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

A. Brinkman et al., Nat. Mater. 6, 493-496 (2007) D. A. Dikin et al., Phys. Rev. Lett. 107, 056802 (2011) Ariando et al., Nat. Commun. 2, 188 (2011) L. Li et al. Nature Physics 7, 762 (2011) J.A. Bert et al.Nature Physics 7, 767 (2011) N. Pavlenko et al. Phys. Rev. B 85, 020407 (2012)

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)