FROM STRANGE INSULATOR TO SPIN-ORBIT
CONDUCTOR: UNVEILING ORBITALSELECTIVENESS AT THE LAO-STO INTERFACE.
M. Gabay
Intensive course by A. Millis: OXIDE INTERFACES,
April 4th, 2012
Ecole Polytechnique
A. Santander-Syro
M. Rozenberg
A. Barthélémy, M. Bibes
Jean-Marc Triscone
 Andrea Caviglia
 Stefano Gariglio
 Nicolas Reyren
A. Fête
The Band story
From diffusion to reconstruction…to confusion
Band inversion (t2g 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
Conduction depends on
 Nature of the layers in contact (SrO/AlO2 vs LaO/TiO2)
 Oxygen pressure
 Mobility
 Temperature
 # of LAO layers
A 2DEG can also be produced at the surface of pure STO
A.F. Santander-Syro. Et al,
Nature 469, 189, 2011
Nature Materials 7, 855 858 (2008)
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
Horizontal scale: use conductivity
at given T, to compare phase
diagrams from different samples
SO metal
A few oddities revealed by transport measurements
in LAO/STO heterostructures

A strange insulator regime

A weird quantum critical point

A dumbfounding parallel magnetotransport
Y=| Y |eif
 For the electronic states Rs=h/e2
 For the Cooper pair state Rs=h/4e2
Ioffe-Regel criterion for localization: kFl~1
In fact localization at T=0 in 2D even if kFl>>1
d (~2-7nm)
 Drude part  d < l (~ 5nm)
 Weak localization part  d < Lin, Lso, Lh (~50 nm)
 Interaction part  d <(D(ħ/kBT))1/2
From measurements of Rsheet, n2D and MR
Courtesy of A. Caviglia
1.12≤kFl ≤4 as T varies from1.5K to 20K
Courtesy A. Caviglia
In the strongly underdoped regime kFl~1
The Band story
Band inversion (t2g 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
Band inversion (t2g 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
Band inversion (t2g 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
STO
LAO
z
et al, Nature 469, 189, 2011
xz, yz orbitals
extend deeper
inside the bulk
The Band story
Band inversion (t2g 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
Courtesy of A. Caviglia
Appl. Phys. Lett 94, 222111 (2009)
pO2=10-5 mbar
10 uc
pO2=10-3 mbar
10 uc
Phys. Rev. Lett. 107, 056802 (2011)
pO2=8 10-5 mbar
Tc=0.12K
The Band story
Band inversion (t2g 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
pO2=1.33 10-5 mbar
10 uc
Phys. Rev. Lett. 103, 226802 (2009)
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
WL correction to conductivity in the diffusive regime
A large spin-orbit effect is uncovered
T=1.5K
Bin =F0/4pD in
Bel =F0/4pD 
BSO =F0/4pD SO
Perpendicular magnetoconductance for different gate voltages
A. Caviglia et al PRL 104, 126803 (2010)
Rashba spin-orbit coupling
H=( ExP ).s
1/SO
SO
=W2

ħWSO = ESO~ 2EkF
m* =( h2/E)√ BSO/F0
s(Drude)=s-Ds (WAL)-Ds(e-e)-Ds(Super)  
m*max ~2.2me
ns~ 1014cm-2
xz, yz orbitals
extend deeper
inside the bulk
PRL 106, 166807, 2011
BRashba=( ExP )
xy band is isotropic in xy plane
Model xz,yz bands as 1D,
xz is // current
s/s = - 1/8 (/EF)2
At Γ point, Exz~EF; Exy<<EF
Courtesy
A. Fête
B=7T
A. Caviglia et al PRL 104, 126803 (2010)