1. FROM STRANGE INSULATOR TO SPIN-ORBIT CONDUCTOR: UNVEILING ORBITAL- SELECTIVENESS AT THE LAO-STO INTERFACE. M. Gabay Intensive course by A. Millis: OXIDE INTERFACES, April 4th, 2012 Ecole Polytechnique April 4th, 2012 Ecole Polytechnique

2.  Jean-Marc Triscone  Andrea Caviglia  Stefano Gariglio  Nicolas Reyren  A. Fête M. Rozenberg A.Barthélémy, M. Bibes A. Santander-Syro

3.  From diffusion to reconstruction…to confusion  Band inversion (t 2g orbitals dxy  dxz, dyz)  (Electric field?) confinement on STO side (mind the dielectric constant)  The carrier concentration puzzle  It takes two (types of bands) to tango The Band story

5. Conduction depends on  Nature of the layers in contact (SrO/AlO2 vs LaO/TiO2)  Oxygen pressure  Mobility  Temperature  # of LAO layers

6. Nature Materials 7, 855 - 858 (2008) A 2DEG can also be produced at the surface of pure STO A.F. Santander-Syro. Et al, Nature 469, 189, 2011

7. A.D. Caviglia, S. Gariglio, N. Reyren, D. Jaccard, T. Schneider, M. Gabay, S. Thiel, G. Hammerl, J. Mannhart, J.-M. Triscone, Nature 456, 624 (2008 ) Diffusion SO metal Horizontal scale: use conductivity at given T, to compare phase diagrams from different samples

8.  A strange insulator regime  Surface reconstruction that avoids polar catastrophe A few oddities revealed by transport measurements in LAO/STO heterostructures  A weird quantum critical point  A dumbfounding parallel magnetotransport

9.  |e i   For the electronic states  For the Cooper pair state Ioffe-Regel criterion for localization: k F l~1 Rs=h/e 2 Rs=h/4e 2 In fact localization at T=0 in 2D even if k F l>>1

10. d (~2-7nm)  Drude part  d < l (~ 5nm)  Weak localization part  d < Lin, Lso, Lh (~50 nm)  Interaction part  d <(D (ħ/k B T)) 1/2 From measurements of R sheet, n 2D and MR

11. Courtesy of A. Caviglia 1.12≤k F l ≤4 as T varies from1.5K to 20K

12. Courtesy A. Caviglia

13. In the strongly underdoped regime k F l~1

15.  Band inversion (t 2g orbitals dxy  dxz, dyz)  (Electric field?) confinement on STO side (mind the dielectric constant)  The carrier concentration puzzle  It takes two (types of bands) to tango The Band story

16.  Band inversion (t 2g orbitals dxy  dxz, dyz)  (Electric field?) confinement on STO side (mind the dielectric constant)  The carrier concentration puzzle  It takes two (types of bands) to tango The Band story

18.  Band inversion (t 2g orbitals dxy  dxz, dyz)  (Electric field?) confinement on STO side (mind the dielectric constant)  The carrier concentration puzzle  It takes two (types of bands) to tango The Band story

20. STOLAO z

21. et al, Nature 469, 189, 2011

22. xz, yz orbitals extend deeper inside the bulk

24.  Band inversion (t 2g orbitals dxy  dxz, dyz)  (Electric field?) confinement on STO side (mind the dielectric constant)  The carrier concentration puzzle  It takes two (types of bands) to tango The Band story

25. Appl. Phys. Lett 94, 222111 (2009) Courtesy of A. Caviglia

26. p O2 =10 -5 mbar 10 uc

27. Phys. Rev. Lett. 107, 056802 (2011) p O2 =10 -3 mbar 10 uc

28. p O2 =8 10 -5 mbar Tc=0.12K

30.  Band inversion (t 2g orbitals dxy  dxz, dyz)  (Electric field?) confinement on STO side (mind the dielectric constant)  The carrier concentration puzzle  It takes two (types of bands) to tango The Band story

31. Phys. Rev. Lett. 103, 226802 (2009) p O2 =1.33 10 -5 mbar 10 uc

33. A.D. Caviglia, S. Gariglio, N. Reyren, D. Jaccard, T. Schneider, M. Gabay, S. Thiel, G. Hammerl, J. Mannhart, J.-M. Triscone, Nature 456, 624 (2008 ) Diffusion SO metal

34. T=1.5K Perpendicular magnetoconductance for different gate voltages A. Caviglia et al PRL 104, 126803 (2010) WL correction to conductivity in the diffusive regime A large spin-orbit effect is uncovered B SO =  0 /4  D  SO B el =  0 /4  D  B in =  0 /4  D  in

35. Rashba spin-orbit coupling ħ  SO = E SO ~ 2 Ek F 1/  SO =   SO   m * =( h 2 / E)√ B SO /  0 H= ( E x P ). s  (Drude)=  -  (WAL)-  e-e) -  (Super)  

36. m* max ~2.2m e

37. PRL 106, 166807, 2011 ns~ 10 14 cm -2 xz, yz orbitals extend deeper inside the bulk

38. B Rashba = ( ExP ) xy band is isotropic in xy plane Model xz,yz bands as 1D, xz is // current At Γ point, Exz~E F ; Exy<<E F  /  = - 1/8 (  /E F ) 2

39. B=7T Courtesy A. Fête

41. A. Caviglia et al PRL 104, 126803 (2010)