Jean-Marc Triscone - University of Geneva

Electric Field Control of the Electronic Properties of the Interfacial LaAlO3/SrTiO3 System

SrO

TiO2

LaO

AlO2

(001)

……

LaAlO3:

band insulator

SrTiO3:

band insulator

quantum paraelectricSTEM by L. Fitting-Kourkoutis, D.A. Muller (Cornell)

SrO

TiO2

LaO

AlO2

(001)

……

Nature 427, 423 (2004)

..............................................................

A high-mobility electron gas atthe LaAlO3/SrTiO3 heterointerfaceA. Ohtomo1,2,3 & H. Y. Hwang1,3,4

1Bell Laboratories, Lucent Technologies, Murray Hill, New Jersey 07974, USA2Institute for Materials Research, Tohoku University, Sendai, 980-8577, Japan3Japan Science and Technology Agency, Kawaguchi, 332-0012, Japan4Department of Advanced Materials Science, University of Tokyo, Kashiwa,Chiba, 277-8651, Japan.............................................................................................................................................................................

Polarity discontinuities at the interfaces between different crys-talline materials (heterointerfaces) can lead to nontrivial localatomic and electronic structure, owing to the presence of dan-gling bonds and incomplete atomic coordinations1–3. These dis-continuities often arise in naturally layered oxide structures,such as the superconducting copper oxides and ferroelectrictitanates, as well as in artificial thin film oxide heterostructuressuch as manganite tunnel junctions4–6. If polarity discontinuitiescan be atomically controlled, unusual charge states that areinaccessible in bulk materials could be realized. Here we haveexamined a model interface between two insulating perovskiteoxides—LaAlO3 and SrTiO3—in which we control the termin-ation layer at the interface on an atomic scale. In the simple ionic

limit, this interface presents an extra half electron or hole pertwo-dimensional unit cell, depending on the structure of theinterface. The hole-doped interface is found to be insulating,whereas the electron-doped interface is conducting, with ex-tremely high carrier mobility exceeding 10,000 cm2V21 s21. Atlow temperature, dramatic magnetoresistance oscillations peri-odic with the inverse magnetic field are observed, indicatingquantum transport. These results present a broad opportunity totailor low-dimensional charge states by atomically engineeredoxide heteroepitaxy.An early discussion of polarity or valence discontinuities arose in

the consideration of the growth of GaAs on (001)-oriented Ge1,2.Both semiconductors have the same crystal structure and nearlyexact lattice match, thus representing promising materials tocombine direct and indirect bandgap semiconductor functions.Just at the interface, however, there are incomplete bonds at thetermination of the group IV Ge layer and the commencement ofIII–V alternations of GaAs. There have been recent attempts todesign interfaces on the atomic scale to compensate for thesedangling bonds7. Layered oxide crystal structures can be viewed asan intimate sequence of valence discontinuities, often involvingcharge-transfer over a few atomic positions. The myriad of stackingsequences such as the perovskite-derived Ruddlesden–Popperphases, constructed as An!1BnO3n!1, for 0 # n # 1, involveaccommodating this charge transfer while maintaining globalcharge neutrality8,9. Recently, lamellar contacts between members

Figure 1 Growth and schematic models of the two possible interfaces between LaAlO3and SrTiO3 in the (001) orientation. a, RHEED intensity oscillations of the specular

reflected beam for the growth of LaAlO3 directly on the TiO2 terminated SrTiO3 (001)

surface. b, Schematic of the resulting (LaO)!/(TiO2)0 interface, showing the composition

of each layer and the ionic charge state of each layer. c, RHEED oscillations for the growthof LaAlO3, after a monolayer of SrO was deposited on the TiO2 surface. d, Schematic ofthe resulting (AlO2)

2/(SrO)0 interface.

letters to nature

NATURE |VOL 427 | 29 JANUARY 2004 | www.nature.com/nature 423© 2004 Nature Publishing Group

µ � 1000 cm2/Vs

2D Electron Gas

SrO

TiO2

LaO

AlO2

(001)

……

A. Ohtomo, H. Hwang, Nature 427, 423 (2004)S. Okamoto, A.J. Millis, Nature 428, 630 (2004)

S. Thiel et al., Science 313, 1942 (2006)N. Nakagawa et al., Nature Materials 5, 204 (2006)

M. Huijben et al., Nature Materials 5, 556 (2006)C.W. Schneider, APL 89, 122101 (2006)

A. Brinkman et al., Nature Materials 6, 493 (2007)G. Herranz et al., PRL 98, 216803 (2007)W. Siemons et al., PRL 98, 196802 (2007)P.R. Willmott et al., PRL 99, 155502 (2007)

A. Kalabukov et al., PRB 75, 121404(R) (2007)Z. Popovic et al., PRL 101, 256801 (2008)

M. Basletic et al., Nature Materials 7, 621 (2008)C. Cen et al., Nature Materials 7, 298 (2008)

S. Thiel et al., PRL 102, 046809 (2009)R. Pentchevaet al., PRL 102, 107602 (2009)M. Salluzzo et al., PRL 102, 166804 (2009)

O. Copie et al., PRL 102, 216804 (2009)M. Sing et al., PRL 102, 176805 (2009)

C. Bell et al., APL 94, 222111 (2009)C. Bell et al., PRL 103, 226802 (2009)

C. Cen et al., Science 323, 1026 (2009)C.L. Jia et al., PRB 79, 081405(R) (2009)

W. Son et al., PRB 79, 245411 (2009) G. Singh-Bhalla et al., Nature Physics (2010)

A. D. Caviglia et al. PRL 105, 236802 (2010)M. Ben Shalom et al. PRL 105, 206401 (2010)A. D. Caviglia et al. PRL 104, 126803 (2010)A. Dubroka et al. PRL 104, 156807 (2010)

M. Ben Shalom et al. PRL 104, 126802 (2010)M. Breitschaft et al., PRB 81, 153414 (2010)

M. R. Fitzsimmons et al. PRL 107, 217201 (2011)C. Cancellieri et al. PRL 107, 056102 (2011)R. Yamamoto et al. PRL 107, 036104 (2011)

P. Delugas et al. PRL 106, 166807 (2011)S. A. Pauli et al. PRL 106, 036101 (2011)

L. Li et al., Nature Physics (2011)J.A. Bert et al., Nature Physics (2011)

D.A. Dikin et al., PRL 107, 56802 (2011)L. Li et al. Science (2011)

Ariando et al. Nature Comm. (2011)H. J Gardner et al. Nature Physics (2011)

Stengel PRL 106, 136803 (2011)H. W. Jang et al. Science (2011)

J. W. Park et al. Nature Comm (2011)

A 2D Superconducting Electron Gas

100mT

H⫽

H⟘

estimate of the POS component of the magneticfield. Assuming a typical electron density of108 cm!3, our measured phase speeds between1.5 and 5 Mm s–1 correspond to projected mag-netic field strengths between 8 and 26G.We notethat circular polarization measurements of coro-nal emission lines can provide an estimate of theLOS component of the magnetic field. Notably,seismology and polarimetry provide complemen-tary projections of the coronal magnetic field,which can be combined to provide an estimate ofboth the strength and the inclination of the mag-netic field. In future work, it will be possible toestimate the plasma density with CoMP obser-vations through the intensity ratio of the FeXIIIlines at 1074.7 and 1079.8 nm (31).

We have analyzed observations from theCoMP instrument that show an overwhelmingflux of upward-propagating low-frequencywavesthroughout the solar corona. These waves prop-agate at speeds typical of Alfvén waves, and theirdirection of propagation mirrors the measuredmagnetic field direction. The waves we resolveddo not have enough energy to heat the solarcorona. We conclude that these ubiquitous wavesare indeed Alfvénic and offer the real possibilityof probing the plasma environment of the solar

corona with a high degree of accuracy throughcoronal seismology.

References and Notes1. H. Alfvén, Nature 150, 405 (1942).2. H. Alfvén, Mon. Not. R. Astron. Soc. 107, 211 (1947).3. D. Osterbrock, Astrophys. J. 134, 347 (1961).4. M. J. Aschwanden, L. Fletcher, C. J. Schrijver, G. Alexander,

Astrophys. J. 520, 880 (1999).5. V. M. Nakariakov, L. Ofman, E. E. DeLuca, B. Roberts,

J. M. Davila, Science 285, 862 (1999).6. C. E. DeForest, J. B. Gurman, Astrophys. J. 501, L217

(1998).7. I. De Moortel, J. Ireland, R. W. Walsh, Astron. Astrophys.

355, L23 (2000).8. M. A. Marsh, R. W. Walsh, Astrophys. J. 643, 540 (2006).9. M. Minarovjech et al., Sol. Phys. 213, 269 (2003).10. D. R. Williams et al., Mon. Not. R. Astron. Soc. 326, 428

(2001).11. J. M. Pasachoff, F. A. Babcock, K. D. Russell, D. B. Seaton,

Sol. Phys. 207, 241 (2002).12. S. Koutchmy, I. D. Zhugzhda, V. Locans, Astron. Astrophys.

120, 185 (1983).13. T. Sakurai, K. Ichimoto, K. P. Raju, J. Singh, Sol. Phys.

209, 265 (2002).14. J. W. Belcher, Astrophys. J. 168, 505 (1971).15. P. Charvin, Ann. Astrophys. 28, 877 (1965).16. S. M. Jefferies et al., Astrophys. J. 434, 795 (1994).17. W. Finsterle et al., Astrophys. J. 613, L185 (2004).18. S. W. McIntosh, B. Fleck, T. D. Tarbell, Astrophys. J. 609,

L95 (2004).19. B. W. Lites, R. Rutten, W. Kalkofen, Astrophys. J. 414,

345 (1993).

20. B. De Pontieu, R. Erdélyi, I. DeMoortel, Astrophys. J. 624,L61 (2005).

21. V. H. Hansteen et al., Astrophys. J. 647, L73 (2006).22. S. W. McIntosh, S. M. Jefferies, Astrophys. J. 647, L77

(2006).23. S. M. Jefferies et al., Astrophys. J. 648, L151 (2006).24. B. De Pontieu et al., Astrophys. J. 655, 624 (2007).25. O. Wikstol, P. G. Judge, V. Hansteen, Astrophys. J. 501,

895 (1998).26. P. G. Judge, A. Pietarila, Astrophys. J. 606, 1258 (2004).27. D. Melrose, Aust. J. Phys. 30, 647 (1977).28. G. L. Withbroe, R. W. Noyes, Annu. Rev. Astron. Astrophys.

15, 363 (1977).29. E. Verwichte, C. Foullon, V. M. Nakariakov, Astron.

Astrophys. 446, 1139 (2006a).30. V. M. Nakariakov, E. Verwichte, Living Rev. Sol. Phys. 2, 3

(2005).31. M. J. Penn et al., Space Sci. Rev. 70, 185 (1994).32. The authors would like to thank M. Knölker and

P. Weis-Taylor for comments on the manuscript.Construction of the CoMP instrument was funded by theNSF through the NCAR Strategic Initiative Fund andHAO/NCAR base funds. The effort of S.M.C. was supportedby grant ATM-0541567 from NSF.

Supporting Online Materialwww.sciencemag.org/cgi/content/full/317/5842/1192/DC1Materials and MethodsTable S1ReferencesMovies S1 to S4

2 April 2007; accepted 27 July 200710.1126/science.1143304

Superconducting Interfaces BetweenInsulating OxidesN. Reyren,1 S. Thiel,2 A. D. Caviglia,1 L. Fitting Kourkoutis,3 G. Hammerl,2 C. Richter,2C. W. Schneider,2 T. Kopp,2 A.-S. Rüetschi,1 D. Jaccard,1 M. Gabay,4 D. A. Muller,3J.-M. Triscone,1 J. Mannhart2*At interfaces between complex oxides, electronic systems with unusual electronic properties canbe generated. We report on superconductivity in the electron gas formed at the interface betweentwo insulating dielectric perovskite oxides, LaAlO3 and SrTiO3. The behavior of the electron gasis that of a two-dimensional superconductor, confined to a thin sheet at the interface. Thesuperconducting transition temperature of ! 200 millikelvin provides a strict upper limit to thethickness of the superconducting layer of ! 10 nanometers.

Inpioneering work, it was demonstrated that ahighlymobile electron system can be inducedat the interface between LaAlO3 and SrTiO3

(1). The discovery of this electron gas at theinterface between two insulators has generated animpressive amount of experimental and theoret-ical work (2–8), in part because the complexionic structure and particular interactions found atsuch an interface are expected to promote novel

electronic phases that are not always stable asbulk phases (9–11). This result also generated anintense debate on the origin of the conductinglayer, which could either be “extrinsic” and dueto oxygen vacancies in the SrTiO3 crystal or“intrinsic” and related to the polar nature of theLaAlO3 structure. In the polar scenario, apotential develops as the LaAlO3 layer thicknessincreases that may lead to an “electronic re-construction” above some critical thickness (5).Another key issue concerns the ground state ofsuch a system; at low temperatures, a charge-ordered interface with ferromagnetic spin align-ment was predicted (4). Experimental evidencein favor of a ferromagnetic ground state wasrecently found (6). Yet, rather than orderingmagnetically, the electron system may alsocondense into a superconducting state. It wasproposed that in field effect transistor config-

urations, a superconducting, two-dimensional(2D) electron gas might be generated at theSrTiO3 surface (12). It was also pointed out thatthe polarization of the SrTiO3 layers may causethe electrons on SrTiO3 surfaces to pair and format high temperatures a superconducting con-densate (13, 14). In this report, we explore theground state of the LaAlO3/SrTiO3 interface andclarify whether it orders when the temperatureapproaches absolute zero. Our experiments pro-vide evidence that the investigated electron gasescondense into a superconducting phase. Thecharacteristics of the transition are consistentwith those of a 2D electron system undergoing aBerezinskii-Kosterlitz-Thouless (BKT) transi-tion (15–17). In the oxygen vacancy scenariothe observation of superconductivity provides astrict upper limit to the thickness of the super-conducting sheet at the LaAlO3/SrTiO3 interface.

The samples were prepared by depositingLaAlO3 layers with thicknesses of 2, 8, and 15unit cells (uc) on TiO2-terminated (001) surfacesof SrTiO3 single crystals (5, 18). The films weregrown by pulsed laser deposition at 770°C and6 ! 10!5 mbar O2, then cooled to room temper-ature in 400 mbar of O2, with a 1-hour oxidationstep at 600°C. The fact that only heterostructureswith a LaAlO3 thickness greater than three ucconduct (5) was used to pattern the samples(19). Without exposing the LaAlO3/SrTiO3 in-terface to the environment, bridges with widthsof 100 mm and lengths of 300 mm and 700 mmwere structured for four-point measurements,as well as two-uc-thick LaAlO3 layers for ref-erence (18).

1Département de Physique de la Matière Condensée,University of Geneva, 24 quai Ernest-Ansermet, 1211 Genève4, Switzerland. 2Experimental Physics VI, Center for ElectronicCorrelations and Magnetism, Institute of Physics, University ofAugsburg, D-86135 Augsburg, Germany. 3School of Appliedand Engineering Physics, Cornell University, Ithaca, NY 14853,USA. 4Laboratoire de Physique des Solides, Bat 510, UniversitéParis-Sud 11, Centre d’Orsay, 91405 Orsay, Cedex, France.

*To whom correspondence should be addressed. E-mail:jochen.mannhart@physik.uni-augsburg.de

31 AUGUST 2007 VOL 317 SCIENCE www.sciencemag.org1196

REPORTS

on N

ovem

ber

19, 2007

ww

w.s

cie

ncem

ag.o

rgD

ow

nlo

aded fro

m

Science 317, 1196 (2007)

��(T = 0) � 60 nm d ≈ 10 nm

Outline

Electric field control of superconductivity, phase diagram

Magneto-transport and spin-orbit coupling

Superconductivity in nanostructures

Daniela Stornaiuolo

Denver Li

Andrea Caviglia(now in Hamburg)Stefano Gariglio

The «Geneva» LaAlO3/SrTiO3 Team

Marc Gabay (University of Paris-Sud)

in collaboration withUniversity of Geneva

• Alberto MorpurgoBenjamin Sacépé

• Didier JaccardGabriel Seyfarth

• Christophe Berthod

Alexandre Fête

and:

• Philippe Ghosez (Liège)

• Phil Willmott (PSI)

• Jochen Mannhart (Stuttgart)

ClaudiaCancellieri(now at PSI) Nicolas Reyren

(now in Paris)

«Standard» LaAlO3/SrTiO3 Samples

Layer-by-layer growthT = 800°C «standard»

P O2 = 1·10-4 TorrFluence = 0.6 J/cm2

Frequency = 1HzPost annealing @ 200 mbar O2

16 18 20 22 24 26 28 30

!""#$

%

&'(

Inte

nsity

(a.u

.))!% !*$

+,(

)-./)"./#0./##./1./0./

Transport Properties

TiO2-plane

Ti O 3.9 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)

VG,b

VSIS VD ID

SrTiO3

Field Effect Experiments

«Standard» Samples

TiO2-plane

Ti O 3.9 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)

Modulation of SC

50 100 150 200 250 300 350 4001x101

1x102

1x103

1x104

Rsh

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

-4 -2 0 2 4-1.2

-1-0.8-0.6-0.4-0.2

00.20.4

Δσ

/(e2 /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

/(e2 /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 AntilocalizationWeak localization

Strong spin-orbit interaction

Weak anti-localization

0.001

0.01

0.1

1

10

B

(T)

-200 100V (V)

0.2

0.4

0.6

0.8

1

T (K

)

T - PRL 104B - PRL 104B - this workB - PRL 104B - this workso

so

i

i

i,so

cc

-100-300 0

WL WAL AM

0.1 1σ (mS)

0.20.40.60.8

1

m*/m

* max

2D

0.1

1

10

B

(T)

B - this workB - this work

el,s

o

so

el

a)

b)

c)

m⇤ =h2

4⇥�

sB

so

⇤0

Rashba spin orbit

B≈1/Dττso∼τel-1

Delugas et al., PRL 106, 166807 (2011)

ns=3.3 10 14 cm-2

Electronic Structure

M. Salluzzo et al., PRL 102, 166804 (2009)

Spin-orbit and Magneto-transport in // Field

0.985

0.99

0.995

1

σ

(mS)

2D

Exp.7T

5.25T3.5T

1.75T

a)

0 50 100 150 200 250 300ϕ (°)

0.985

0.99

0.995

1

σ

(mS)

2D

Theory

7T

5.5T

3.5T

1.75T

c)

0 2 4 6 8B (T), Φ=90°

0.989

0.994

0.999

1.004

σ

(mS)

ExperimentTheory

2D

2

2.02

2.04

σ

(mS)

2D

Exp.7T

5.25T

3.5T1.75T

b)

0 50 100 150 200 250 300ϕ (°)

2

2.02

2.04

2.06

σ

(mS)

2D

Theory

7T

5.5T3.5T1.75T

d)

0 2 4 6 8B (T), Φ=90°

2

2.03

2.06

σ

(mS)

ExperimentTheory

2D

�(B, ⇥) ⇥B B �(B = 0) = 1

�(B = 0) = 2⇥ �

⇥(B,⌅ = �/2)

dxz dyz

mh ⇥ 20me

dxz dyz

� B ⌅ = 0B ⌅ = �

2

EF E�

�B = 0

g(EF ) ⇥⌅ = 0 EF ⇥ E�

EF E� g(EF )B = 0

E� dxy

EF E� dxz

EF g(EF )dxz

⇤B

⌅ BB

⇥⌅ dxz EF

(⇥(B, ⌅ = �/2) � ⇥(B,⌅ = 0))/⇥(B,⌅ = 0) =1/8(⇥so/EF )2

⇥so

t2g

B

3 2 3� �4 2

�

Bso Bi

m⇤ ⌅D VB = 0

�⌅WL(B = 0) =e2

⇤h

✓Log[(1 +

Bso

Bin)(1 +

2Bso

Bin)

12 ]� Log[

Bel

Bin]◆

⇧so ⇧ 2�⇥

so

= ⇤2so⇧ �so ⇥ ~⇤so = 2�EkF

E kF m⇤

Bso Bso = �04�D⇥

so

m⇤ =h2

4⇤�E

rBso

⇥0

⇧ Bel = �04�D⇥ ⇥0 = h

2e D = 12vF

2⇧

�⌅WL(B = 0) Bel

µD µ Bel

�⌅WL(B = 0)

!

0.001

0.01

0.1

1

10

B

(T)

-200 100V (V)

0.2

0.4

0.6

0.8

1

T (K

)

T - PRL 104B - PRL 104B - this workB - PRL 104B - this workso

so

i

i

i,so

cc

-100-300 0

WL WAL AM

0.1 1σ (mS)

0.20.40.60.8

1

m*/m

* max

2D

0.1

1

10

B

(T)

B - this workB - this work

el,s

o

so

el

a)

b)

c)

A. Fête et al. arXiv:1203.5239

a)

b) c)

σ =-1/2

σ =+1/2

B

J

BRashba

ext

J

BRashbaBext

y

y

k

E (m

eV)

x

B= 1 T

k

E (m

eV)

x

B= 1 T

k

E (m

eV)

x

B= 0 T

EΓ

0.985

0.99

0.995

1

σ

(mS)

2D

Exp.7T

5.25T3.5T

1.75T

a)

0 50 100 150 200 250 300ϕ (°)

0.985

0.99

0.995

1

σ

(mS)

2D

Theory

7T

5.5T

3.5T

1.75T

c)

0 2 4 6 8B (T), Φ=90°

0.989

0.994

0.999

1.004σ

(m

S)ExperimentTheory

2D

2

2.02

2.04

σ

(mS)

2D

Exp.7T

5.25T

3.5T1.75T

b)

0 50 100 150 200 250 300ϕ (°)

2

2.02

2.04

2.06

σ

(mS)

2D

Theory

7T

5.5T3.5T1.75T

d)

0 2 4 6 8B (T), Φ=90°

2

2.03

2.06

σ

(mS)

ExperimentTheory

2D

�(B, ⇥) ⇥B B �(B = 0) = 1

�(B = 0) = 2⇥ �

⇥(B,⌅ = �/2)

dxz dyz

mh ⇥ 20me

dxz dyz

� B ⌅ = 0B ⌅ = �

2

EF E�

�B = 0

g(EF ) ⇥⌅ = 0 EF ⇥ E�

EF E� g(EF )B = 0

E� dxy

EF E� dxz

EF g(EF )dxz

⇤B

⌅ BB

⇥⌅ dxz EF

(⇥(B, ⌅ = �/2) � ⇥(B, ⌅ = 0))/⇥(B,⌅ = 0) =1/8(⇥so/EF )2

⇥so

t2g

B

A. Fête et al. arXiv:1203.5239

1mSΔso=2.5 meV

2mSΔso=7 meV

Some Correlations

0.1 1σ (mS)

0

0.2

0.4

0.6

0.8

τ (p

s)

0

0.5

1

1.5

2

2.5

m*/m

Ref. [13]this workRef. [13]this work

2D

e

0

Signature of a spin-orbitprotected transport in the 2Dconducting sheet ?

Are the dxz, dyz bands playinga special role forsuperconductivity?

4

2D case, one expects a periodic variation of the MC with�, displaying crests for B along y and troughs for B alongx.

In the framework of this 1D picture and with the ad-ditional simplifying assumption that the variation of �2D

with � is entirely due to the dxz sub-band closest to EF ,we find (�2D(B,� = ⇡/2) � �2D(B,� = 0))/�2D(B,� =0) = 1/8(�so/EF )2 when the Zeeman energy is largerthan the condensation energy of the Rashba state (�so)(see also [29]). Beyond the qualitative 1D model, we havemodelled the evolution of the band structure for the t2gorbitals in the applied B. We use a tight binding modelfeaturing kinetic and Rashba terms and we take into ac-count the finite value of mh and the anisotropy of � in thexy plane for the dxz, dyz orbitals. The mobility, � and thegyromagnetic factor g all depend on V , but we considerthat they do not change appreciably with � nor with themagnitude of B in our experiments. For a given V , thevariation of �n – i.e. the change in the dxz, dyz carrierconcentrations – with � and B depends on the values ofthe spin-orbit and of the Zeeman energies. The conduc-tance �2D(B,�) is then proportional to �n. Experimen-tal data and plots obtained from the model are shownin Figures 2 (c) and (d). We note that while �2D(B,�)increases monotonically with B at fixed � for �0

2D = 2mS, such is not the case for �0

2D = 1 mS, a feature whichis correctly captured by our model. Figure 3 displays theevolution of ��2D = �2D(B,� = ⇡/2) � �2D(B,� = 0)versus B according to our model and the experimental re-sults. We find good agreement using �SO = 7(2.5) meVfor �0

2D = 2(1) mS respectively. These values fall withinthe range of previous experimental estimates [13, 14].

Figure 4 shows the evolution of the experimental oscil-lation amplitude ��2D as a function of �0

2D for differentmagnetic fields. As can be seen, ��2D tends to zero for asheet conductance in the 0.1�0.3 mS range. These sheetconductance values – which lie in the diffusive regime –are close to the QCP, suggesting a potentially importantrole played by the dxz, dyz orbitals in establishing super-conductivity.

In summary, our findings underscore the evolution thattakes place in the LaAlO3-SrTiO3 heterostructure, as onetunes the gate voltage in the range where superconduc-tivity is observed at low temperature. For low V , con-duction is diffusive and is dominated by the dxy orbitals,as the impact of disorder is expected to be more severefor the 1D-like dxz, dyz states. For larger values of V , thenature of transport changes and the out of plane dxz, dyzorbitals start contributing to the zero field conductivity,as evidenced by the evolution of m⇤, Bel, Bso and bythe oscillations of the in-plane magnetoconductance. Forthese orbitals, the effect of the strong spin-orbit interac-tion has to be taken into account at the band structurelevel for the calculation of their contribution to the trans-port.

We would like to thank M. Lopes and S. C. Müller

0 2 4 6 8B (T)

0

10

20

30

Δσ

(μ

S)2D

σ = 2 mS2D0

0

5

10

15

20

Δσ

(μ

S)

ExperimentTheory

σ = 1 mS

2D

2D0

FIG. 3: (color online) Experimental and model determinedplots of ��2D versus B for �0

2D = 1 mS and �02D = 2 mS.

7T5.25T

3.5T

1.75T

0.1 1σ (mS)

0

5

10

15

20

Δσ

(μ

S)

2D

2D

0

FIG. 4: (color online) Evolution of the amplitude of the ex-perimental oscillations ��2D (��2D = �2D(B,� = ⇡

2 ) ��2D(B,� = 0)) as a function of �0

2D . "Plus" symbols pertainto measurements performed on an additional sample at 7 T.

for their technical assistance. This work was supportedby the Swiss National Science Foundation through theNational Center of Competence in Research, Materialswith Novel Electronic Properties, MaNEP and divisionII, by the Institut Universitaire de France (MG), and theEuropean Union through the project OxIDes.

2D-SC

Conclusions

Magneto-transport and superconductivity reveal the importance of the sub-band structure

Magneto-transport and SdH analyses display signatures of the presence of spin orbit in the system

The gas properties are preserved in «nano-structures» - that may reveal signatures of the SC gap