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Sveta Anissimova Ananth Venkatesan Mohammed Sakr (now at UCLA)

Spin susceptibility near the 2D metal-insulator transition. Sveta Anissimova Ananth Venkatesan Mohammed Sakr (now at UCLA) Sergey Kravchenko (presenting author) Alexander Shashkin Valeri Dolgopolov Teun Klapwijk. In very clean 2D samples, there exists a practically universal

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Sveta Anissimova Ananth Venkatesan Mohammed Sakr (now at UCLA)

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  1. Spin susceptibility near the 2D metal-insulator transition Sveta Anissimova Ananth Venkatesan Mohammed Sakr (now at UCLA) Sergey Kravchenko (presenting author) Alexander Shashkin Valeri Dolgopolov Teun Klapwijk Leiden 2005

  2. In very clean 2D samples, there exists a practically universal metal-insulator transition: Klapwijk’s sample: Pudalov’s sample: (Note: samples from different sources, measured in different labs) Leiden 2005

  3. Magnetic field, by aligning spins, changes metallic R(T) to insulating: (spins aligned) Leiden 2005

  4. Magnetoresistancein a parallel magnetic field Simonian et al., PRL 1997 Such a dramatic response to parallel magnetic field suggests unusual spin properties Leiden 2005

  5. How to study magnetic properties of 2D electrons? Leiden 2005

  6. Method 1: magnetoresistancein a parallel magnetic field T = 30 mK Bc Shashkin, Kravchenko, Dolgopolov, and Klapwijk, PRL 2001 Bc Bc Spins become fully polarized (Okamoto et al., PRL 1999; Vitkalov et al., PRL 2000)

  7. Method 2: weak-field Shubnikov-de Haas oscillations high density low density (Pudalov et al., PRL 2002; Shashkin et al, PRL 2003) Leiden 2005

  8. Method 3: Measurements of thermodynamic magnetization suggested by B. I. Halperin (1998); first implemented by O. Prus, M. Reznikov, U. Sivan et al. (2002) 1010 Ohm - + Gate Current amplifier Vg SiO2 Modulated magnetic field B + dB Si 2D electron gas Ohmic contact i ~ dm/dB = - dM/dns Leiden 2005

  9. Magnetic field of the full spin polarization vs. ns spontaneous spin polarization at nc: non-interacting 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 Leiden 2005

  10. Raw magnetization data: induced current vs. gate voltage dm/dB = - dM/dn 1 fA!! insulator B|| = 5 tesla Leiden 2005

  11. Raw magnetization data: induced current vs. gate voltage Integral of the previous slide gives M (ns): complete spin polarization at ns=1.5x1011 cm-2 B|| = 5 tesla Leiden 2005

  12. Spin susceptibility c = M /B Leiden 2005

  13. dm/dB vs. ns in different parallel magnetic fields: Leiden 2005

  14. Magnetic field of full spin polarization vs. electron density: Spontaneous spin polarization at nc? Leiden 2005

  15. Method 4: Measurements of the thermodynamic density of states 1010 Ohm - + Gate Current amplifier Vg SiO2 Si 2D electron gas Ohmic contact Modulated gate voltage Vg + dVg i ~ dm/dns + const. Leiden 2005

  16. Jump in the density of states signals the onset of full spin polarization D-1 fully spin-polarized electrons ns spin-unpolarized electrons Leiden 2005

  17. Magnetic field of full spin polarization vs. electron density: data become T-dependent, possibly due to localized band-tail electron density (1011 cm-2) Leiden 2005

  18. Anderson insulator Disorder increases at low density due to reduced screening disorder paramagnetic Fermi-liquid Wigner glass? Density-independent disorder electron density Leiden 2005

  19. Summary of the results obtained by four (or five) independent methods Leiden 2005

  20. Spin susceptibility exhibits critical behavior characteristic of the existence of a phase transition: c ~ ns/(ns – nc) insulator cannot measure Leiden 2005

  21. g-factor or effective mass? Leiden 2005

  22. dm/dB vs. ns in perpendicular magnetic field Leiden 2005

  23. dm/dB vs. ns in perpendicular magnetic field Leiden 2005

  24. g-factor and effective mass: g-factor: Leiden 2005

  25. g*, m*, and c vs. ns Leiden 2005

  26. Very recent theoretical development: Leiden 2005

  27. …our solution gives a physical picture that is in qualitative agreement with the experimental situation. In particular, it is shown that 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 Punnoose and Finkelstein, preprint (2005) Leiden 2005

  28. CONCLUSIONS: • In strongly interacting 2D electron system in silicon, Pauli spin susceptibility critically grows near a sample-independent density nc: behavior that is characteristic of the existence of a phase transition. • In clean samples, ncpracticallycoincides • with themetal-insulator transition point • We find no sign of increasing g-factor, but • the effective mass is strongly (×3) enhanced • near nc Leiden 2005

  29. Appendix: Difference between our results and those of Prus, Reznikov, Sivan et al. (PRB 2003): Raw data shifted up to obtain correspondence with transport results Leiden 2005

  30. Data of Prus, Reznikov, Sivan et al. PRB 2003 Leiden 2005

  31. Only three data points are relevant to the metallic regime Data of Prus, Reznikov, Sivan et al. PRB 2003 Leiden 2005

  32. Indeed, the (inverse) spin susceptibility has a Curie form characteristic of local moments Data of Prus, Reznikov, Sivan et al. PRB 2003 Leiden 2005

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