Electronic Properties of the LaAlO₃-SrTiO₃ Interfaces and Related Heterostructures

Thesis

Reference

Electronic Properties of the LaAlO

-SrTiO

Interfaces and Related Heterostructures

LI, Danfeng

Abstract

Les pérovskites constituent une classe importante de structure cristalline. Les oxydes de cette famille présentent une physique riche et des propriétés électroniques remarquables. Ces matériaux peuvent être combinés par des techniques de croissance en couche de sorte à former des hétéro-structures artificielles. La maitrise de la qualité structurelle aux interfaces a été rendue possible grâce aux récents progrès réalisés dans la fabrication et la caractérisation de ce type de structures ou une large gamme d'oxydes peut être construite.

Cette thèse étudie l'hétéro-structure LaAlO₃/SrTiO₃, deux isolants de bande à structure pérovskite, où un liquide d'électrons bidimensionnel (2DEL) se forme à l'interface. l'apparition de ce liquide entre deux matériaux isolants est un exemple de l'émergence de nouvelles propriétés propres à la physique des interfaces.

LI, Danfeng. Electronic Properties of the LaAlO₃-SrTiO₃ Interfaces and Related Heterostructures. Thèse de doctorat : Univ. Genève, 2016, no. Sc. 5008

URN : urn:nbn:ch:unige-902733

DOI : 10.13097/archive-ouverte/unige:90273

Available at:

http://archive-ouverte.unige.ch/unige:90273

Disclaimer: layout of this document may differ from the published version.

Département de Physique de la Matière Quantique Dr. Stefano Gariglio

Electronic Properties of the

LaAlO ₃ -SrTiO ₃ Interfaces and Related Heterostructures

THÈSE

présentée à la Faculté des Sciences de l’Université de Genève pour obtenir le grade de docteur ès Sciences, mention Physique

par

Danfeng Li

de Xinxiang (Chine)

Thèse n^◦5008

GENÈVE

Atelier d’impression ReproMail 2016

The past few years during my PhD study has been an incredible journey. Along the path, many people have been essential for the production of this thesis. I would like to acknowledge everyone of them.

First, I wish to express my sincere gratitude to Prof. Jean-Marc Triscone for giving me this great opportunity of working in his group, which has been a wonderful experience. Without his everlasting support, trust, enthusiasm, or his vast knowledge of physics, I would never have traveled so far. Throughout these years, he continuously showed high concentration, dedication and motivation, which I have benefited from and have learnt a great deal. His kindness and leadership not only created a stimulating and encouraging working environment, including the opportunities to interact with high level researchers and collaborators, but also contributed to a positive and lively lab life.

I would also like to thank Dr. Stefano Gariglio, who is the co-advisor of this thesis, for all his supervision and guidance from Day 1, both on physics and experimental techniques. His rigorous and diligent working principles, with his spirit of always getting to the bottom of things, have influenced me and shaped me into a better researcher. His support and broad knowledge of the field have been vital to make this thesis possible. Numerous discussions that we had have become invaluable fortune to me.

I am grateful to Prof. Guus Rijnders, Prof Marc Gabay and Prof. Dirk van der Marel for their essential role in evaluating this thesis. I thank them for the enlightening questions and discussions. I am especially thankful to Marc, for many instructive and heuristic discussions that we had on different ideas over the years.

I owe thanks to Claudia Cancellieri for her guidance and help during the first few months and also for establishing a highly efficient and productive collaboration on the alloy project. I would also like to take this opportunity to thank other people in

"the Geneva LAO-STO team": Nicolas Reyren, Andrea Caviglia, Daniela Stornaiuolo, Alexandre Fête, Wei Liu, Zhenping Wu, Margherita Boselli, Giulio Tieri, Adrien Waelchli and Ritsuko Eguchi for all the fruitful scientific discussions and brainstorming moments.

My thanks goes to all the remaining present and past group members including Céline Lichtensteiger, Pavlo Zubko, Raoul Scherwitzl, Alessia Sambri, Jill Guyonnet, Stéphanie Fernandez, Sara Catalano, Jennifer Fowlie, Davide Valentinis, Michel Viret, Christian Weymann, Hugo Meley, Elias Ferreiro, Dirk Groenendijk, Joeri de Bruijckere and Claribel Dominguez. I cherish the memory that we have created together. A very special thanks goes to Marta Gibert, who has been such a considerate and amazing officemate for long time.

Over the years, I have had the privilege and the pleasure to collaborate with different people: Philippe Ghosez, Sébastien Lemal, Nicholas Bristowe, Denis Fontaine, Mathilde Reinle-Schmitt, Phil Willmott, Alexandre Gloter, Odile Stéphan, Daniele Marré, Ilaria Pallecchi, Alessio Filippetti, Jochen Mannhart, Rainer Jany, Vladimir Strokov, Charles Ahn, Ke Zou, Christophe Berthod and Didier Jaccard.

I also want to thank Zhe Wang, Lin Wang, Iaroslav Gaporenko, Benedikt Ziegler, Cedric Blaser, Yulia Lisunova, Philippe Tuckmantel, Sandra Sopic, Ignacio Gutierrez, Dong Keun Ki, Davide Costanzo, Enrico Giannini, Alberto Morpurgo and Patrycja Paruch.

My research has benefited from the professional technical assistance of Marco Lopes, Sébastian Muller and Spiros Zanos. I also thank our secretary team including Denise Borjon, Fabienne Hartmeier, Esther Schwarz, Nathalie Buret, Natacha Triscone and Christoph Schwarz.

I wish to express my heartful thanks to my family: my parents, my wife Xiaolian and my lovely daughter Stella.

Les pérovskites constituent une classe importante de structure cristalline. Les oxydes de cette famille présentent une physique riche et des propriétés électroniques remarquables.

Ces matériaux peuvent être combinés par des techniques de croissance en couche de sorte à former des hétéro-structures artificielles. La maitrise de la qualité structurelle aux interfaces a été rendue possible grâce aux récents progrès réalisés dans la fabrication et la caractérisation de ce type de structures ou une large gamme d’oxydes peut être construite. Cette thèse étudie l’hétéro-structure LaAlO3/SrTiO3, deux isolants de bande à structure pérovskite, où un liquide d’électrons bidimensionnel (2DEL) se forme à l’interface. l’apparition de ce liquide entre deux matériaux isolants est un exemple de l’émergence de nouvelles propriétés propres à la physique des interfaces.

Dansle premier chapitre, nous décrirons les propriétés supraconductrices et mag- nétiques de ce liquide d’électrons. L’origine du liquide bidimensionnel est communé- ment décrite par un modèle de reconstruction électronique due au potentiel électrique qui apparaît entre la surface non-polaire de SrTiO3 et polaire du LaAlO3. Dans ce travail, l’intérêt est principalement porté sur l’état supraconducteur bidimensionnel existant pour des températures inférieures à∼ 250 mK. Cet état peut être modulé par effet de champ électrique, donnant naissance à un riche diagramme de phase métal/supraconducteur/isolant.

Dansle deuxième chapitre, nous discutons en détails le modèle de «catastrophe polaire» et les plus importantes observations expérimentales qui soutiennent ce modèle de dopage d’interface intrinsèque lié à un transfert de charge. Afin de tester ce modèle, nous avons conçu une expérience qui permet, par l’utilisation d’un alliage entre le LaAlO3 et le SrTiO3, de moduler en fonction du niveau de dopage, la polarisation intrinsèque du matériau. Il est prédit, combinant des calculsab-initioavec des mesures diélectriques, que l’épaisseur critique suive une loi inverse de la polarisation intrinsèque et donc de la quantité de SrTiO3 ajoutée à la couche de LaAlO3. Les expériences confirment cette évolution, compatible avec le modèle de «catastrophe polaire».

Selon ce modèle, la modulation de la discontinuité polaire produit une densité différente de charges transférées à l’interface LaAlO3/SrTiO3. l’extension hors plan de la zone supraconductrice (largeur du potentiel de confinement) du 2DEL à l’interface alliage/SrTiO₃ peut être extraite des mesures du champ critique. Nous mettons en

évidence l’augmentation significative de cette épaisseur en comparaison avec l’Interface LaAlO3/SrTiO3, résultat qui est en accord avec une modélisation du confinement par les équations de Poisson et Schrödinger. L’extension du puit quantique semble confirmer, par ailleurs, un transfert d’électrons avec une densité de 0,5 e/u.c et 0,25 e/u.c respectivement à l’interface LaAlO₃/SrTiO₃et à l’interface alliage/SrTiO₃.

Le troisième chapitreest consacré à la fabrication de l’hétéro-structure métallique supraconductrice LaAlO3/SrTiO3où le 2DEL est hébergé dans une couche de SrTiO3

obtenue par croissance plutôt que directement sur le substrat monocristallin, de manière à pouvoir réaliser des super-réseaux LaAlO3/SrTiO3. Nos résultats montrent que les hautes températures de croissance et la maîtrise de la terminaison de SrTiO3 sont des conditions déterminantes pour obtenir le 2DEL. Des mesures de microscopie à force atomique ont permis de montrer que l’effet de la ségrégation du SrO, observé en conditions normales de croissance, conduit à l’absence d’état métallique robuste et à l’apparition de défauts cristallins. l’utilisation de températures de croissance élevées est un moyen de palier ce problème. Suivant ces observations, nous avons fabriqué la bi-interface(LaAlO3/SrTiO3)2qui possède deux interfaces conductrices.

Dansle quatrième chapitre, sont présentés les mesures de transport et d’effet de champ du systèmebi-interfacialsupraconducteur. Le diagramme de phase de l’état supraconducteur modulé par effet de champs diffère de celui mesuré dans le cas d’une interface simple. D’autres expériences seront cependant nécessaires pour comprendre l’éventuel couplage entre les plans supraconducteurs.

En dernière partie seront exposés les principales conclusions ainsi que les perspec- tives et les questions ouvertes que soulève cette étude, là où une physique riche et passionnante doit continuer à être explorée.

An important class of materials with rich physics and outstanding electronic properties is perovskite oxides in which diverse functionalities were discovered. These materials take a similar structure and thus provide an opportunity of combining them in an artificial way to create new heterostructures. Advances in the material fabrication and characterisation have enabled deposition of a large range of heteroepitaxial oxide structures with sharp interfaces. In this thesis, we have investigated the heterointerface between two perovskite band insulators, LaAlO3and SrTiO3, where a two dimensional electron liquid (2DEL) is present. The combination of these two perovskite oxides creates a sparkling example of new emergent phenomena arising at the interface that do not exist in their bulk form.

InChapter 1, we see that the two dimensional electron liquid at the LaAlO₃/SrTiO3

heterointerface displays a broad spectrum of fascinating electronic properties, including superconductivity, complex magnetotransport properties at low temperatures, strong Rashba spin-orbit coupling and even traces of magnetism. The origin of this 2DEL has been related to the polar discontinuity across the interface due to the polar/non-polar nature of two surfaces. Of particular interest to this work, a 2D superconducting ground state is present with a transition temperature of the order of∼250 mK. The superconductivity of the system can be gate modulated by field-effect revealing a rich phase diagram with a quantum critical point separating a superconducting and an insulating ground state.

InChapter 2, we have discussed in great detail the "polar catastrophe" model and revisited the important experimental observations that support this intrinsic charge- transfer doping mechanism. In order to test the "polar catastrophe" model, we have designed a new material with a reduced polarisation by alloying the LaAlO₃ film with SrTiO3. Combiningfirst principles calculations with dielectric measurements, we predict that the threshold thickness required to observe interface conductivity scales with the inverse of the polarisation strength and hence evolves with the amount of SrTiO3 added to the layer. Experiments confirm this evolution, providing strong evidence of the "polar catastrophe" model.

The modified polar discontinuity also produces a different transferred charge density. This will result in a confining potential that is different from that of the

LaAlO3/SrTiO3 interface. We have seen that 2D superconductivity is present at this new oxide interface and its strength can also be tuned by field-effect. The supercon- ducting thickness (i.e. an estimation of the width of the confining potential) of the 2DEL at the alloy/SrTiO3interface can be extracted from anisotropic critical field mea- surements. We show that this thickness is significantly increased in comparison with the LaAlO3/SrTiO3interface. This perfectly agrees with our Poisson-Schrödinger mod- elling. These results indicate that electrons with density of 0.5 e⁻/u.c. and 0.25 e⁻/u.c.

are transferred to the LaAlO₃/SrTiO₃and alloy/SrTiO₃ interface respectively, which leads to conductivity.

Chapter 3is devoted to the fabrication of metallic and superconducting LaAlO3/ SrTiO₃interfaces where the 2DELs are hosted in SrTiO₃thin films rather than in the single-crystal substrates, in order to realise LaAlO3/SrTiO3 superlattices. We start from homoepitaxial SrTiO3films. Our results show that the growth temperature and the SrTiO₃layer termination are essential. Local friction force microscopy has been used to show that in normal growth conditions, the absence of a robust metallic state is due to the nanoscale SrO segregation occurring on the SrTiO3 film surface and the associated structural imperfections in the SrTiO₃film. By adopting an extremely high SrTiO3growth temperature, we have demonstrated a way to realise metallic and superconducting interfaces.

Following this pathway, we have fabricated the LaAlO₃/SrTiO₃ bi-interfacewith both top and bottom LaAlO3/SrTiO3 interfaces conducting. InChapter 4, we have provided direct experimental proofs from transport measurements and TEM-EELS studies to demonstrate the presence of the 2DEL in the SrTiO₃ thin film in thisbi- interface. We have also shown a first superconductivity and field-effect experiment on the LaAlO3/SrTiO3bi-interface. Thebi-interfaceis superconducting with a gate- tunable phase diagram that is remarkably different from the standard LaAlO₃/SrTiO₃ interface. Further experiments and investigations are required to understand the possible coupling between the superconducting planes.

We draw our conclusions inChapter 5, and list some relevant open questions and perspectives, where exciting new physics still waits to be explored.

2D Two Dimensional

2DEL Two Dimensional Electron Liquid

3D Three Dimensional

AFM Atomic Force Microscopy

BHF Buffered Hydrofluoric acid DFT Density Functional Theory

DOS Density of States

EELS Electron Energy Loss Spectroscopy FFM Friction Force Microscopy

LDA Local Density Approximation MIT Metal-Insulator Transition PLD Pulsed-Laser Deposition

RHEED Reflection High-Energy Electron Diffraction SIT Superconductor-Insulator Transition

TEM Transmission Electron Microscopy

u.c. Unit Cell

XRD X-ray Diffraction

e Electron charge

Dielectric permittivity

m_e Electron mass

m^∗ Effective mass

n2D(ns) Sheet carrier density σ_2D(σ_s) Sheet conductance

µ₀H_⊥^∗(µ₀H_k^∗) Perpendicular and parallel superconducting critical field

R_H Hall coefficient

Rs Sheet resistance

Rxy Hall resistance

T_c Superconducting transition temperature T_g(T_growth) Growth temperature

Vg Gate voltage

Acknowledgements i

Résumé iii

Abstract v

List of Symbols vii

Overview 1

1 Introduction 3

1.1 Functional oxides . . . 3

1.1.1 Perovskite oxides . . . 3

1.1.2 SrTiO3 . . . 4

1.2 The LaAlO3/SrTiO3functional interface . . . 8

1.2.1 Polar discontinuity . . . 10

1.2.2 Electronic structure . . . 13

1.2.3 Superconductivity . . . 16

1.2.4 Field-effect experiments . . . 17

1.2.5 Magnetism . . . 21

1.3 Fabrication and characterisation of the interface . . . 23

1.3.1 PLD growth. . . 23

1.3.2 Growth mode studied by RHEED . . . 26

1.3.3 Other structural characterisations . . . 27

2 Testing the Polar Catastrophe Model 29 2.1 Introduction . . . 29

2.2 The origin of the 2DEL at the LaAlO3/SrTiO3 interface . . . 29

2.2.1 Chemical (extrinsic) doping scenario . . . 29

2.2.2 Electronic (intrinsic) doping scenario . . . 31

2.3 Polar catastropheat the LaAlO₃/SrTiO₃ interface . . . 33

2.3.1 LaAlO3critical thickness. . . 33

2.3.2 The electric field in the LaAlO3layer . . . 33

2.3.3 New theoretical considerations . . . 34

2.4 Tuning the electric potential in the polar thin-film . . . 36

2.4.1 The idea of a new interface by alloying LaAlO₃ . . . 36

2.4.2 First principlescalculations . . . 36

2.4.3 Properties of the alloy/SrTiO3 interface . . . 40

2.4.4 Discussions . . . 44

2.5 Intrinsic electron confinement at oxide interfaces . . . 44

2.5.1 Confining potential . . . 45

2.5.2 Superconducting thickness of the alloy/SrTiO₃interface . . . 47

2.5.3 Discussions . . . 48

3 LaAlO₃/SrTiO₃Interface with SrTiO₃ Films 51 3.1 Introduction . . . 51

3.2 The role of different deposition parameters on the LaAlO₃/SrTiO₃interface properties . . . 51

3.2.1 LaAlO3thickness. . . 52

3.2.2 Oxygen pressure . . . 53

3.2.3 LaAlO₃stoichiometry . . . 54

3.2.4 Growth temperature . . . 56

3.3 Fabrication of superconducting interfaces between artificially grown LaAlO₃and SrTiO₃thin films . . . 61

3.3.1 Motivation . . . 61

3.3.2 Experimental . . . 62

3.3.3 Homoepitaxial SrTiO₃ thin-films grown at 800^◦C . . . 64

3.3.4 SrTiO3thin-films grown at 1100^◦C . . . 69

3.3.5 Conclusion . . . 73

4 LaAlO₃/SrTiO₃Bi-interface 75 4.1 Introduction . . . 75

4.2 Transport properties of SrTiO₃-based heterostructures . . . 75

4.3 LaAlO3/SrTiO3bi-interface . . . 76

4.3.1 Demonstration of the LaAlO3/SrTiO3bi-interfaceheterostruc- tures. . . 77

4.3.2 Structural and spectroscopic characterisations of the LaAlO3/SrTiO3 bi-interfaceheterostructures . . . 79

4.3.3 Superconducting properties of the LaAlO₃/SrTiO₃ bi-interface 85 4.4 Discussions . . . 87

5 Conclusions and Perspectives 91

A Friction Force Microscopic Measurements 95

B RHEED for step-flow growth 99

References 109

Figure 1 –Lego bricks pattern, PSDgraphics.com

Inspire and develop the builders of tomorrow

— LEGO.com One story that my parents always love to tell is how I was amazed by the toy bricks when I was a little child. Though I barely recall, apparently my favourite was to "leg godt" (the Danish words meaning "play well" from which the name "Lego"

derives) these bricks. The paramount amusement that dragged me into obsession must be the collection of diverse colours, the breathtaking process to construct different objects and eventually to become a builder of my own "masterpiece". As stated by the world’s largest toy company, the Lego bricks have inspired millions of people to become builders of tomorrow.

As solid state physicists, we sometimes have the aspiration to be the builders of future. Experience shows that we are. The success of field-effect transistors (FETs), which are the fundamental building blocks of modern information and communication technology, stands as a prominent example. Nowadays, thousands of millions of FETs are fabricated for the widely used pocket-size smart devices. Like the spirit in the Lego

patterns, scientists have successfully fabricated so-called heterostructures combining different semiconductor materials with different functionalities as their use of different

"colours". One particular interest, which the Lego bricks do not offer, is the creation of novel functionalities at the interfaces between the materials, which are absent in the parent compounds. Indeed, it is the interfaces that offer the playground to generate new electronic properties which have potential in applications.

An important class of materials with rich physics and outstanding electronic prop- erties is transition metal oxides in which diverse functionalities were discovered. These materials often take a similar structure and thus provide an opportunity of combining them in an artificial way to create new heterostructures. Advances in the material fabrication and characterisation have enabled deposition of a large range of heteroepi- taxial oxide structures with sharp interfaces. The quest for novel phases and electronic properties at oxide interfaces has ignited the research community to use all possible

"colours" to design their new "toys", just like in the Lego games.

In this thesis, we have investigated the heterointerface between two band insulators, LaAlO3and SrTiO3, where a two dimensional electron liquid is present. The combi- nation of these two perovskite oxides creates a sparkling example of new emergent phenomena arising at the interface that do not exist in their bulk form. InChapter1, we will give a broad overview of a glaring member of the perovskite oxide family, SrTiO₃. We will also introduce the celebrated LaAlO₃/SrTiO₃interface system, and its intriguing properties. This thesis will develop along two main lines: one is towards understanding the origin of the 2DEL at the interface; the other is to tackle the technical issues that lie in the pathway towards realising such 2DEL in an artificially grown SrTiO3 film as well as fabricating LaAlO3/SrTiO3multilayers.

InChapter2, we will present a landmark experiment using materials design to tune the polar discontinuity, aiming to provide direct evidences of the so called "polar catastrophe" scenario. The change in the polar discontinuity, induced by alloying LaAlO3with SrTiO3, produces a clear shift in the threshold thickness for the appearance of the 2DEL and also modifies the quantum confinement at the interface.

Chapter3 is devoted to the fabrication of superconducting interfaces between LaAlO3 and a homoepitaxially grown SrTiO3 thin film. This structure serves as a starting point for the realisation of multilayers (or superlattices). We show that high growth temperature for SrTiO3is key to hosting a superconducting 2DEL residing in the SrTiO3 film. We also propose a model to explain why standard growth temperature for SrTiO3is not adequate to obtain conducting interfaces.

Building on the knowledge acquired in Chapter3,Chapter4discusses the fabrica- tion of the LaAlO3/SrTiO3 bi-interfaceheterostructures. Besides the demonstration of high crystalline quality from transmission electron microscopy (TEM) study, we show that 2DELs are present both at the top and bottom interfaces in suchbi-interface heterostructure. We also fabricated the first field-effect device on this LaAlO3/SrTiO3

bi-interface, and present a fully detailed study of its superconducting properties.

We will draw our conclusions inChapter5, and list some relevant open questions and perspectives, where exciting new physics still waits to be explored.

INTRODUCTION

1.1 Functional oxides

1.1.1 Perovskite oxides

Perovskite compounds have the general formulaABX₃, whereAandBdenote a large cation and a small cation, respectively, andXstands for an anion, which is usually either oxygen or halogen, that bondsAandB. So, just as the name implies, perovskite oxides represent the family with formulaABO3; this family of compounds will be at the centre of my study.

Due to the multiple choices for theAandBcations, perovskite oxides have a large variety of chemical combinations and of crystal symmetries, such as cubic, tetragonal, orthorhombic, rhombohedral and monoclinic. Besides that, oxygen stoichiometry [1], the amount of cationic vacancies [2], doping by solid solution [3] and chemical substi- tution [4] are all effective parameters that change the properties of these compounds.

As a result of all these possibilities, perovskite oxides show a broad spectrum of physical properties including metallic, semiconducting, insulating, superconducting, pyroelectric, piezoelectric, ferroelectric, (anti-)ferromagnetic as well as multiferroic behaviours [5,6]. These behaviours can be dramatically changed, enhanced or tuned especially when the perovskite oxides are under or near a structural phase transition controlled by a change of temperature, pressure or composition. When prepared in thin film form, substrate clamping effect, size effect, electric field effect can also have a great impact on these properties [7,8].

A unit cell of a perovskite oxide with cubic structure, such as BaTiO3or LaVO3, is drawn in Fig.1.1(a). TheAions are at the corners of the cube whileBions are at the centre of the cell surrounded by 6 first-neighbour oxygen atoms which form an octahedron. When arranged in a periodic structure as shown in Fig.1.1(b), these octahedra are connected, sharing one oxygen atom between two of them. TheBO6

octahedron is very important since many electronic properties depend onB-O bonding lengths andB-O-Bbonding angles.

A perovskite oxide can also be considered as a sequence of alternatingAO and

A B O

(a) (b) (c)

Figure 1.1 – Schematic sketch of the perovskite oxideABO3structure:(a) One cubic unit-cell of perovskite oxide withAions at the corners, aBion at the centre of the cube, and O ions at the centre of every faces; (b) Perovskite oxide structure with oxygen octahedra shown in blue; (c)ABO3structure can also be described as a stacking ofAO andBO2

atomic planes.

BO2 atomic layers. The schematic is shown in Fig.1.1(c). This kind of description is essential for the work presented here and will be used later in Chapters1and2when the polar discontinuity at the LaAlO3/SrTiO3interfaces is discussed.

1.1.2 SrTiO3

Transition metal oxides in the form of perovskite exhibit rich physics and extraordinary properties. Among them, SrTiO3 is a twinkling example. SrTiO3has been intensively studied during the past decades. This is not only because SrTiO3is a band insulator (indirect band gap 3.2 eV) with large dielectric constant and an incipient ferroelectric instability [9] (Tc → 0 K), but also because of its unique conducting properties:

it can be tuned from an insulator into a semiconductor or a metal by doping [10].

Even superconductivity can be achieved in doped SrTiO3 with critical temperatures

≤400 mK [11,12]. SrTiO3 can be prepared as single crystal and it is commonly used as a substrate for growing many oxide thin films, like ferroelectrics [7], high-Tc

superconductors (HTSs) [13] and colossal magnetoresistance (CMR) oxides [14]. In this work, SrTiO3 is also used as a substrate. SrTiO3 is cubic at room temperature (space groupP m¯3m) with a lattice constant of 3.905 Å. In this cubic structure, the Ti- O-Ti bond angles are 180^◦. Below 110 K, the material undergoes an antiferrodistortive (AFD) transition in which neighboring TiO6 octahedra slightly rotate in opposite directions about a vertical axis [Fig.1.2(a)] [15]. This transition makes SrTiO3to be tetragonal (space groupI4/mcmwitha⁰a⁰c⁻rotation pattern in Glazer notation) [16]

and is second order. However, SrTiO3 remains centro-symmetric, hence it is not ferroelectric down to the lowest temperatures.

It has been predicted that, there should be another phase transition occuring at about 40 K, at which Ti ions would move with respect to oxygen ions [Fig.1.2(b)]. This would lead to a spontaneous polarisation and thus ferroelectricity. In fact, this transition is suppressed by the AFD and presents itself in the form of quantum fluctuations so that ferroelectricity cannot be established in pure SrTiO₃[17]. Therefore SrTiO₃is regarded as an incipient ferroelectric and remains a quantum paraelectric when temperature approaches zero Kelvin [9]. However, due to the incipient ferroelectric quantum fluctuations, the dielectric permittivity of single-crystal SrTiO₃increases dramatically

Figure 1.2 – Schematics of two soft-mode-driven phase transitions in SrTiO3single crystals:(a) Cubic-to-tetragonal second-order antiferrodistortive (AFD) phase transition at about 110 K; (b) The ferroelectric phase transition which is suppressed by quantum fluctuation. The grey circles are O ions and the solid circles are Ti ions.

with decreasing temperature, from a few hundred at room temperature to up to∼10⁴ at 4 K. This increase of dielectric constant is similar to the one observed in other ferroelectric materials, when they approach the paraelectric-ferroelectric transition [18].

The large dielectric constant measured at low temperatures is strongly reduced upon application of an electric field [19].

Of relevance to this thesis, SrTiO3displays fascinating electronic transport prop- erties. An insulator-to-metal transition can easily be induced in SrTiO₃crystals upon elemental substitutions or chemical off-stoichiometry. This happens at a critical carrier density as low as 10¹⁶cm⁻³[20]. La- [21,22], Nb-doping [4,23,24] (Sr1−xLaxTiO3

or SrTi1−yNb_yO₃), or oxygen reduction [10,23,25] (SrTiO3−δ) can produce metallic behaviour with a broad range of electron densities and mobilities [20]. For the case of SrTiO3−δ, in a simple picture, each oxygen vacancy generates two electrons. De- tailed study on the electronic transport properties of doped SrTiO₃ started from the 1960s [23,26]. The origin of the insulator-to-metal transition occuring at low doping is linked to the large dielectric constantr. In the hydrogen model for the shallow donors, the donor binding energyE_D, and Bohr radiusa_Bare determined by:

ED=−13.6 eV(m^∗_e me

)(1 r

)² (1.1)

aB= 0.53 (r)(me

m^∗_e) [Å] (1.2)

wheremeandm^∗_eare free electron and effective masses. Considering an effective mass m^∗_e ∼2-10m_eand_r∼10⁴(T = 4.2 K),E_Dis very small (10⁻¹µeV at 4.2 K), while aBcan be rather large (∼10³Å). This means that the charges easily unbind and thus contribute to the transport. Other phenomena, like the almost temperature-independent Hall coefficient measured in crystals, can also be explained by this model, where the shallow donors remain ionised in the full temperature range [20].

Figure1.3illustrates density of states (DOS) and a calculated band structure of

Ti 3d3z2-r2, x2-y2

O 2p Band gap

Ti 3dxy, yz, xz

Figure 1.3 – Calculated DOS and band structure of SrTiO₃using LDA:Left- DOS marked by a band gap between Ti3dand O2porbitals with Ti3dorbitals further split into two branches (eg andt2g); Right- band structure revealing an in-direct band gap.

Adapted from [27].

Figure 1.4 – 3dorbitals of Ti in different environments:Energy levels of Ti 3dorbitals in different symmetry configurations. The values of the splittings are determined by both theoretical and experimental studies. Adapted from [28].

(a)

(b)

(c)

E -E

(e V )

Figure 1.5 – Electronic structure of the conduction band bottom of SrTiO3 in the absence of spin-orbit coupling:(a) Dispersion of thexy−,yz−andxz−bands along theΓ−X andΓ−Y directions in a perfect cubic SrTiO3; (b) A breaking of degeneracy atΓpoint due to tetragonal distortion, leading to a higher energy ofxy−band with∆T≈ 3 meV; (c) LDA band dispersion of the un-doped SrTiO3alongΓ−X direction. Fermi energies for different doping levels are indicated [29].

un-doped cubic SrTiO3using local density approximation (LDA) calculation without details in the low energy regime atΓpoint [27]. For the un-doped SrTiO3, Ti is in a4+valence state with3d⁰ electronic configuration. An in-direct band gap can be observed with the valence band (VB) maximum at theR point and the conduction band (CB) minimum at the zone centre. The gap has a smaller value than the one found experimentally, which is a known problem for LDA calculations. Ti3dorbitals compose the CB of SrTiO3while the VB is formed by O2pstates. For momenta near theΓpoint, the crystal field in cubic SrTiO3further splits thedband into triplet low energyt_2gbands (d_xy,d_yzandd_xz) and doublet higher energye_g (d_x²_−y²,d_3z²_−r²) bands, with a gap of typically∼2 eV. We can also see this splitting effect by looking at the energy of the Ti3dorbitals in different environments (Fig.1.4). For lightly doped SrTiO₃, it is therefore sufficient to consider only the t_2g bands when constructing the electronic structure at the CB bottom. For cubic SrTiO3, theset_2gsub-bands are degenerate at theΓpoint if spin-orbit interactions are neglected, as shown in Figs.1.3 and1.5(a). However, along different axes in the momentum space, the hopping terms are different for different orbitals, resulting in an anisotropic band dispersion with effective massesm^∗_h,m^∗_l, as shown in Fig.1.5(a).

The degeneracy at theΓpoint is lifted by two phenomena: a structural transition to a tetragonal low temperature phase (with energy term∆T) and the spin-orbit interaction (∆_SO). They produce effects in energy scales that are relevant to the Fermi energy of doped SrTiO3 for a wide range of doping levels. As discussed earlier, above 110 K, SrTiO3 has a cubic symmetry while below, the symmetry is lowered to tetragonal due to a rotation of the oxygen octahedra [30,31]. As a consequence, this transition breaks thet_2gstates into two groups of states by shifting thed_xyorbital about 3 meV higher in energy than thedxz/dyzorbitals (and a similar split occurs for theegstates).

The resulting electronic structure is shown in Fig.1.5(b). LDA calculation on the

band dispersion of the un-doped SrTiO3alongΓ−Xdirection is shown in Fig.1.5 (c) [29,32]. Furthermore, the atomic spin-orbit coupling is also at play, adding another element in defining the fine electronic structure, especially around the CB minimum.

In order to accurately characterise the electronic structure in the vicinity of theΓpoint, MacDonald and coworkers [33,34] have constructed ak·pmodel that captures the electronic structure with the splittings due to the presence of∆Tand∆SO. They found a band structure where the bands have mixed orbital character. This method sets up an effective Hamiltonian that can be used to derive the low energy physics for ad⁰ perovskite. The parameters, i.e. effective masses m^∗_h, m^∗_l, tetragonal splitting∆T, spin-orbit interaction∆SO, etc., of this model can be determined using Shubnikov-de Haas (SdH) oscillation experiments, as discussed in [34] .

Interest in doped SrTiO3was also promoted by the discovery of a superconducting dome upon varying the carrier concentration [12], with transition temperaturesTc

in the range of a few hundred of mK. In the seminal paper of Schooley et al.[12], superconductivity was observed with a carrier density as low as∼10¹⁸cm⁻³. This makes SrTiO3the superconductor known so far with the lowest carrier concentration – "the most dilute superconductor" [35].T_ccan be varied upon changing the doping level by chemical doping (Nb- or La doping), reducing oxygen and field-effect [36].

Figure1.6shows the extension of superconducting state in a temperature (Tc) - carrier density (n) plane as measured in 1967 [37] and from recent data [38]. In Fig.1.6(b), we see that superconductivity can be observed for a carrier concentration of∼10¹⁷cm⁻³, where a superconductor-to-insulator transition (SIT) occurs. For the case of SrTiO3−δ, this means a remarkably low concentration of oxygen vacancies (less than 0.03%) [39].

By measuring the evolution of the frequencies in the SdH oscillations, Linet al.[38]

uncover different bands in the electron-doped SrTiO3 single crystals with different cyclotron masses and the corresponding Fermi energy. They identify two critical dopingsn_c1andn_c2[40], which mark different regimes of superconductivity due to the filling of the different bands.

Beyond the interesting physics reviewed here on SrTiO3crystals, other intriguing properties have been unveiled for the system in the thin film form. Using MBE, La- doped SrTiO3films showing extremely high electron mobility have been fabricated [41].

Two dimensional (2D) superconductivity and SdH oscillations have been demonstrated in ultrathin Nb-doped films grown by pulsed-laser deposition (PLD) [42]. Giant thermopower Seebeck coefficient was observed in such SrTiO3-doped superlattices [43].

These properties set a significant application potential for this material.

1.2 The LaAlO

/SrTiO

functional interface

In this thesis, we study the electronic properties of a two dimensional electron liquid (2DEL) present in SrTiO3when a LaAlO3/SrTiO3 interface is fabricated. This field of research was launched by the pioneering work of Ohtomo and Hwang [44]. In their 2004 landmark paper, they discovered that by depositing a few atomic layers of an insulating material, LaAlO3, on top of a (001) oriented single-crystal of SrTiO3

(terminated with TiO2planes), the interface is conducting. The two dimensional nature of this electron system was later confirmed by different experiments [45–51]. Due to

(a)

(b)

Figure 1.6 – Superconducting transition temperaturesTc as a function of carrier concentration (n) for doped SrTiO3 single crystals: (a) The solid circles represent experimental data; the empty circles demonstrate the results of the theoretical calculations;

the bracketed solid circles are data used as input for theTccalculation [37]; (b)Top- measured frequencies in SdH oscillations resulting from the progressive filling of different bands; Bottom-T_c as a function of three dimensional (3D) carrier density estimated from Hall measurements. Solid squares represent reduced crystals (SrTiO3−δ) and open squares show Nb-doped crystals (SrTi1−xNbxO3withx= 0.001, 0.002, 0.01, and 0.02, repectively). Error bars indicate the width of the transitions. Adapted from [38].

(a) (b)

Figure 1.7 – The LaAlO₃/SrTiO₃ interface: (a) Atomic configuration of LaAlO3/SrTiO3 interface along [001] crystallographic direction: the0, +and−rep- resent the formal ionic charge of each atomic planes; (b) Temperature dependence of the sheet resistance of a standard LaAlO3/SrTiO3interface.

the carrier density higher than that in semiconductor electron gases and to account for the electronic interaction characteristics of the oxides [52,53], this system is referred as 2D electron liquid. In this section, we will discuss the origin of the charge carriers appearing between the two insulators, present the description of the electronic band structure and the transport properties both in the normal and superconducting states of this fascinating system.

1.2.1 Polar discontinuity

Although more and more evidence point to an intrinsic origin for the 2DEL, there is still an on-going debate on the origin of the conduction at the LaAlO3/SrTiO3interface.

Two main scenarios have been proposed: on one side, a doping mechanism related to the polar/non-polar nature of the interface; on the other side, a chemical doping mechanism due to the formation of oxygen vacancies in SrTiO3(or intermixing). While several experiments have proven that oxygen vacancies in SrTiO3are possibly not at the origin of the charges in samples prepared in proper conditions, the details of the polar mechanism are discussed. Figure1.7(a) shows the atomic planes with the ionic charges for the heterostructure along the [001] crystallographic orientation. We can see that the layer stacking SrO⁰/TiO⁰₂/LaO⁺¹/AlO⁻¹₂ across the interface (n-type interface) leads to a polar discontinuity: this has been suggested by Nakagawa et al.[54] to explain the formation of the 2DEL. On the other hand, the interface with stacking of TiO⁰₂/SrO⁰/AlO⁻¹₂ /LaO⁺¹(p-type) is insulating. In this picture, the polar discontinuity produces a diverging potential in the LaAlO3layer, which causes an electronic break- down (Zener breakdown). For then-type interface, electrons with density of 0.5 per 2D unit-cell (3.3×10¹⁴cm⁻²) are thus transferred at a critical thickness of the LaAlO₃ layer from the top surface into the SrTiO3 in order to compensate the electric field.

Experiments have confirmed that the charge transfer occurs only when the LaAlO3

layer thickness exceeds 3 u.c. [55], a value predicted by theory.

(a)

(b)

(c)

Figure 1.8 – Schematics of the band alignment at the LaAlO3/SrTiO3interface along the normal directionzfor the surface oxygen vacancy scenario:(a) Below the LaAlO3

critical thickness; (b) The creation of oxygen vacancy donor state at the LaAlO3surface and the transfer of two electrons to the interface; (c) Accumulation of charges at the interface. Adapted from [56].

After this initial model, different experiments have reported the sensitivity of the 2DEL to the LaAlO3 surface state. Xieet al. reported a large modulation of the interfacial conductivity by using surface adsorbates [57] or surface modification [58].

In their work, by covering the LaAlO3surface with polar molecules (such as water, acetone, ethanol, etc.), an enhancement of the conductivity has been observed. This clearly emphasises the importance of the LaAlO3 surface states on the conducting properties of the interface. Furthermore, the group of Jeremy Levy at the University of Pittsburgh has developed a way to create nanometer-sized conducting regions using a conductive atomic force microscopic (C-AFM) technique on samples that are on the verge of the insulator-to-metal transition (i.e. a LaAlO3thickness of∼3 u.c.) [59,60].

The mechanism is related to additional charges and electric field produced by the adsorbate layer at the LaAlO3surface to stabilise the 2DEL [61,62].

Theoretical work has recently been put forward investigating how different surface defects in the LaAlO₃layer could be at the origin of the conductivity. The formation energy of these defects was calculated in the presence of an electric field. According to Yu and Zunger’s calculations [63], cationic anti-site defects (La↔Sr and Ti↔Al) can form as the LaAlO₃ layer grows before reaching the critical thickness. They argue that these anti-site defects contribute to compensating the electric field inside LaAlO3and can be the source of the possible magnetism discovered in the system (see Section1.2.5). When the thickness of the LaAlO₃layer reaches the critical thickness, oxygen vacancies spontaneously form on the LaAlO3 surface since their formation energy drops below zero [56]. According to their theory, these oxygen vacancies provide the free electrons that under the effect of the electric field are transferred into the Ti3dbands at the interface, as shown in Fig.1.8. Bristoweet al.[56,64] predicted that oxygen vacancies can also be created by redox reaction involving water on the surface at a critical LaAlO₃ thickness of∼4 u.c.. The formation of such oxygen vacancies was also discussed in [63].

Besides these plausible "intrinsic" doping mechanisms, off-stoichiometry, espe- cially oxygen vacancies, in SrTiO3 has also been considered to be relevant to the observed conductivity. As we discussed in Section1.1.2, SrTiO3can be doped to be- come conducting by oxygen vacancies via an annealing process at elevated temperature in vacuum. We will discuss these different doping scenarios in details in Chapter2. We already note that in order to avoid as much as possible oxygen vacancies formed during the LaAlO3 thin-film growth by PLD (See Section 1.3), an annealing step in high oxygen pressure is generally employed after each sample growth. Samples fabricated using the general growth conditions, which will be described in the next section, are called "standard samples".

Figure1.7(b) shows a temperature dependent sheet resistance curve of a standard LaAlO₃/SrTiO₃ sample. A metallic behaviour is observed with a room-temperature sheet resistance of ∼20 kΩ. Transport experiments performed at 4 K on standard samples reveal a carrier mobility in the order of ∼1000 cm²V⁻¹s⁻¹ and a 2D car- rier density of a few 10¹³ cm⁻² [65,66]. This carrier density, estimated from Hall effect measurement, is smaller than that calculated from the "polar discontinuity"

model (3.3×10¹⁴cm²V⁻¹s⁻¹), possibly due to charge trapping and/or localisation for different sub-bands.

1.2.2 Electronic structure

Quantum confinement adds one important constraint to the electronic structure of the 2DEL. As a consequence, the electronic structure of the LaAlO₃/SrTiO₃ interface has been shown to be distinct from the one of bulk SrTiO3. This difference has stimulated considerable research interest and has been studied intensively. Before discussing the electronic structure, it is worth mentioning the study on the thickness of the conducting layer, which provides an estimate of the quantum confinement. Basletic et al.[46] "imaged" the conducting layer by using conductive atomic force microscopy (C-AFM) on the cross-section of a sample. From their work, the confinement of the electrons and the role of the oxygen post-annealing were clearly revealed: at room temperature the 2DEL was found to be confined within a few nanometers in fully oxidised samples while the conducting region extends to hundreds of nanometers in samples prepared without oxygen annealing. Following this work, Copieet al.[47]

measured the temperature dependence of the thickness of the 2DEL, which evolves from∼4 nm at room temperature (an estimation probably limited by the tip resolution) to∼12 nm at 8 K, as shown in Fig.1.9(a). Using an electric field dependent dielectric permittivity (E), they also modelled the confining potential as well as the charge distribution by solving Poisson equation self-consistently. As they are transferred to the interface, electrons induce an electric field that lowers the dielectric constant . The consequence is to reduce the screening efficiency of SrTiO3and confines the electrons within a few nanometers next to the interface, as observed experimentally.

Figure 1.9 (b) illustrates the electric field and confinement length calculated as a function of the carrier density n2D. Forn2D ≥ n^lim_2D, the electric field increases dramatically, resulting in an enhanced confinement. Inversely, for n_2D < n^lim_2D the electron liquid extends a few hundred nanometers inside the SrTiO3 crystal. This first study highlights the relationship between the confinement and the carrier density; we will come back to this in Chapter2. Infrared ellipsometry experiments [50] performed at 10 K confirmed that the 2DEL extends for about 11 nm. At room temperature, different experiments including hard X-ray photoelectron spectroscopy [67], soft X-ray angle resolved photoemission spectroscopy (ARPES) [68] suggest that the 2DEL is extremely confined within 1-3 u.c.. This change in confinement with temperature is due to the giant temperature dependence of the dielectric constant of SrTiO3.

The effect of the quantum confinement is to modify the orbital order of the bands and to generate sub-bands due to the quantisation of the out of plane component of the momentum. In a quantum well, the energy levels (E_ψ) associated with states ψ having an effective mass m^∗_⊥ along the confinement direction are quantised as Eψ ∝1/m^∗_⊥(ⁿ_L)², beingLthe quantum well width andnthe quantisation number.

As a consequence, for a confinement alongz,dxy orbitals have a lower energy than d_xz/d_yzorbitals since their effective mass alongzis large [(m^∗_xy)⊥∼7-10, (m^∗_xy)_k ∼ 0.7-2].Ab initiocalculations without considering spin-orbit effects support this orbital reconstruction [69]. In the case of a strong confinement (thickness of a few u.c.), they show thatd_xy orbitals appear lowest in energy (Fig.1.10). However, these orbitals are probably filled with charges subject to in-plane localisation, which consequently do not contribute to transport [71]. At higher energies sitdxz/dyzorbitals that extend over several layers and contribute markedly to transport [71,72]. This effect will

(a)

(b)

Figure 1.9 – The thickness of the LaAlO3/SrTiO3interface:(a) Measured by C-AFM at 300 K and 8 K showing a conducting thickness of 4 nm and 12 nm, respectively; (b) Calculated confinement length and electric fieldEas a function of the 2D carrier density n2D. Then^lim_2D marks the criticaln2Dabove which the electrons are confined within a few nanometers close to the interface. Adapted from [47].

(a) (b)

Figure 1.10 – Band structure for the LaAlO3/SrTiO3 interface (1): (a) Ab initio calculation of the band structure for a sheet carrier densitynsof 0.5 /2D u.c. [69]; (b) Fermi surface measured by soft X-ray resonant ARPES compared with DFT calculations [70].

The O2psurface band refers to the hole pocket predicted in the Zener breakdown scenario forming at the LaAlO3surface.

Figure 1.11 – Band structure for the LaAlO₃/SrTiO₃interface (2): A sketch of the electronic structure according to experimental observations.

further be discussed in Chapter2. When the thickness of the 2DEL becomes large (for instance, due to a low carrier density), the confinement is less effective. In this case, the electronic structure is rather similar to that of bulk SrTiO3,dxz/dyzbeing lowest in energy [73]. The first measurements on the electronic structure of the LaAlO3/SrTiO3

interface was performed by Salluzzoet al.[74] using X-ray absorption spectroscopy.

They found that the degeneracy of the Ti 3d t2g orbitals is lifted and an electronic reconstruction occurs at the interface. The Ti 3dxy orbitals become the first available states in the system. This orbital reconstruction is sketched in Fig.1.4. The electronic structure of the system has also been investigated by soft X-ray resonant ARPES measurements [68,70,75], suggesting a reconstructed Fermi surface, as compared to bulk SrTiO₃. The experimental picture of the electronic structure is sketched in Fig.1.11. No signature of further sub-bands splitting (d_xy1,d_xy2, ...,d_xz,yz1,d_xz,yz2, ..., etc.), as suggested byab initiocalculations, has so far been observed. This discrepancy may originate from the difference between the thickness measured experimentally at low temperature and the thickness imposed by the calculations. Rashba spin-orbit coupling also modifies the electronic structure [76,77], for instance, by mixing different orbital states and creating features at crossings between bands of different orbitals.

However, these features are currently below the resolution of the ARPES technique, thus difficult to be revealed.

1.2.3 Superconductivity

One of the most exciting phenomena that the system demonstrates is superconductiv- ity. Cooling the LaAlO₃/SrTiO₃interface down to dilution temperatures, the 2DEL undergoes a transition into a superconducting state with aT_caround 250 mK. This was discovered in our lab by Reyrenet al.[78] in 2007. The transition temperature of the interface is comparable to the one of bulk SrTiO₃(Section1.1.2). However, further de- tailed analysis of the transition shows that superconductivity possibly sets in through a Kosterlitz-Thouless (KT) transition, as expected for a 2D superconductor [45,53,78,79].

Scaling analysis of theI−V characteristics and theT dependence of the resistance is consistent with this picture [78]. Figure1.12(a) shows the superconducting transitions when a magnetic field is applied perpendicular (top) and parallel (bottom) to the inter- face. The critical fields (H_⊥^∗,H_k^∗) for these two orientations are reported in Fig.1.12 (b). We observe a large anisotropy of the system that is attributed to the confinement of the superconducting 2DEL. With these measurements, the in-plane superconducting coherence length and the superconducting thickness are extracted to be∼70 nm and

∼11 nm, respectively, using the two formula listed below (Eqs.1.3and1.4).

ξ_k(T) = s

Φ0

2πµ₀H_⊥^∗(T) (1.3)

whereΦ₀ is the flux quantum andξ_k(T)is the in-plane coherence length.

Assuming a superconducting layer thicknessd_SCmuch smaller than the penetration depthλand the coherence length, theH_k^∗(T)is linked todSC as

(a) (b)

Figure 1.12 – The anisotropy of the superconducting properties of the LaAlO3/SrTiO3 system: (a) Sheet resistance as a function of temperature for differ- ent magnetic fields applied perpendicular (upper panel) and parallel (lower panel) to the interface; (b) Detailed analysis of the characteristic magnetic fields as a function of tem- perature for the perpendicular and parallel configurations showing a large anisotropy. The inset of the upper panel shows details of the perpendicular field data. Adapted from [45].

d_SC =

√ 3Φ0

πξ_k(T)µ₀H_k^∗(T) (1.4)

from which, dSC can be extracted. The fact that the critical field for the parallel direction exceeds the paramagnetic limit (Clogston-Chandrasekhar) by a factor 4-5 is a possible signature of the presence of a large spin-orbit coupling in the system [80,81].

1.2.4 Field-effect experiments

In SrTiO₃crystals, as shown in Fig.1.6, the superconducting transition temperatureT_c depends on the doping level. At the LaAlO3/SrTiO3interface, it has been shown that tuning the carrier density by electric field effect modifiesTcas well as other physical properties.

The 2DEL being sandwiched between two good dielectric materials naturally provides a fertile ground for electrostatic field effect experiments. In particular, SrTiO3

is a superior dielectric material possessing a remarkably large dielectric constant at low temperature. This offers a unique opportunity to induce large polarisations to achieve high tunability of carrier density. The first field effect experiment was reported by Thielet al.[55]. In their work, they demonstrated that samples with LaAlO₃thickness of 3 u.c., which are insulating but on the verge of the insulator-to-metal transtion, can be switched to a metallic state upon applying 100 volts across the 500µm thick SrTiO₃substrate, as shown in Fig.1.13(a). Figure1.13(b) demonstrates the switching behaviour of the 3 u.c. sample upon the gate modulation in the working mode of a field-effect transistor. Surprisingly the system maintains an ON state also for zero gate voltage applied. Efforts have also been made to fabricate devices using LaAlO₃as the

(a) (b)

Figure 1.13 – Electric field effect experiments on a 3 u.c. LaAlO3/SrTiO3 sample:

(a) Transport data (sheet resistance vs. temperature) taken upon 100 Volts applied across the substrate, in comparison with those of samples of 4 and 6 u.c., showing the 2DEL can be turned on by electric field effect; (b) Memory behaviour of the 2DEL: (lower panel) gate voltage applied and (upper panel) the corresponding resistance switching. Adapted from [55].

gate dielectric material. In this way, the group of Jochen Mannhart has successfully fabricated integrated circuits containing tens of thousand of field-effect transistors (FETs) based on the LaAlO₃/SrTiO₃ interface [82].

In our lab, by fabricating LaAlO₃/SrTiO₃field effect devices, Cavigliaet al. demon- strated electrostatic field effect control of the ground state of the system [79]. Sweeping the back-gate voltage (Vg), a superconducting dome is revealed as shown in Fig.1.14 (a), with a superconductor-to-insulator transition (SIT) at large negative voltages. This quantum critical point (QCP) seems related to the position of the Fermi level being at the edge of the heavy bands (dxz/dyz). Given the behaviour ofTcupon gate voltage, the phase diagram can be divided into an "under-doped" regime and an "over-doped"

regime, separated by an optimal doping whereTcis maximum. Some authors relate this optimal doping level to a critical carrier density that corresponds to the filling of the heavy bands [Fig.1.14(b)] [83]. However, in another study it was argued that this critical density, which is characterised by the occurrence of a non-linearity of the magnetic field dependence of the Hall resistance, happens at a lower doping level: a density that corresponds to the onset of the superconductivity [28]. Beyond the super- conducting region, in the depletion regime (negativeV_g), an insulating ground state was uncovered while in the accumulation regime (positiveVg), a metallic behaviour is observed [84].

The suppression of superconductivity in the "under-doped" regime was discussed in the framework of superconducting quantum fluctuations which lead to a dependence ofTconVg with a critical exponentz¯ν = 2/3[Fig.1.14(a)]. This mechanism has recently been supported by a tunnelling experiment through an ultra-thin LaAlO₃layer into the 2DEL [53]. As we can see in Fig. 1.15, from the tunnelling spectrum, a superconducting gap can be observed across the phase diagram. In the "under-doped"

regime, whereT_cestimated from transport is strongly suppressed, the gap∆remains finite with an even increasing trend. This experiment suggests that phase fluctuations play an important role in determining Tc in the "under-doped" regime for this 2D system. The superconducting phase diagram has stimulated enormous research interest,

(a) (b)

Figure 1.14 – Superconducting phase diagram of the LaAlO3/SrTiO3interface: (a) A superconducting dome revealing a tunableTc; the suppression of superconductivity in the "under-doped" regime is argued to be the result of possible superconducting fluc- tuations; adapted from [79]; (b) A correlation between superconductivity and a critical density; adapted from [83].

(a) (b)

Figure 1.15 – Tunnelling experiments on the LaAlO3/SrTiO3 interface: (a)dI/dV spectra for different gate voltages showing a superconducting gap behaviour; (b) (Upper panel) superconducting gap (∆) andTc(estimated from transport) as a function of gate voltage; (lower panel) image of the device used for transport and tunnelling experiments:

the outer and centre gold rings are the electrodes for transport measurements while a middle ring is the contact for tunnelling across the LaAlO3layer into the 2DEL. Adapted from [53].

(a) (b)

(c)

Figure 1.16 – Tunable Rashba spin-orbit interaction at the LaAlO3/SrTiO3 inter- face:(a) Magnetoconductance for different back gate voltages; (b) Characteristic spin- orbit and inelastic fields extracted from fittings of magnetoconductance curves as a function of the gate voltage using Maekawa-Fukuyama formula [85]; (c) The spin-orbit and inelas- tic scattering time as a function of the gate voltage (open circle: the prediction of the spin relaxation time as a function of gate voltage based on the Elliott-Yafet (EY) mechanism, which clearly differs from the data, confirms the spin-orbit interaction being Rashba type).

Adapted from [80].

for instance, which aims at understanding the link between the interfacial and the bulk SrTiO3 superconductivity.

Apart from the electric field control of superconductivity, the magnetotransport properties in the normal state can also be tuned by the field effect. As shown in Fig.1.16(a), at 1.5 K, the magnetoconductance changes dramatically upon changing V_g, featuring a crossover from weak localisation (at -300 V) to weak anti-localisation (at +50 V), eventually to a completely negative magnetoconductance. A large tunable Rashba-type spin-orbit interaction arising from the interfacial breaking of inversion symmetry was revealed, by the application of an external electric field [80,86]. This certainly sets a new paradigm for the realisation of the spin field effect transistor based on interfaces between complex oxides. Fitting the magnetoconductance using the Maekawa-Fukuyama formula [85] allows the strength of the characteristic magnetic field related to the spin-orbit and inelastic scattering times to be extracted [Fig.1.16 (b) and (c)]. The evolution of the spin-orbit coupling across the phase diagram and its correlation to the emergence of superconductivity remains two of the most interesting questions on the spin-orbit interaction in the 2DEL [87]. The correlation between spin-orbit coupling and superconductivity was also carefully discussed by Ben Shalom et al.[81].