Castellani-DiCastro-Lee-Ma’s term OSU 2008

15. Recent development: two-loop RG theory disorder takes over disorder QCP interactions metallic phase stabilized by e-e interaction Punnoose and Finkelstein, Science 310, 289 (2005) OSU 2008

16. Samples • What do experiments show? • What do theorists have to say? • Experimental test of the Punnoose-Finkelstein theory • Summary OSU 2008

17. Experimental test First, one needs to ensure that the system is in the diffusive regime (Tt < 1).One can distinguish between diffusive and ballistic regimes by studying magnetoconductance: - diffusive: low temperatures, higher disorder (Tt < 1). - ballistic: low disorder, higher temperatures (Tt > 1). The exact formula for magnetoconductance (Lee and Ramakrishnan, 1982): 2 valleys for Low-field magnetoconductance in the diffusive regime yields strength of electron-electron interactions In standard Fermi-liquid notations, OSU 2008

18. Experimental results (low-disordered Si MOSFETs; “just metallic” regime; ns= 9.14x1010 cm-2): S. Anissimova et al., Nature Phys. 3, 707 (2007) OSU 2008

19. Temperature dependences of the resistance (a) and strength of interactions (b) This is the first time effective strength of interactions has been seen to depend on T OSU 2008

20. Experimental disorder-interaction flow diagram of the 2D electron liquid S. Anissimova et al., Nature Phys. 3, 707 (2007) OSU 2008

21. Experimental vs. theoretical flow diagram(qualitative comparison b/c the 2-loop theory was developed for multi-valley systems) S. Anissimova et al., Nature Phys. 3, 707 (2007) OSU 2008

22. Quantitative predictions of the one-loop RG for 2-valley systems(Punnoose and Finkelstein, Phys. Rev. Lett. 2002) Solutions of the RG-equations for r << ph/e2: a series of non-monotonic curves r(T). After rescaling, the solutions are described by asingleuniversalcurve: rmax r(T) Tmax g2(T) For a 2-valley system (like Si MOSFET), metallic r(T) sets in when g2 > 0.45 g2 = 0.45 rmax ln(T/Tmax) OSU 2008

23. Resistance and interactions vs. T Note that the metallic behavior sets in when g2 ~ 0.45, exactly as predicted by the RG theory OSU 2008

24. Comparison between theory (lines) and experiment (symbols) (no adjustable parameters used!) S. Anissimova et al., Nature Phys. 3, 707 (2007) OSU 2008

25. g-factor grows as T decreases ns = 9.9 x 1010 cm-2 “ballistic” value OSU 2008

26. SUMMARY: • Interactions in low-disordered two-dimensional systems stabilize the metallic state and lead to the existence of the metal-insulator transition • When temperature is decreased, the interaction amplitude growson the metallic side of the transition and decreases on the insulating side • The metal-insulator transition occurs at r ~ ph/e2 • In excellent agreement with Punnoose-Finkelstein • theory,the metallic behavior (dr/dT>0) sets in once • the interaction amplitude reaches g2 = 0.45 • The metallic side of the transition is • accurately described by the Punnoose- • Finkelstein theory without any fitting • parameters OSU 2008