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Interfacial effects and superconductivityin oxide heterostructures
Jean-Marc Triscone University of Geneva
The LaAlO3/SrTiO3 interface
SrO
TiO2
LaO
AlO2
(001)
……
LaAlO3:
band insulator
SrTiO3:
band insulator
quantum paraelectric
Nature 427, 423 (2004)
..............................................................
A high-mobility electron gas at
the LaAlO3/SrTiO3 heterointerface
A. Ohtomo1,2,3 & H. Y. Hwang1,3,4
µ ∼ 1000 cm2/Vs
A conducting interface
Superconductivity at low T
SrO
TiO2
LaO
AlO2
(001)
……
Science 317, 1196 (2007)
200 300 400 500 600
0
100
200
300
400
500
Rsheet(Ω
/)
T (mK)
Superconducting Interfaces BetweenInsulating OxidesN. Reyren,1 S. Thiel,2 A. D. Caviglia,1 L. Fitting Kourkoutis,3 G. Hammerl,2 C. Richter,2
C. W. Schneider,2 T. Kopp,2 A.-S. Rüetschi,1 D. Jaccard,1 M. Gabay,4 D. A. Muller,3
J.-M. Triscone,1 J. Mannhart2*
Magnetism
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H φ
(a) (b)
LaAlO3
Sample 1 5 u.c. LaAlO3 on SrTiO3
SrTiO3
Ag back gate
Nb ohmic contact
Sample 2 0 u.c. LaAlO3 on SrTiO3
SrTiO3
Ag back gate
Nb ohmic contact
(c) (d)
µ0H ( T ) µ0H ( T )
m
Li et al. Bert et al. Brinkman et al.
Temperature (K)
Rs(k
Ω p
er
)
01 10 100
50
100
150
1
1
2
2
3
3
4
4
–1.0 –0.5 00
5
10
15
0.5 1.0
V (V)
dV
/dI (
kΩ)
b
c
(AlO2)–
(LaO)+
(AlO2)–
(LaO)+
(TiO2)0
(SrO)0
(TiO2)0
(SrO)0
e–/2
e–/2
R. Yamamoto et al. PRL 107, 036104 (2011)
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SrO
TiO2
LaO
AlO2
(001)
……
A new field of research
21 DECEMBER 2007 VOL 318 SCIENCE www.sciencemag.org
Published by AAAS
Breakthrough of the Year
BEYOND SILICON? Sixty years ago, semiconduc-
tors were a scientific curiosity. Then researchers tried putting
one type of semiconductor up against another, and suddenly
we had diodes, transistors, microprocessors, and the whole electronic
age. Startling results this year may herald a similar burst of discoveries at
the interfaces of a different class of materials: transition metal oxides.
Transition metal oxides first made headlines in 1986 with the Nobel
Prize–winning discovery of high-temperature superconductors. Since
then, solid-state physicists keep finding unexpected properties in these
materials—including colossal magnetoresistance, in which small
changes in applied magnetic fields cause huge changes in electrical
resistance. But the fun should really start when one oxide rubs shoulders
with another.
If different oxide crystals are grown in layers with sharp interfaces,
the effect of one crystal struc-
ture on another can shift the
positions of atoms at the inter-
face, alter the population of
electrons, and even change how
5
Tunable sandwich. In lanthanumaluminate sandwiched between layers of strontium titanate, a thickmiddle layer (right) produces conduction at the lower interface; a thin one does not.
S. Stemmer Y. Iwasa J. Lesueur G. Logvenov D. Pavuna …
Gennadi
The LaAlO3/SrTiO3 system - Outline
Why oxide interfaces?
Origin of the conductivity capping experiments
FE control of the electronic properties
Superconductivity the role of shape resonances
two gap superconductivity
Recent developments
AFD order
Superconducting
Ferroelectric
BaTiO3
PbTiO3
Ferromagnetic
Orbital order
CaTiO3
SrTiO3
Conducting
Insulating
+
–
+
–
+
–
+
–
Sr1–xLaxTiO3
La1–xSrxMnO3
Nd1–xSrxMnO3
Mn3+ Mn4+O2–
ABO3
O
B
A
P. Zubko et al., Ann. Rev. Cond. Matter Phys. 2, 141 (2011)
Perovskite Structure
Oxides display a variety electronic properties
Complex phase diagrams
Manganites
Cuprates
Y. Tokura, Rep. Prog. Phys. 69, 797 (2006)
P. Phillips, Nature Phys. 6, 931 (2010)
Like Lego bricks
SrTiO3 paraelectric at all temperatures (a=b=c=3.905Å)
PbTiO3 ferroelectric T<TC Tetragonal and ferroelectric (a=b=3.904Å, c=4.152Å)
La
Al
Sr
Ti
O
It is possible today to assemble these perovskite materials with atomic layer control in heterotructures
Atomic construction
Dave Muller, Cornell
Oxide heterostructures
Epitaxial Growth of Functional Compounds
D.G. Schlom et al. (2001)A.K. Gutakovskii et al. (1995)
La
Al
Sr
Ti
O
It is possible today to assemble these perovskite materials with atomic layer control in heterotructures
Atomic construction
Dave Muller, Cornell
Oxide interface physics
Tsukazaki et al. Science 315, 1388 (2007) Ohtomo and Hwang Nature 427, 423 (2004)
Haeni et al. Nature 430, 758 (2004)
Tokura and Nagaosa Science 288, 462 (2000)
DyScO3/SrTiO3
LaAlO3/SrTiO3
LaAlO3/SrTiO3
ZnO/(Mg,Zn)O
PbTiO3/SrTiO3Bousquet et al. Nature 452, 732 (2008)
Caviglia et al. PRL 104, 126803 (2010)
Charge Orbital
Lattice
Spin
Strain
Frustration
Charge transfer
Symmetry
breaking
Electrostatic
coupling
–
+
–
Interface physics in complex oxide heterostructures
P. Zubko et al., Annual Review of Condensed Matter Physics 2, 141 (2011)
The LaAlO3/SrTiO3 system
Andrea Caviglia(now in Delft)
ClaudiaCancellieri
(now at EMPA)
Nicolas Reyren(CNRS Paris)
Daniela Stornaiuolo
(now in Naples)
in collaboration with
The «Geneva» LaAlO3/SrTiO3 Team
Stefano Gariglio Denver Li Alexandre Fête Margherita Boselli
•Marc Gabay
University of Paris-Sud
•Jochen Mannhart
MPI Stuttgart
Zhenping Wu
Davide Valentinis, Christophe Berthod, Dirk van der Marel
LaAlO3 epitaxial growth by PLD
Layer-by-layer growth T = 720, 800, 890°C
P O2 = 1·10-4 Torr Fluence = 0.6 J/cm2
Frequency = 1Hz Post annealing @ 200 mbar O2
16 18 20 22 24 26 28 30
!""#$
%
&'(
Inte
nsity (
a.u
.)
)!% !*$
+,(
)-./
)"./
#0./
##./
1./
0./
SrTiO3
Substrate
(001)
L. Fitting-Kourkoutis, D.A. Muller (Cornell)
The polar catastrophe scenario
SrO0
SrO0
LaO+
AlO2
-
LaO+
AlO2
-
TiO2
0
TiO2
0
LaAlO 3
SrTiO
3
0
0
0
0
+1
-1
+1
-1
The polar catastrophe scenario
0000
1+1-1+1-
SrO0
TiO20
ρ
SrO0
TiO20
LaO+
AlO2-
LaO+
AlO2-
VE
N. Nakagawa et al., Nature Materials (2006).
GaAs/Ge W.A. Harisson et al. PRB 18, 4402 (1978).
00
0
0
1+1-
1+1-
ρ V
SrO0
TiO20
LaO+
AlO2-
LaO+
AlO2-
SrO0
TiO20
0.5+
0.5-
3 1014 e/cm2
Chemical Doping
J. Mannhart, D.G. Schlom, Nature N&V 430, 620 (2004)
SrTiO3
SrTiO3-x
Nat. mater. 5, 204 (2006)
La/Sr intermixing
P.R. Willmott et al. PRL 99, 155502 (2007) A.S. Kalabukhov et al. PRL 103, 146101 (2009)
n-type
Fraction
0
0
0.2
0.4
0.6
0.8
1.0
0.1
Ti
Ti3+
La
Residual
Why some interfaces cannot be sharp
NAOYUKI NAKAGAWA1,2, HAROLD Y. HWANG1,2 AND DAVID A. MULLER3*1Department of Advanced Materials Science, University of Tokyo, Kashiwa, Chiba 277-8561, Japan2Japan Science and Technology Agency, Kawaguchi 332-0012, Japan3School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14583, USA
*e-mail: davidm@ccmr.cornell.edu
Infinite parallel plate capacitors:
E= σ/εr ε0
+
-E
Intermixing and / or oxygen vacancies do not bring net charges - does not help solving the polar catastrophe problem.
Bringing net charges on one side would make the system even more unstable.
Only solution is a charge transfer from the top LAO surface to the interface.
Testing the polar catastrophe scenarioBreakdown
STO LAO
"E
E=(σ0 / εr ε0) dc = Vc/E
with Vc=3.35 V, σ0 = 3 1014 e/cm2 and εr =25, dc = 3.5 u.c.
See also R. Pentcheva and W. Pickett PRL 102, 107602 (2007)
Ec
Ev
Eg(STO)
= 3.2 eV
STO LAO
Eg(LAO)
= 5.6 eV
VBO=
0.15 eV
Previous
!E=
3.35 eV
dLAO
LaAlO3 critical thickness
S. Thiel et al. Science 313, 1942 (2006)
Replacing LAO by (LAO)x(STO)1-x
TiO2
TiO2
SrO
SrO
(La,Sr)O
(Al,Ti)O2
-1/2
+1/2
0000
(001)
(La,Sr)O
(La,Sr)O(Al,Ti)O2
(Al,Ti)O2
-1/2
-1/2+1/2
+1/2
εr’ ≈ εr ⇒ E’=E/2 ⇒ dc’=2dc
σ0’ = σ0 /2
10-9
10-8
10-7
10-6
10-5
10-4
Conducta
nce [
1]
0 5 10
Film thickness [u.c.]
10-9
10-8
10-7
10-6
10-5
10-4
Sheet conducta
nce [
-1/ ]
Set 1
Set 2
10-8
10-7
10-6
10-5
Conducta
nce [
-1]
10-9
10-8
10-7
10-6
10-5
10-4
10-9
10-8
10-7
10-6
10-5
10-4
Conducta
nce [
-1]
10-9
10-8
10-7
10-6
10-5
10-4
Sheet conducta
nce [
-1/ ]
10-9
10-8
10-7
10-6
10-5
10-4
x = 1.0
x = 0.75
x = 0.50
LaAlO3
x=0.75
x=0.5
x=1
M.L. Reinle-Schmitt et al. Nat. Com. 3, 932 (2012)
with PSI and Liège
Oxygen vacancy formation at the LAO surface
N. C. Bristowe et al., Phys. Rev. B 83, 205405 (2011)
N. C. Bristowe et al., J. Phys.: Condens. Matter 26 143201 (2014)
See also, Liping Yu and Alex Zunger Nat. Com. 2015
J. Zhou et al. Singapore, UBC
M. Basletic et al, Nat. Mater. 7, 621 (2008)
O. Copie et al, Physical Review Letters. 102, 216804 (2009)
12 nm at low T
RT d<7nm
A. Dubroka et al, PRL 104, 156807 (2010)
11 nm at 10K
Confinement and electronic structure
Thickness of the superconducting layer
100mT
H⫽
H⟘
Science 317, 1196 (2007)
2D superconductivity
µ0H‖(T ) =
√
3Φ0
πdξ‖(T )
µ0H⊥(T ) =Φ0
2πξ2
(T )
ξ‖(T = 0) ∼ 60 nm
d ≈ 10 nm
N. Reyren et al. APL 94, 112506 (2009)
The electrons are in the Ti 3d band - in t2g «orbitals»
M.Basle)cetal,Nat.Mater.7,621(2008)
12 nm at low TRT d<7nm
Confinement and electronic structure
Crystalfieldsplitting
The electrons are in the Ti 3d band - in t2g «orbitals»
M.Basle)cetal,Nat.Mater.7,621(2008)
12 nm at low TRT d<7nm
M. Salluzzo et al., PRL 102, 166804 (2009)
Son et al., PRB 79, 245411 E
ne
rgy (
eV
)
L Γ X
xy0xy1
xy2
xziyzi
xy3
LAOSTOT
iO2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
AlO
2
Delugas et al., PRL 106, 166807 (2011)
ns=3.3 10 14 cm-2
Confinement and electronic structure
Issues: Thickness measurements at low T and RT
What is the thickness probed? Modelization with limited cell size Dielectric constant in 0K calculations is
« low »
En
erg
y (
eV
)
L Γ X
xy0xy1
xy2
xziyzi
xy3
LAOSTO
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
AlO
2
Transport and FE control
TiO2-plane
Ti O3.9 Å
~2-8×1013/cm2
mobilities 100-1000 cm2/Vs
200 300 400 500 600
0
100
200
300
400
500
Rsh
ee
t(Ω
/)
T (mK)
SrO
TiO2
LaO
AlO2
(001)
……
VG,b
VSIS VD ID
SrTiO3
-0.5 0.0 0.5 1.0 1.5
0.01
0.1
1
10
σ (
mS
)
Vside gate
(V)
Side gating
VG,t
Transport and field effect control
SrTiO3
LaAlO3
2DEL
Vg
Decreasing n2d
A superconducting switch
A.D. Caviglia et al. Nature 456, 624 (2008)
Modulation of SC
50 100 150 200 250 300 350 4001x101
1x102
1x103
1x104R
sh
ee
t(Ω
/)
T (mK)
320 V
- 300 V
RQ
A
50 150 250 3500
5
10
15
20
RQ
Rsh
ee
t (kΩ
/)
T (mK)
B
A.D. Caviglia et al, Nature 456, 625 (2008)
See also C. Bell et al. PRL 103, 226802 (2009).
System phase diagram
S. Gariglio et al. APL Mat. 4, 060701 (2016)
See also C. Bell et al. PRL 103, 226802 (2009)
In LaTiO3/SrTiO3 J. Biscaras et al. PRL 108, 247004 (2012)
The electrons are in the Ti 3d band - in t2g «orbitals»
M.Basle)cetal,Nat.Mater.7,621(2008)
12 nm at low TRT d<7nm
M. Salluzzo et al., PRL 102, 166804 (2009)
Son et al., PRB 79, 245411 E
ne
rgy (
eV
)
L Γ X
xy0xy1
xy2
xziyzi
xy3
LAOSTOT
iO2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
TiO
2
AlO
2
Delugas et al., PRL 106, 166807 (2011)
ns=3.3 10 14 cm-2
Confinement and electronic structure
Hall response and parallel field measurements
0 2 4 6 8 10 12 14
-600
-500
-400
-300
-200
-100
0
B (T)
Rxy (Ω
)
b
Vg<0
Vg>0
0.1 1 10
0
0.1
0.2
0.3
0.4
0.5
0.6
σ2D (mS)
[R' x
y (B
*)-R
' xy (0
T)]
/R' x
y (0
T)
d
B* = 7 T
B* = 14 T
0
0.985
0.99
0.995
1
σ (m
S)
2D
Exp.7T
5.25T
3.5T
1.75T
a)
0 50 100 150 200 250 300
ϕ (°)
0.985
0.99
0.995
1
σ (m
S)
2D
Theory
7T
5.5T
3.5T
1.75T
c)1.004
(mS
) Experiment
2
2.02
2.04
σ (m
S)
2D
Exp.7T
5.25T
3.5T
1.75T
b)
0 50 100 150 200 250 300
ϕ (°)
2
2.02
2.04
2.06σ
(m
S)
2D
Theory
7T
5.5T
3.5T
1.75T
d)
2.06
(mS
) Experiment
Bulk and Interface Superconductivity
Superconductivity in bulk SrTiO3
PHYSI CAL RE VIEW VOLUME 163, NUMBER 2 10 N OVRMB R R 196'l
Suyerconducting Transition Temperatures ofSemiconducting SrTiOs
C. S. KOONCE* AND MAEVIN L. COHEN)
Department of Physics, University of California, Berkeley, California
J. F. SCHOOLEY, f. W. R. HOSLER, ct AND E. R. PZEIZEER1Vationa/ Bureau of Standards, Washington, D C. .
(Received 5 July 1967)
The superconducting transition temperature T, of SrTiO3 has been measured for specimens having elec-
tron carrier concentrations n. from 6.9X10" to 5.5&(10' cm '. The curve exhibits a maximum in T, forn, near 9)&10"cm '. The transition temperature has also been calculated using one adjustable parameter
(, the intervalley deformation potential, in addition to the known normal-state properties of SrTi03. A good6t to the experimental curve is obtained.
I. INTRODUCTION
FOLLOWING the application of the theory of super-
conductivity to the case of degenerate semiconduc-
tors and semimetals, ' superconductivity was observed
in the semiconducting compounds GeTe, ' SrTiQ3, ' andSnTe.4 A brief discussion of the variation of the super-
conducting transition temperature T, with electronic
carrier density e, for SrTi03 has been presented. ' Inthat paper we pointed out that the curve of T, versuse, for SrTiO3 contains a maximum value of T„al-though a rough application of the simple BCS expres-sion' T, eD expI—1/LN(0) V)I would predict a mon-
atonic dependence of lnT, on (n, )Its through the rela-
tion" N(0)~n, tt' We a.lso mentioned that the observed
dependence of T, on n, could be explained qualitatively
through the proper inclusion of screening of intervalley
and intravalley interactions. We now have found the
transition temperature at a larger number of concen-
trations in order to fix the curve T, versus m, more
accurately, and, in addition, we have performed quan-
titative calculations which show that the experimental
curve can be Q.tted quite closely using the measured
properties of the system in the normal state and both
intervalley and intravalley interactions.
*Present address: National Bureau of Standards, Washington,D.C. Supported in part by the National Science Foundation.
t A. P. Sloan Foundation Fellow. Supported in part by theNational Science Foundation.
f. Supported in part by the Advanced Research Projects Agency.) Supported in part by the National Aeronautics and Space
Agency.' M. L. Cohen, Phys. Rev. 134, A511 (1964).'R. A. Hein, J. W. Gibson, R. Mazelsky, R. C. Miller, and
J.K. Hulm, Phys. Rev. Letters 12, 320 (1964).3 J. F. Schooley, W. R. Hosier, and M. L. Cohen, Phys. Rev.
Letters 12, 474 (1.964) .' R. A. Hein, J.W. Gibson, R. S. Allgaier, B.B.Houston, Jr.,R. Mazelsky, and R. C. Miller, in Proceedings of the ninth Inter-national Conference on I.ow Temperature Physics, edited by J. G.Daunt, D. V. Edwards, F. J. Milford, and M. Yaqub (PlenumPress, Inc, , New York, 1965), p. 604.' J. F. Schooley, W. R. Hosier, E. Ambler, J. G. Becker, M. L.Cohen, and C. S. Koonce, Phys. Rev. Letters 14, 305 (1965).' J. Bardeen, L. N. Cooper, and R. SchrieGer, Phys. Rev. 108,
1175 (1957).7 See for example, Charles Kittel, Introduction to Solid State
Physics (John Wiley 8z Sons, Inc. , New York, 1956), 2nd ed, ,p. 250.
163
Strontium titanate has been found to have a super-conducting transition temperature greater than 0.05'Kfor electron concentrations in the conduction band be-
tween 8.5&(10' and 3.0&10 cm . This is the widestrange of charge carrier concentrations over which anysuperconductor has been shown to be superconduct-
ing. In addition, these concentrations represent the
lowest concentrations at which superconductivity has
been observed. s
Because superconductivity occurs at such low carrier
concentrations, we may assume a parabolic behavior
of the conduction band near the Fermi surface which
will be near the minima of the conduction band, and
use the normal-state properties of the material to cal-culate the superconducting properties. The values forthe normal-state properties used, along with references
to the experiments by which they were measured, are
given in Table I.Since the complete curve of superconducting transi-
tion temperature as a function of carrier concentrations
has been obtained, we can use the wealth of informa-
tion contained in this curve to test our knowledge of
the normal-state properties of SrTiQ3, and also to testthe theory of superconductivity. Since the deformation
potential for intervalley processes is not known for
SrTi03, a value for it will be taken which gives asuperconducting transition temperature near the ex-
perimental transition temperature at a given electronic
concentration. The same value of the deformation po-tential will then be used to calculate the transition
temperature at all concentrations. All other physical
properties entering into the calculations will be takenwithin the experimental uncertainty in their measure-
ment in the normal state. Since the transition tempera-
ture increases, reaches a maximum, and then decreases
vnth increasing concentration, a one-parameter fit tothe curve is quite demanding on the many norma]. —
state parameters. Any substantial variation in the
SAddition of a few percent BaTiO3 reduces the minimumcarrier concentration for superconductivity by more than anorder of magnitude thus increasing the superconducting rangeeven further. See J. F. Schooley, H. P. R. Frederikse, W. R.Hosier, and E.R. Pfeiffer, Phys. Rev. 159, 301 (1967).380
382 ROON C E, COHEN, S CHOOLE Y, HO SLER, AND P FEIF PER
TABLE II. Properties of SrTi03 specimens.
Specimen
HR5HR52 slab
TiR2bTiR10 slabHR51 slabHR22HR28 slabNb8 slabHR27c slab
TiR11 slabHR70 slabNb9 slabHR6 sphHR6 slabHR72 slab
HR3TiR19 slab
HR33 stressHR33 slabHR57
HR24 sphHR61 slab
TiR13 slabNbioHR73 slabHR74 slabTiR2c slabHR69 slab
HCR2
e, (4.2'K)(cm ')
6 9X10'87 6X]018('I.6X10")7.8X10j88 5X10'89.4X10"1.0X10»1.3X10»1.3X10»1.4X10»
1.5X10»1.66X10»1.89X10'(2.5X 10&9)d
2.5X10»2.7X10ia
3 1X10»4 9X10»
(6.3X10»)~6.3X10»6.7X10»(7.2X10»)(1.0X10")d1.1X10'o
i.2X10M1.5X1Q'o1.66X10so1 95X102o2.1X10so3.OX102o(4 OX1P0)5 5X10'o(5 5X1P')
p (4.2'K)(n cm)
3.8X10 4
2 7X10 4
3.6X10 4
3.4X10 4
4.2X10 4
2.8X10 4
2.4X10 4
9.0X10-52.9X10-4
3.2X10 4
3.3X10 4
7.5X10-5(2.3X10 4)2.3X10 4
2.6X10 4
4.0X10-42.6X10 4
(2.8X10 ')2.8X10 4
2 ~ 3X10 4
(2.8X10 4)
2 ~ 6X10 4
2, 4X10-46.1X10 5
2.2X10 4
2.3X10 4
2.6X10 4
2.1X10 4
1.7X10 4
& (4.2'K.)(cm'/V sec)
24403120
2280221016202280205054701580
133011704510(1110)1110912
516504
(364)364415
(280)224
222699175143117102
68
Measuredr. ('K)
&0,06(0 ~ 05) ~
&0.070.06—0.070.085&0.050.12Q. 090.057
0.070.1270.1830.1460.1660.213 o
0.2040.1660.273
0.2780.2730.275(0.290)$0.2680 280 o
0.2830.2850.410.1980.1200.2950.06(0 030)a&0.05(0 020) s
CalculatedT, ('K)
&0.070.07
0.07
0.09
0.10 b
0.10
0.14960.14770.15
0.170.25 b
0.26
0.260.300.30
0.260.21
0.150.120.040.010 ' 002
Transition temperatures assumed for purposes of the calculation.Double value indicates the range of purely computational uncertainty in the numerical calculation.
o Values found experimentally in two separate experiments.~ Normal-state properties measured on companion samples.
mens on which Hall and resistivity measurements had
been made and which thus required no further special
handling.
Table II contains a summary of normal-stat|'. and
superconductivity data for the specimens discussed in'this paper. Note that the mobility p of the Nb-doped
samples is 2 to 3 times larger than that of HR- orTiE;reduced specimens for a given carrier concentra-
tion, in spite of the fact that the Nb-doped samples
were polycrystalline. The degeneracy temperature foreven the most lightly reduced sample is near 3'K,assuming a "density-of-states" mass m&*=5m0.' Themobility also becomes constant with temperature atlow temperatures which, assuming impurity scattering,
suggests complete degeneracy.
B. T, Measurements and Results
T, Meuslrements
The temperature dependence of the magnetic sus-
ceptibility of each specimen was observed from about
'H. P. R. Frederikse, W. R. Hosier, and W. R. Thurber, J.Phys. Soc. Japan Suppl. 21, 32 (1966).
I I j I I I I I I I I I I III
Tc
0.2—
0.1—
~ Experimental
0 Theory ('I) 0 ~ ~g-o—d,
g+
e~S~go 0
~ Og
O~o f$
I I I
10
,a8- ~(~)
10 10
FIG. 2. Transition temperature as a function of carrier con-centration. The plain solid circles represent experimental data.The bracketed solid circles are fictitious data used as inputin the transition temperature calculation. The open circles showthe results of the calculation, and the smooth dashed curve wasdrawn for illustrative purposes.
0.05'K through T„using a mutual inductance appa-ratus operating at 270 Hz.A schematic drawing of the low-temperature portion
of the apparatus is shown in Fig. 3.For ease of handling,
Superconductivity in bulk SrTiO3
See also X. Lin et al. PRL 112, 207002 (2014)
Bulk and interface SC
Bulk and interface SC
n3D=n2D/d Virgin: n2D=3 1013 cm-2
d=10nm
Bulk and interface SC
Bulk and interface SC
Mapping the 2D phase diagram on the 3D one
n3D=n2D/d
Determination of the SC thickness
(b)
(a)
N. Reyren et al. APL 94, 112506 (2009) M. Ben Shalom et al. PRL 104, 126802 (2010)
0.1 1 100
20
40
60
80
100
0
100
200
300
400
500
σ2D (mS)t , ξ
// (
nm
)
Tc
50
% (
mK
)
Zoom bulk Tc
0.1 1 100
20
40
60
80
100
0
100
200
300
400
500
σ2D (mS)
t , ξ
// (
nm
)
Tc
50
% (
mK
)
The underdoped regime
0.1 1 100
20
40
60
80
100
0
100
200
300
400
500
σ2D (mS)
t , ξ
// (
nm
)
Tc
50
% (
mK
)
The « overdoped » regime
S. Gariglio et al. review
APL Mat. 4, 0601701 (2016)
-200 -100 0 100 200
2
3
4
5
6
T = 0.03 K
dI/d
V (
µS
)
V (µV)
-300 V
-200 V
-100 V
0 V
-50 V
50 V
100 V
VG = 300 V
200 Va
c
b
0
25
50
75
100
∆/Γ
Tc
Γ
∆ (
µe
V)
∆
-400 -200 0 200 4000
50
100
150
Γ (
µe
V)
VG (V)
0
1
2
∆/Γ
0
100
200
300
400
500
Tc (
mK
)
C. Richter et al. Nature 502, 528 (2013)
Unconventional SC?
Tc from tunneling
S. Gariglio et al. review
APL Mat. 4, 0601701 (2016)
Breaking of inversion symmetry and spin orbit coupling
M.Basle)cetal,Nat.Mater.7,621(2008)
12 nm at low TRT d<7nm
Son et al., PRB 79, 245411
SrTiO3 LaAlO3
Next talk by Andrea Caviglia
-4 -2 0 2 4-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
Δσ
/(e
2/π
h)
μ0H (T)
-300 V
-100 V
-50 V
0 V
+50 V
+100 V
-4 -2 0 2 4
-1
-0.5
0
0.5
1
Δσ
/(e
2/π
h)
μ0H (T)
-300 V
-100 V
-50 V
0 V
+50 V
+100 V
LAOSTO
T=1.5K
A.D. Caviglia et al., Phys. Rev. Lett. 104, 126803 (2010)
Weak localization to weak antilocalization
Weak localization
Strong spin-orbit interaction
Weak anti-localization
100 -300 -200 -100 0 1000
2
4
6
8
10
1
2
3
4
5
" (1
0-1
2 eV
m)
V (V)
# (
meV
)
c
2 -300 -200 -100 0 1000
100
200
300
Tc (m
K)
V (V)
SC
d
∆ = 2αkF
α =~
m
r
~eHso
2
Very large tunable spin-orbit coupling
Δ=10meV is much larger than the SC
gap (~40µeV)
« Recent » results Exciting developments
High mobility samples
Layer-by-layer growth T = 650°C
P O2 = 1·10-4 Torr Fluence = 0.6 J/cm2
Frequency = 1Hz Post annealing @ 200 mbar O2
Low sheet carrier density Mobilities up to 8000 cm2/Vs
ωcτ = µB >> 1
~ωc = ~eB/m > kBT
High mobility samples
0 2 4 6 8
B (T)
200
220
240
260
280
300
320
Rsh
ee
t (Ω
/sq
)
800mK
50mK
5.23mS
500mK
A. Fête et al. New Journal of Physics 16, 112002 (2014)
Y. Xie et al. Solid State Com. 197, 25 (2014)
SdH at low temperature
0 2 4 6 8
B (T)
200
220
240
260
280
300
320
Rsh
ee
t (Ω
/sq
)
800mK
50mK
5.23mS
500mK
0 2 4 6 80
0.1
0.2
0.3
0.4
0.5
0.6
0.7
B (T)
MR
5.27mS
1.6mS
50mK
Oscillations periodic in 1/B Oscillations depend only on the perpendicular component of the field - the system is 2D
m*= 2.13me
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
Δσ
(m
S)
× e
5/B
5.27mS
50mK
Experiment
1 band + Rashba+
Zeeman theory
a)
0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-8
-6
-4
-2
0
2
4
6
8
10
∂Δσ
/∂B
-1 (
mS
T
) ×
e5/B
1/B (1/T)
5.27mS
50mK
m*= 2.25me
b)
0.203 0.208 0.213 0.218
-0.002
0
0.002
0.004
0.006
0.008
0.01
1/B (1/T)
Δσ
(m
S)
5.23mS 50mK
800mK
c)
0.22 0.225 0.23 0.235 0.24
-0.008
-0.006
-0.004
-0.002
0
0.002
1/B (1/T)
Δσ
(m
S)
5.23mS 50mK
800mK
n2D = 1.825 (1012/cm2)
α = 3.4 (10-12eV/m)
g* = 5.2 or -3.4
Γ+
= 0.065 √B (meV)
Γ-
= 0.095 √B (meV)
One band including Rashba and Zeeman
α=3.4 10-12 eV/m
m*=2.19
Other substrates - multilayersARTICLE
Received 12 Jul 2010 | Accepted 22 Sep 2010 | Published 19 Oct 2010 DOI: 10.1038/ncomms1096
Creation of a two-dimensional electron gas at an oxide interface on siliconJ.W. Park1, D.F. Bogorin2, C. Cen2, D.A. Felker3, Y. Zhang4, C.T. Nelson4, C.W. Bark1, C.M. Folkman1,
X.Q. Pan4, M.S. Rzchowski3, J. Levy2 & C.B. Eom1
t
ed
e
,
101
102
103
104
105
Temperature (K)
1012
1013
1014
1015
Ca
rrie
r co
nce
ntr
atio
n (
cm
–2)
Temperature (K)
100
101
102
103
104
Mo
bili
ty (
cm
2 V
–1s
–1)
Temperature (K)
104
105
106
107
108
109
1010
LAO thickness (uc)
Measurement limit
Sh
ee
t re
sis
tan
ce
( –
1)
Sh
ee
t re
sis
tan
ce
( –
1)
10 100 10 100
10 100 0 2 4 6 8 10 12 14 16
C.B. Eom, Madison
Writing nanoscale electronic circuits
C. Cen et al, Nat. Mater. 7, 298 (2008) C. Cen et al. Science 323, 1026 (2009)
Jeremy Levy in Pittsburgh
Geneva data
DOI: 10.1126/science.1168294 , 1026 (2009); 323Science
et al.Cheng Cen,Oxide Nanoelectronics on Demand
The following resources related to this article are available online at
Fig. 2. SketchFET device.(A) Schematic diagramof SketchFET structure.S, source electrode; D,drain electrode; G, gateelectrode. (B) I-V char-acteristic between sourceand drain for differentgate biases VGD = –4 V,–2 V, 0 V, 2 V, and 4 V.(C) Intensity plot of ID(VSD, VGD).
–0.4
0
0.4
V2
3 (m
V)
100
50
0
dI/d
V (μ
S)
–50 –40 –30 –20 –10 0 10
Vsg (mV)
–0.5
0
0.5
V34 (m
V)
1
2
3
4 5
LaAlO3
SrTiO3
1 μm
a b
c
Side gate
Barrier
QD
Device schematic and transport characteristics. a, Device barrier to sense leads. b, Device A dI/dV characteristics (colou
Pairing without superconductivity
LETTERdoi:10.1038/nature14398
Electron pairing without superconductivityGuanglei Cheng1,2, Michelle Tomczyk1,2, Shicheng Lu1,2, Joshua P. Veazey1, Mengchen Huang1,2, Patrick Irvin1,2, Sangwoo Ryu3,Hyungwoo Lee3, Chang-Beom Eom3, C. Stephen Hellberg4 & Jeremy Levy1,2 Nature 2015
Localized states probed using thermopower
Ilaria Pallecchi et al.Nature Com. 6, 7668 (2015)
Injection of spin polarized electrons
(b)(a)
H
VI
M W
d
L
H
Vg
+ -
0
(b)
-0.4 -0.2 0.0 0.2 0.48.028
8.030
8.032
8.034
RA
Ω
0 ⊥ (T)
= 2 K
= 50 nA
≈ 0.13 V
0
50
100
∆V
(d)
Hanle measurements
N. Reyren et al. Phys. Rev. Lett. 108, 186802 (2012)
Texte
CNRS/Thales, Paris
LETTERSPUBLISHED ONLINE: 7 DECEMBER 2015 | DOI: 10.1038/NMAT4491
Tunable spin polarization and superconductivity inengineered oxide interfaces
D. Stornaiuolo1,2*, C. Cantoni3, G. M. De Luca1,2, R. Di Capua1,2, E. Di. Gennaro1,2, G. Ghiringhelli4,
B. Jouault5, D. Marrè6, D. Massarotti1,2, F. Miletto Granozio2, I. Pallecchi6, C. Piamonteze7, S. Rusponi8,
F. Tafuri2,9 and M. Salluzzo2*
T (K)
1
1 10 100
−25 V
−35 V
−50 V
−60 V
2
3
4
5
Rsq
(kΩ
/
)
b
c
Nature Materials 15, 278 (2016)
LaO
TiO2
EuOTiO2
La Ti
Eu
a
Rxy
(Ω
)A
N0
−30 0
Vg (V)
Vg = +32 V
T (K)
30 5 10 15 20
5
10
b c
Kondo nc FM (below nc, no xz,yz)
EuTiO3 - ferro below 7-8K
A spin-polarized 2DELNaples group
http://www.sc.doe.gov/bes/reports/abstracts.html#GC
A. Ohtomo et al. Nature 419, 378 (2002)
Other conducting oxide interfaces
0.0 0.1 0.2 0.3 0.40
1
2
3
150V
-70V
-10V
-200V
-150V
0V10V
30V20V
40V
60V100V
RS
(kΩ
/)
T (K)
200V
b
-200 -150 -100 -50 0 50 100 150 2000
1
2
3
Rs
RS
(kΩ
/)
VG
(V)
c
0.00
0.05
0.10
0.15
0.20
TC
TC
(K)
0.0 0.4 0.8 1.2 1.6 2.0 2.4R
S(kΩ/ )
-50 0 50 100 150 200
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
T(K
)
VG
(V)
INS
UL
AT
OR
SUPERCONDUCTOR
a
Tc
NATURE COMMUNICATIONS | ARTICLE
Two-dimensional superconductivity at a Mott insulator/bandinsulator interface LaTiO /SrTiO
J. Biscaras, N. Bergeal, A. Kushwaha, T. Wolf, A. Rastogi, R.C. Budhani & J. Lesueur
Nature Communications 1, Article number: 89 doi:10.1038/ncomms1084
Received 29 July 2010 Accepted 06 September 2010 Published 05 October 2010
Abstract
3 3
Jérôme Lesueur, ESPCI
P. Moetakef et al., APL 99, 232116 (2011)
Charge transfer with expected number of carriers + heterostructure with scalable carrier density
P. Moetakef et al., APL 101, 151604 (2012)
2D SdH oscillations
S. Raghavan et al., APL 103, 212103 (2013)
Tunneling between 2 STO/GTO quantum wells reveals their subband structure
C. A. Jackson, PRB 88, 180403 (2013)
Interface induced magnetism is revealed by magnetotransport in ultra-thin STO layers
embedded in GTO
Other conducting oxide interfaces
GdTiO3/SrTiO3 S. Stemmer Santa Barbara
A new oxide electronics?
1947 Bell Labs 2009 UNIGE
2009-2014 - a million transistors
0 2 4 6
0.0
0.4
0.8
VGS
=0.9 V
VGS
=0 V
I D(m
A)
VDS
(V)
R. Jany et al.
J. Mannhart - MPI Stuttgart
J. Mannhart, and D. G. Schlom, Science 327, 1607 (2010)
P. Zubko, S. Gariglio, M. Gabay, P. Ghosez, and J.-M. Triscone, Annu. Rev. Condens. Matter Phys. 2, 141 (2011)
H. Y. Hwang, Y. Iwasa, M. Kawasaki, B. Keimer, N. Nagaosa, and Y. Tokura, Nature Materials 11, 103 (2012)
Charge Orbital
Lattice
Spin
Strain
Frustration
Charge transfer
Symmetry
breaking
Electrostatic
coupling
–
+
–
Reviews
S. Gariglio, M. Gabay, and J.-M. Triscone, APL Materials 4, 060701 (2016)
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