Oxide superconducting thin films and interfaces studied using field effect

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Thesis

Reference

Oxide superconducting thin films and interfaces studied using field effect

REYREN, Nicolas

Abstract

Nous avons étudié trois systèmes supraconducteurs quasiment bidimensionnels (2D): le NdBa2Cu3O7-δ, un supraconducteur à haute température critique (HTS), le SrTiO3 dopé au Nb (Nb-STO) et l'interface LaAIO3. Dans ces trois systèmes, nous avons examiné les propriétés de l'état supraconducteur pour mettre en évidence les signatures d'une transition 2D Berezinskii-Kosterlitz-Thouless. Dans le cas du HTS, en utilisant l'effet de champ électrostatique, nous avons, entre autre, vérifié la relation entre densité superfluide et température critique en accord quantitatif avec la relation d'Uemura. L'étude du Nb-STO était focalisée sur la modulation locale de la densité de charge par effet de champs ferroélectrique et ses conséquences sur les propriétés supraconductrices dans une hétérostructure supraconducteur/ferroélectrique. Finalement l'interface LaAIO3/SrTiO3 a été caractérisée dans l'état supraconducteur, en champ magnetique, ansi que par effet de champ électrostatique: ces mesures relèvent un diagramme de phase riche et une épaisseur de la couche supraconductrice de 10 nm.

REYREN, Nicolas. Oxide superconducting thin films and interfaces studied using field effect. Thèse de doctorat : Univ. Genève, 2009, no. Sc. 4118

URN : urn:nbn:ch:unige-39556

DOI : 10.13097/archive-ouverte/unige:3955

Available at:

http://archive-ouverte.unige.ch/unige:3955

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

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Université de Genève Faculté des Sciences

Département de physique Professeur J.-M. Triscone

de la matière condensée

Oxide Superconducting Thin Films and Interfaces Studied using Field

Eﬀect

Thèse

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

par Nicolas Reyren

de Begnins (VD)

Thèse n^◦4118

Genève

Atelier d’impression ReproMail 2009

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Résumé en Français

Les oxydes de métaux de transitions sont des matériaux qui présentent une très grande diversité de propriétés électroniques, pouvant dépendre du dopage, de la température, du champ magnétique ou de la pression, et donnant lieu à des di- agrammes de phase complexes. La richesse de ces matériaux et leurs propriétés électroniques variées ont motivé un grand effort de recherche et ont déjà mené à des applications pratiques. Parmi ces oxydes, les pérovskites sont une classe de matériaux particulièrement intéressante. En effet, on trouve dans cette famille de composés, des matériaux présentant des propriétés très différentes, telles que, par exemple, la supraconductivité à haute température critique ou la magnétorésistance colossale. Leur formule chimique ABO₃ relativement simple cache la diversité élec- tronique des phases existantes, tirant leur origine des multiples états de valences possibles des métaux de transitions et des instabilités structurales de ces composés.

Depuis quelques dizaines d’années, la recherche sur les pérovskites a énormément progressé, en partie grâce au développement des techniques de déposition, telle que la déposition par pulses laser (pulsed laser deposition), qui permettent aujourd’hui le contrôle précis de la croissance. La maîtrise de la croissance au niveau atomique permet la réalisation de structures artificielles comme des hétérojonctions ou des super-réseaux, matériaux artificiels qui ne se trouvent pas dans la nature. Le champ des oxydes et des interfaces d’oxydes fournit un terrain de jeu formidable pour ex- plorer les couplages des différents degrés de liberté dans ces nouveaux matériaux qui peuvent potentiellement amener à la découverte de nouvelles propriétés électron- iques.

Parmi la panoplie de techniques expérimentales disponibles, l’effet de champ est un outil de choix qui permet de modifier de façon réversible la concentration de porteurs et ainsi les propriétés électroniques de ces systèmes. En particulier, cette technique permet de changer de façon continue le nombre de porteurs sur une plage assez large pouvant, dans certain cas, générer des transitions de phase, et permettant en particulier l’exploration détaillée de transitions de phase quantiques. De plus, cette approche permet d’étudier l’évolution des propriétés électroniques en utilisant un seul échantillon (dont la densité de porteurs est variée), évitant ainsi les variations d’échantillon à échantillon. Dans cette thèse, nous avons exploré des systèmes supraconducteurs bidimensionnels en utilisant l’effet de champ pour moduler leurs

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propriétés électroniques.

Nous avons commencé par l’étude de NdBa₂Cu₃O_7−δ, un supraconducteur à haute température critique (chapitre 2). En utilisant des films extrêmement minces (3 mailles cristallines) et des échantillons chimiquement sous-dopés, la technique de l’effet de champ nous a permis de moduler la température critique sur une échelle de température remarquablement large (∼ 10K), résultat inédit au moment où ces recherches ont eu lieu. Après avoir vérifié la consistance de nos mesures ré- sistives avec une transition de type Berezinskii-Kosterlitz-Thouless (BKT), nous avons évalué la température critique TBKT associée et avons montré qu’il existe, près du point quantique critique, à l’extrémité sous-dopée du dôme supraconducteur, une relation linéaire entre la variation de TBKT, le changement du nombre de porteurs ainsi que de l’inverse carré de la longueur de pénétration à température nulle1/λ²(0). Ce fait signifie que l’approche du point critique quantique à la transition supraconducteur-isolant se fait avec un exposant égal à un, signature d’une transition se produisant à deux dimensions. Nous avons aussi trouvé un accord quantitatif avec les mesures collectées par Uemura, reliant linéairement la température critique et1/λ²(0) (“relation d’Uemura”).

Nous avons ensuite travaillé sur des hétéro-structures composées d’une couche fer- roélectrique de Pb(Zr,Ti)O₃ et d’une fine couche de SrTiO₃ dopé au Nb (chapitre 3). Dans ce système, l’effet de champ ferroélectrique a été utilisé pour modifier l’état électronique du SrTiO₃ dopé. La polarisation de la couche ferroélectrique est réalisée par microscope à force atomique sur une échelle nanoscopique. Les régions de différentes polarisations peuvent être lues, écrites et effacées. Dans ce système, sur une certaine plage de température, il est possible de choisir localement l’état du SrTiO₃ dopé: métallique ou supraconducteur. Il est ainsi possible de dessiner des circuits ou des structures avec des interfaces “parfaites” (celle-ci étant pure- ment électronique) entre les régions métalliques et supraconductrices, ce qui ouvre de grandes perspectives. Il est envisageable, par exemple, d’étudier des fils supraconducteurs unidimensionnels couplés dans un bain métallique ou de contrôler la présence de “phase slips”. Nous avons amélioré l’effet de champ ferroélectrique dans ces hétéro-structures en réduisant l’épaisseur de la couche de SrTiO₃ dopé.

Finalement, nous avons étudié l’interface entre deux oxydes isolants de bande, LaAlO₃ et SrTiO₃, qui, dans certaines conditions, se trouve être métallique (chapitre 4). L’origine de la présence d’un gaz électronique dans cette hétéro-structure est probablement due à une reconstruction électronique induite par la discontinuité po- laire de l’interface. Nous avons découvert que l’état fondamental de ce système est un condensat supraconducteur (T_c ≈ 200mK) et que celui-ci est extrêmement sensible à l’eﬀet de champ électrostatique. Nous avons aussi reproduit une des plus remarquables propriétés de cette interface, le saut en conductance lorsque l’épaisseur de la couche de LaAlO₃ passe de 3 à 4 mailles cristallines. Des mesures précises de la résistance en champ magnétique et des caractéristiques tension-courant près de

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Résumé en Français vii la transition nous ont permis de déterminer que le gaz supraconducteur est bidi- mensionnel. Nous avons montré que son comportement est compatible avec une transition du type BKT. Le diagramme de phase température-dopage du système a aussi été tracé et révèle un dôme supraconducteur ainsi qu’une phase (à très faible dopage) qui n’est pas supraconductrice et semble être faiblement localisée. Il a été récemment démontré qu’il est possible d’écrire des structures métalliques dans des échantillons isolants (dont l’épaisseur de LaAlO₃ n’est que de 3 mailles cristallines) au moyen d’un microscope à force atomique. Cette approche rejoint d’une certaine manière celle utilisée avec l’eﬀet de champ ferroélectrique avec la diﬀérence impor- tante qu’il est en principe possible d’écrire des structures supraconductrices dans un milieu isolant.

Dans un futur proche, nous pouvons espérer trouver de nouvelles hétéro-structures, interfaçant des matériaux avec d’autres propriétés physiques, exploitant la richesse des oxydes, comme, par exemple, des systèmes ferromagnétiques avec des électrons 100% polarisés. L’ingénierie des interfaces et l’“oxytronique” vont certainement aboutir à des nouveaux systèmes, utiles à la fois pour les applications et pour la physique fondamentale.

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Chapter 1 Introduction

Transition metal oxides display a rich variety of electronic properties. These properties can depend on the doping, temperature, magnetic ﬁeld or pressure, leading to complex phase diagrams. This richness of phenomena has been motivating many researchers to study these materials in great detail. It has also led to practical applications. Within oxide compounds, perovskites are of particular interest: high- temperature superconductivity and colossal magneto-resistance are exquisite examples of phenomena found in this large family. Their simple chemical formula ABO₃, where A and B are cations, hides the diversity of possible phases originating from the multiple valences of transition metals and related to the many structural instabilities found in these systems. Fig.1.1 illustrates this variety of electronic phases found in some oxides (as well as other carbon based materials) as a function of their carrier concentration.

In the last twenty years, research on perovkites has experienced remarkable progress partially due to the advancement in the deposition techniques, such as pulsed laser deposition, where precise control of the epitaxial growth is achieved. This control at the atomic level enables nowadays the realization of artificial structures, like heterojunctions or superlattices, that cannot be found in nature. The field of oxides and oxide interface engineering provides an amazing playground for the physicists to explore the possible coupling of different degrees of freedom in these artificial materials.

The ability to reversibly tune the carrier density and hence the electronic properties has made the electric field effect a tool of choice to explore the electronic phase diagrams in these systems. As shown at the bottom of Fig.1.1, the range of doping potentially reachable by field effect modulation allows different quantum phase transitions to be explored. This is particularly interesting in the study of the critical behavior close to a quantum critical point, where the carrier density can be continu- ously tuned. Moreover, the field effect approach allows one to explore the properties of one single sample, thus avoiding intersample variations.

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Figure 1.1: Illustration of the zero temperature behavior of various correlated materials as a function of sheet charge density. Silicon is shown as a reference. Examples of high-temperature superconductors and colossal magnetoresistive manganites are YBa₂Cu₃O₇ and (La,Sr)MnO₃, respectively. Top bar shows schematically the richness of materials available for field-effect tuning and the spectrum of their phases. AF, FM, I, M, SC, FQHE, and Wigner stand for antiferromag- netic, ferromagnetic, insulator, metal, superconductor, fractional quantum Hall effect, and Wigner crystal, respectively. (Image and caption from [1])

Overview of the thesis

In this thesis, we explore the field effect approach to modify the electronic properties of superconducting thin films. We start by studying extremely thin layers of NdBa₂Cu₃O_7−δ, a high temperature superconductor, to probe the electronic properties in the vicinity of a quantum phase transition (chapter 2). We then investigate heterostructures made of ferroelectric Pb(Zr,Ti)O₃ and thin Nb-doped SrTiO₃ layers. In this system, we use the ferroelectric field effect to modify the electronic properties by controlling the ferroelectric polarization with an atomic force microscope (chapter 3). Local ferroelectric field effect is a very promising technique which offers the possibility to change the carrier concentration on a very small scale. It is also non-volatile and reversible: the ferroelectric domains are switchable many times (∼ 10⁷) before any significant reduction in their polarization (section 3.4).

Finally, we study LaAlO₃/SrTiO₃ (two band insulators) heterostructures which can display a conducting interface. The origin of the conducting electron layer conﬁned at this polar heterojunction interface is most probably due to an electronic reconstruction. We discovered that the ground state is a superconducting condensate which is extremely tunable with an electric ﬁeld (chapter 4).

The thin ﬁlms are grown in Geneva and Augsburg using magnetron sputtering or pulsed laser deposition. Starting from a single crystalline substrate, we grow epitaxial ﬁlms having a crystalline quality approaching that of the substrate. These “high quality” materials allow us to study the electronic properties in optimal conditions.

The different growth techniques are briefly described for the different materials in sections 2.2, 3.2 and 4.2.

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3 The deposition of thin films is the first step in our job, these films must then be characterized. Indeed, their quality is found to be very sensitive to the deposition parameters. Structural characterizations are performed using different probes: X- ray diffraction (XRD), discussed in sections 2.2, 3.2 and 4.2; atomic force microscopy (AFM) and especially piezoresponse microscopy used to image ferroelectric domains, described in section 3.4; and reflection high-energy electron diffraction (RHEED) used during the growth of Nb-doped SrTiO₃ and LaAlO₃, described in sections 3.2 and 4.2.

Electronic properties were studied by magnetotransport measurements at low temperatures 2.4, 3.3, 4.3 and 4.4. For field effect experiments, we realized devices with different geometries as described in sections 2.3, 3.4 and 4.6

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Chapter 2 A Field Eﬀect Study of Under-Doped NdBa ₂ Cu ₃ O _7−δ Thin Films near the Quantum Phase Transition

2.1 A Short Introduction to High Temperature Su- perconductivity

In 1911, G. Holst and H. Kamerlingh Onnes discovered superconductivity [2], three years after the first liquefaction of helium. They observed that mercury, cooled below Tc ≈ 4K, its critical temperature, becomes a perfect conductor providing no resistance to the flow of current. Successively, many other metals and alloys were found to be superconducting. It took 40 years to develop a microscopic theory to explain the phenomenon. The theory proposed by Bardeen, Cooper and Schrieffer (BCS) describes the origin of superconductivity observed in metals and metallic alloys. In these materials, the maximal critical temperatures observed are around 20 K. In 1986 the experimental discovery of superconductivity by Bednorz and Müller in a completely different class of materials with higher critical temperatures [3], gave new hopes to, one day, reach room temperature superconductivity. Due to the critical temperatures substantially higher than before, this new phenomenon was called high temperature superconductivity (HTS) and has generated a fantastic amount of work, with thousands of scientific papers and with the perspective of different practical applications, such as new types of magnets, SQUIDS, superconducting wires, motors, current limiters, MRI and NMR. The discovery was so groundbreak- ing that in just a few years many research activities were refocused, allowing the rapid discovery of new compounds reaching a maximum Tc of about 138 K in Tl doped HgBa₂Ca₂Cu₃O_8+δ [4]. These HTS all have in common CuO₂ planes where superconductivity is believed to occur: for this reason this family of compounds

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were called cuprates. In 2006, high temperature superconductivity was observed in iron oxypnictide [5] compounds and, soon, other iron based compounds (containing AsFe planes) with a maximum T_c of ∼ 56K [6, 7] were discovered, suggesting that other ingredients (layered structure, magnetic instabilities) are fundamental for HTS beyond copper. (For a general introduction to superconductivity, seee.g. Ref. [8].)

2.1.1 Structure of NdBa

₂

Cu

₃

O

₇_−δ

We studied in detail the compound NdBa₂Cu₃O_7−δ(NBCO), a member of the family REBa₂Cu₃O_7−δ (RE stands for a rare earth element) of which the most well known is YBa₂Cu₃O_7−δ. At the oxygen content of interest, NBCO has an orthorhombic structure very close to the tetragonal Pmmm . The structure can be seen as three perovskite units stacked on top of each other (schematic view of on Fig.2.1). Two CuO₂ planes are in the center, and “support” superconductivity, the Cu atoms on top and bottom form chains with oxygen which act as charge reservoirs. The total height of the unit cell (along the c−axis) is about 12 Å with an approximately square base of 4 Å side, the exact dimensions depending on the oxygen content.

This layered structure gives rise to anisotropic electronic properties. In epitaxial thin films, thea andb axes are mixed due to the anchorage of the film on the cubic SrTiO₃ (STO) substrate. More precisely, as the rectangular basis of the film cannot be accommodated on the square surface of the substrate, the film creates domains with a and b-axes swapped and slightly distorted, leading to so-called twins.

Figure 2.1: Crystalline structure of NdBa₂Cu₃O₇₋δ. On the left, the NdBa₂Cu₃O₆ and on the right the NdBa₂Cu₃O₇ structure. Hole doping is achieved by changing the oxygen content of the Cu-O chains. (Adapted from [9])

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2.1. A Short Introduction to High Temperature Superconductivity 7

2.1.2 Phase Diagram

The cuprates share a common temperature-doping electronic phase diagram (see e.g. Ref. [10]). The undoped parent compounds are Mott insulators with anti- ferromagnetic order. By doping, both with electrons (Nd_2−xCe_xCuO₄) and holes (YBa₂Cu₃O_76+δ, La_2−xSr_xCuO₄, Bi₂Sr_2−xLa_xCuO₆, Bi₂Sr₂CaCu₂O_8+δ) metallicity and superconductivity (SC) appear, hole-doped compounds displaying the highest Tc. In this work we focused our attention on NdBa₂Cu₃O_7−δ, a hole-doped material with its phase diagram sketched in Fig.2.2. For carrier concentration n ≈ 0 and up to room temperature the system displays a Mott insulating phase with an anti- ferromagnetic order (AFMI). For largern values, a superconducting phase appears.

The superconducting region forms a dome in theT−nphase diagram, culminating at about 90 K for NBCO. The two sides of the dome are usually described as “under- doped” (ud, left side) and “over-doped” (od, right side). For higher doping and low temperatures, the system seems to behave as a “Fermi liquid” (FL). In the under-doped part, below the dashed line shown in Fig.2.2, the opening of a gap (the pseudogap) in some parts of the Fermi surface has been detected by diﬀerent probes, possibly indicating the presence of preformed Cooper pairs that are not phase coherent. According to these interpretations, the strength of the superconducting pairing is given by the pseudogap energy scale. One question which generates a lot of interest is the understanding of the edges of the SC pocket, whereT_c vanishes. In particular, in the under-doped part, a quantum superconductor to insulator (QSI) phase transition occurs [11].

An explanation of the general shape of the phase diagram has been proposed in [12].

Both quantum and classical phase fluctuations can destroy superconductivity. One can associate a temperature to the strength of fluctuations,T_θ^max for classical phase fluctuations. A “mean field” temperature TMF corresponding to the gap energy (or the pairing energy) also control superconductivity. Locally, Cooper pairs are formed belowT_MF. The actualT_c, the temperature at which phase coherence is established, is bounded by the fluctuations and pairing temperatures. T_θ^max is determined by the superfluid density and in superconductors as under-doped NBCO with “low carrier density” (which means a small phase stiffness and a poor screening), phase fluctuations of the order parameter is the dominant phenomena which determinesTc. Close to the quantum critical point (QCP), quantum fluctuations can be dominant, and the actual T_c is lower than T_θ^max. Fig.2.2(b) illustrates this discussion.

The microscopic mechanism responsible for high temperature superconductivity is still a subject of intense debates. Exploring the end-points of the SC dome where superconductivity appears and vanishes can bring information, possibly restricting the spectrum of theoretical scenarios. In the under-doped part of the SC dome, where the QSI transition takes place, an empirical relation (the “Uemura relation”) relates Tc to the superﬂuid density ns (the density of Cooper pairs in the superconducting state) and the magnetic ﬁeld penetration depth λ: T_c ∝ n_s ∝ λ⁻²(0) [13]. This

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Figure 2.2: (a)Schematic temperature T−carrier concentrationn phase diagram of the hole- doped HTS cuprates. (b)Scenario of Emery and Kivelson [12]: TMF is the mean ﬁeld transition temperature, Tθ^max is the upper bound on the phase ordering temperature and Tc is the actual transition temperature.

relation is predicted by the quantum analog of the Berezinskii-Kosterlitz-Thouless (BKT) theory of vortex unbinding [8] and for a Bose-Einstein condensate in 2D.

Recent measurements [14–20], as illustrated in Fig.2.3 suggest a different relation between T_c and λ(0). The difference could find its origin in the sample dimensionality or in the way in which doping is achieved.

To try solving this issue, we concentrate here on the field effect study of the quantum superconductor to insulator phase transition at the under-doped edge of the phase diagram. It will be shown below that the disorder [22] can play a role in the dimensionality of the phase transition and hence in the “Uemura relation”. Using field effect on ultra thin NBCO films, we analyzed the variation ofTc as a function of carrier concentration and penetration depth. We also show that one can modulate very substantially theT_c of cuprates, a result interesting by itself.

A relation, as observed by Uemura, is expected to occur close to a QSI transition in a two-dimensional (2D) superconductor [11]. The scaling theory of critical phenomena indeed predicts that close to a QSI transition, Tc scales as δ^z¯^ν where δ is a tuning parameter, which will be here the change in the areal carrier density Δn_2D:

Tc ∝(Δn2D)^z¯^ν , (2.1)

where z is the dynamic and ν¯ is the critical exponent of the zero-temperature in- plane correlation lengthξ˜_ab ∝Δn^−¯_2D^ν [11, 23]. As will be shown later in this chapter, we used the electrostatic ﬁeld eﬀect to explore the phase diagram, thus changing only the carrier concentration. From the analysis of the critical behavior of Tc, we found an exponent zν¯ ≈ 1 compatible with a QSI in 2D (see section 2.4). Since

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2.2. Thin Films Preparation 9

Figure 2.3: Data collected from diﬀerent papers, showing a non universal relation between Tc

andλ⁻²(0)(for details see Ref. [21] from which the graph is extracted).

close to a QSI transitionλ_ab(0) scales as

1/λ²_ab(0) ∝Δn^¯^ν(D+z−2)_2D , (2.2)

whereD is the system dimensionality, it follows, with Eq.2.1 that:

T_c ∝Δn_2D ∝ 1

λ²_ab(0) . (2.3)

Hence, from the point of view of QSI transitions, the Uemura relation is expected for a 2D system. In 3D, however, one expectsTc ∝1/λ. A clean experiment testing the relation between T_c and λ can thus reveal the dimensionality of the system. In the next sections, we will describe the experimental eﬀorts allowing us to check the relation of Eq.2.3.

2.2 Thin Films Preparation

In order to study the under-doped region of the phase diagram and to perform field effect experiments (see e.g. [24–26]), ultrathin films with low carrier concentration are needed to allow for significant changes in the carrier density and substantial

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modifications of the properties of the superconducting films. In this section, we will briefly describe the thin film growth, their characterization by X-ray diffraction (XRD) and the patterning technique.

Sample growth

NBCO films are grown on (001) TiO₂-terminated STO substrates, 0.5 or 0.1 mm thick (area of 5×5mm²) by RF “off-axis” magnetron sputtering. The growth procedure is the following: The sample is pasted with silver epoxy on an inconel plate, and then introduced into the chamber (base pressure∼5·10⁻⁷mTorr). A gas flow (mixture of Ar and O₂ with a ratio 10:1) is introduced and a butterfly-valve adjusts the pressure to115mTorr. Then the substrate is heated by a thermocoax to∼730℃ in about 20 minutes and the film is deposited at a rate of about 1 uc per minute.

The 2 inch sputtering gun is situated ∼6.5cm below the substrate and∼3.8cm off horizontally, perpendicular to the substrate surface (off-axis). Figure 2.5 shows the deposition geometry during a plasma discharge. The deposition is directly followed by a post-anneal in O₂ during the slow cooling (1 hour). We note that the oxygen pressure in the chamber during the annealing determines the oxygen chemical doping of the NBCO layer (see Fig.2.4). To obtain “optimally-doped” samples, a 640 Torr O₂ pressure is necessary, while much lower pressures (down to 5 mTorr) are used to get samples with lowT_c (about 5 K). To improve the contact resistance for very thin films, gold contacts were deposited in situ at room temperature, using a shadow mask. Finally an amorphous layer of NBCO is deposited (also in situ at room temperature) on top of the crystalline layer to protect the film and prevent changes in the oxygen content.

Substrate preparation

The surface of a SrTiO₃ substrate can present two chemical atomic terminations, SrO and TiO₂. SrTiO₃ substrates after polishing exhibit both terminations: the surface then presents half-unit cell steps between TiO₂ and SrO planes. This mixed termination can aﬀect the growth of NBCO ﬁlms, sensitive to the starting chemical conditions [27]. For these reasons, in this study, we used a chemical etching method [28, 29] to obtain stable TiO₂ terminated surfaces. We performed the following sequence of steps: cleaning in H₂O for 10’ in an ultrasonic bath, immersion for 4’40”

in a buﬀered HF solution followed by 10’ in H₂O in an ultrasonic bath. The buﬀered HF solution is composed of 0.1M NH₄F solution and in addition a 1% HF solution (1.5%-vol), reaching a pH of about 5.5. AFM images of untreated substrates do not show any regular features. After the etching process, unit cell steps are clearly visible. Fig.2.6 shows an AFM topography of a treated substrate with steps of about 4 Å, corresponding to one unit cell of STO.

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Figure 2.4: Resistance versus temperature characteristics of very thin NBCO ﬁlms annealed at diﬀerent oxygen pressures, the lower the pressure, the lowerTc.

X-ray diﬀraction techniques

After deposition, the crystalline quality is checked by XRD. Three kinds of measurements are performed: θ−2θ scans, rocking-curves and low angle reﬂectometry.

In a four-circle diﬀractometer, four degrees of freedom are available, deﬁned by the angles of rotation around the axes shown on Fig.2.7.

During aθ−2θscan,ω =θ, andφandχare kept fixed whileθand2θare swept.¹ A diffraction peak is detected if the interference between the wave functions scattered by the atomic planes is constructive. This implies the condition 2dsin(θ) = nλ, wheredis a length corresponding to the periodicity of the structure along the normal to the diffracting planes (for example, the unit cell size along the z direction of a (001) oriented crystal for χ= 0),n ∈N is the order of the diffraction, and λ is the X-ray wavelength (hereλKα1 of copper, 1.5406Å.). The intensity of these diffraction peaks is modulated by the structure factor, the Lorentz polarization factor and other parameters [30,31]. Performingθ−2θscans (for different values ofφandχ) allows us to determine the sample’s crystalline lattice and to check that there are no parasitic crystalline phases.

During a rocking-curve scan, only ω is swept while the other angles are kept ﬁxed.

If these angles are chosen such that they satisfy the Bragg condition for a particular reﬂection, then scanningωwill give information about the coherence (the alignment) of the diﬀraction planes. This measurement is also performed to align the sample

1This is the ideal situation, in reality, there is an alignment procedure leading to some correction inω. Hence, during aθ−2θ scan,ω=θ+C, where Cis an oﬀset angle.

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Figure 2.5: Deposition of a NBCO layer. The sample is glowing in red (heated at ∼ 730℃) above the gun illuminated by the plasma which appears white (overexposure).

(see footnote 1). Having a rocking curve of a similar width for the substrate and for the ﬁlm is a good indication of coherent growth.

Typical NBCO thin ﬁlms X-ray diﬀractograms

Fig.2.8 shows θ −2θ scans for NBCO films of different thicknesses. At low angle, 2θ < 5°, we observe oscillations due to the finite thickness of the amorphous and crystalline layers (we will call them “low angle fringes”). The contributions from these two layers sum up in the measured intensity, sometimes creating rather complicated diffraction patterns as for the 17 uc sample. The(001)diffraction peak of the NBCO

Figure 2.6: AFM topography of a SrTiO₃ substrate after a chemical etching using buﬀered HF.

4 Å unit cell steps are visible. The termination is TiO₂.

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Figure 2.7: Geometry of a four-circle diﬀractometer (courtesy of N. Stucki).

is situated at2θ ≈7.5°. The width of the peak, as well as the period of its satellites is related to the thickness of the crystalline ﬁlm.

The “low angle fringes” result from the presence of parallel interfaces with different refraction indices (for the X-rays, all the indices deviate from1only by a few 10⁻⁵, meaning that a substantial reflection will only occur at very low angles). In the thin film case, one has two interfaces: air / film and film / substrate. The substrate is usually much thicker than the X-ray penetration depth (few tens of microns), implying that the contribution from the substrate / air interface can be neglected.

At each interface, a reﬂection occurs and as a function of the angle, the amplitudes sum or subtract, producing intensity oscillations. The intensity can be calculated as a function of the refraction indices n_j = 1−α_j −iβ_j, the incident angle θ and the thicknesst2 of the ﬁlm:

I ∝

a⁴^f_f²₂^−f_+f³₃ + ^f_f¹₁^−f_+f²₂ a⁴^f_f²₂^−f_+f³₃^f_f¹₁^−f_+f²₂ + 1

2

, (2.4)

where a = exp(−iπf₂t₂/λ) and f_j =

θ²−2α_j −2iβ_j and j is the index corresponding to different media (air, film, substrate). Note that in this measurement only the flatness of the interfaces is important, the film can be amorphous or crystalline, oscillations will be observed as well . In Fig.2.8, the low angle fringes with short periodicity are due to the amorphous layer : in the case of the 3 uc sample, the intensity is fitted between2θ= 0.5and 3.5^◦ (dotted line in Fig.2.8) using Eq.2.4 with t₂ = 326Å, which provides an estimation of the thickness of the amorphous protective layer.

Finite size fringes can be fitted using a simple model, considering N planes which diffract with the same amplitude. The diffracted intensity is then the square of the sum of all the diffracted wave functions and results in:

I ∝

N j=1

exp

i2π

λ 2dsin(θ)

2

∝

sin(2π·N ·dsin(θ)/λ) sin(2π·dsin(θ)/λ)

₂

, (2.5)

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whered is the inter-plane distance andλ the wavelength. This model does not take into account structure factors and other complications, but in a narrow enough 2θ window around a diffraction peak, it can reliably fit X-ray diffractograms with only the thickness and thec−axis value as free parameters (plus the peak normalization of the intensity). On Fig.2.8, fringes due to finite thickness around the NBCO (001) peak are fitted according to Eq. 2.5 (dashed lines).

Figure 2.8: θ−2θ diffractograms for NBCO films of different thicknesses (plain lines). The two kinds of finite size fringes are fitted according to Eq. 2.5 and Eq. 2.4 (dashed and dotted lines respectively, see text for details).

Patterning

Field effect experiments were performed in a well defined measurement geometry set by optical lithography and dry etching. A positive photoresist (S1813, 1.3μm thick) is used to protect the measurement path while the rest of the sample is exposed to Ar ion milling. The sample is pasted on a sapphire plate which is fixed on top of a water-cooled copper finger to reduce heating of the sample during the ion bombardment. Exposition to Ar ions can turn insulating STO into conducting oxygen reduced STO (a few minutes are enough to observe conduction with the ion beam parameters used in our experiment). The patterned structure consists of a 500μm wide path with voltage probes on each side, 600μm apart from each other (see Fig.2.9). This geometry is convenient for our field effect measurement: it allows us to keep the area of the gate relatively small, which reduces the risk of breakdown (see next section).

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2.3. The Field Eﬀect Technique 15

Figure 2.9: NBCO sample patterned for a 6 point measurement. The dark region at the center is the gate contact on the backside of the substrate. The current ﬂows through the horizontal path and voltage probes are positioned along the current path, allowing the Hall eﬀect and the longitudinal resistance to be measured. The width of the path is500μm.

2.3 The Field Eﬀect Technique

In this section, we discuss the basic ideas of the electric field effect, focusing mainly on the approach used in our study of NBCO. This method is analogous to the one used in semiconductor integrated circuits. We will come back to the field effect in section 3.4, where we will use a more original approach.

Basic ideas about the ﬁeld eﬀect

At the heart of most of our electronic devices are transistors which for logic applications are often field effect transistors (FET). The principle behind a field effect transistor is the modulation of the carrier density and hence the channel resistance between two terminals, called the source and the drain, by applying a voltage to a third terminal called the gate. The conducting channel between the source and the drain is usually doped silicon. To form the gate, this channel is covered by a thin insulating oxide layer (usually SiO₂, more recently HfO₂) layer with a metallic electrode on top. A bias voltage applied between the gate and the channel modulates the carrier density of the latter, tuning its conductance (see Fig.2.10).

A similar technique can be used as a tool to study the properties of a material as a function of its carrier concentration. In our experiments, we investigate the transport properties of a NBCO ﬁlm used as the channel, varying the gate voltage.

This approach has diﬀerent advantages over the more conventional chemical doping technique: the carrier density is modulated in a “clean” way as compared to chemical doping since the intrinsic disorder is not changed. The approach is also reversible and can be local. This technique has however its limitations such as the need for good

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Figure 2.10: Schematic of a ﬁeld eﬀect transistor (FET, here MOSFET) viewed from the side.

The channel resistance between the drain and the source is modulated by the voltage applied to the gate. (Image from [32])

gate dielectrics and the requirement of very thin channel layers (the screening length being very short at metallic densities). Indeed the induced carrier density, that is related to the gate voltage, is limited by the breakdown voltage, the maximum bias voltage that the gate dielectric can sustain before a discharge occurs. The electric ﬁeld present at the interface between the gate dielectric and a metallic channel is screened by the mobile charges over a typical length, called theThomas-Fermi(TF) screening lengthλT F:

λT F =

₀E_F

6πne² , (2.6)

where 0 is the vacuum permittivity, the relative permittivity of the studied material, EF and n being its Fermi energy and carrier concentration respectively, and ﬁnally e the elementary charge.

FET structures based on NBCO

For our field effect experiments, we fabricated FET devices as shown in figure 2.11.

In this conﬁguration, the gate dielectric is the STO substrate itself. Indeed STO has interesting properties in that respect: its dielectric constant reaches 10⁴ at low temperatures [33–36] and STO can sustain large ﬁelds, at least up to 4 MV/m, the maximum value used in our measurements.

Although strontium titanate can sustain very large fields, for different experimental reasons, too large voltages cannot be used. Indeed, the insulation of the wires is not guaranteed at high voltages, and some measurements are done in Helium, the gas may ionized at such large voltages. In order to reduce the voltage for a given electric field, and hence a given carrier density modulation, a simple solution is to reduce the thickness of the gate dielectric. Using a grinding machine, the center of the 0.5 mm substrates were thinned down to about 100μm. We also started with substrates only 0.1 mm thick, but they turned out to be more difficult to manipulate, particularly removing the sample from the holder after deposition is delicate. Figure 2.9 shows a FET device realized by grinding a 0.5 mm substrate. The gate electrode can be seen on the backside of the substrate.

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2.3. The Field Effect Technique 17 The charges induced by the field effect can be measured by two different means.

The ﬁrst method uses an electrometer (Keithley 6514) in series with the voltage source (Kepco APH1000DM or Keithley 2410). This way we directly measure by integrating the charging current how many charges are brought to the interface.

However, one must take care of the leakage current. In our measurements, we integrated the charging current only when the voltage is swept and we checked that the leakage current is negligible once the bias is set.

Figure 2.11: Left: Schematics of the resistance measurement setup. The STO substrate is milled to reduce the thickness down to about 100μm below the measured path [37]. A gold electrode (G) is deposited on the backside of the STO and is connected by silver paint. Contacts to the NBCO ﬁlm are realized by wire-bonding on gold (depositedin situ) pads. An amorphous NBCO layer (a-NBCO) protects the ultrathin crystalline NBCO layer. Right: Schematics of the measurement setup used to determine the charge modulation. Another method uses an LCR meter instead of the electrometer.

The other method to evaluate the charge modulation is to measure the diﬀeren- tial capacitance C(V). We measured the capacitance with an LCR-meter (Agi- lent 4284A) with an autobalancing bridge method. For an ideal capacitor with capacitance C, one expects that, for a bias V, the charge brought to the interface ΔQ(V) = CV. The situation is more complicated with a dielectric such as STO.

Indeed, the dielectric constant of STO changes by two orders of magnitude as the temperature is decreased from room temperature (≈300) to 4 K (≈10 000), and is also bias dependent at low temperatures [35,37], see Figure 2.12. In this case, the induced charge can be calculated as

ΔQ(V) = _V_G

0 C(V)dV . (2.7)

Once the number of induced chargesΔQis known, the change in areal carrier density Δn2D is calculated as Δn2D = _eS¹ ΔQ, where S is the area of the NBCO path over- lying the back-gate electrode. This formula neglects side eﬀects (the precise shape

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Figure 2.12: Left: Capacitance as a function of temperature for a 0.1 mm thick STO substrate with gold electrodes 0.85×0.65 mm². Center: Diﬀerential capacitance at 5 K as a function of bias voltage. Both measurements are performed with a LCR-meter at 1 V ac and 1 kHz signal. Right:

Comparison between the gate voltage dependence of the capacitance measured by an electrometer and a LCR meter atT = 4.2K for a 0.1 mm thick STO and 20 mm² electrodes.

of the field lines) but nevertheless seems to give reliable enough results. Indeed, we checked using Hall effect measurements on a thin film of doped STO at 100 K (see section 3.4) that the values obtained using the methods described above agree with the changes observed in the Hall response. We did not use Hall effect in NBCO, as it is temperature dependent and cannot be simply interpreted. Note that in our discussion, we assume that all of the induced carriers Δn2D are mobile. Salluzzo et al [38] performed x-ray absorption spectroscopy in the presence of an electric field to study the mechanism of field-effect doping in the 123 HTS. Their analysis shows that holes are created at the CuO chains of the charge reservoir and that field-effect doping of the CuO₂ planes occurs by charge transfer, from the chains to the planes, of a fraction of the overall induced holes.

According to Eq.2.6, and using values suitable for NBCO (E_F ≈ 1eV, ≈ 10 and n≈10²¹/cm³), one ﬁnds that the ﬁeld is screened over a typical distance of ∼1nm.

This means that the carrier concentration is substantially changed over one unit cell only. For this reason, we grew ﬁlms only 3 uc thick, the thinnest ﬁlms that are superconducting with our preparation conditions (see Fig.2.4 and 2.8).

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2.4. Modulation of the Superconducting Properties by Field Eﬀect 19

2.4 Modulation of the Superconducting Properties by Field Eﬀect

As stated in the introduction, although the phase diagram Tc as a function of the carrier dopingn has been extensively studied, the Tc(n)dependence is still an open issue. Here we are presenting our results on the relation between T_c, the change in the sheet carrier densityΔn2D and 1/λ²_ab(0). Some of the following results have been published in Ref. [39].

Figure 2.13: Resistance as a function of temperature for a thin NBCO film and for different applied gate voltages. There are four different measurements for 0V gate bias, showing the re- versibility of the field effect. The curves with positive gate voltages correspond to carrier depletion, NBCO being a hole-doped compound. (sample 6)

Relation between the critical temperature and the induced charges As described in Section 2.2, we used low oxygen pressures during the in situ post anneal to fabricate under-doped thin films withTc close to zero. Then we applied an electrostatic field effect as described in section 2.3. A schematic view of the wiring is shown in the inset of Fig.2.13 and in Fig.2.11. Using the sign convention that the bias voltage VG is the one applied to the gate electrode, negative gate voltages correspond to adding carriers (holes) to the system. As can be seen in Fig.2.13, the superconducting transitions are shifted towards higher temperatures by several degrees as we increase the carrier density (negative gate voltages), while for positive voltages the resistance remains finite down to 4 K and increases significantly as V_G

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is raised. During the experiment, the gate leakage current has been checked to be of the order of a nanoampere, while the measurement current was between 1 and 10μA.

To estimate Tc we analyze the resistive transitions according to the Berenzinskii- Kosterlitz-Thouless (BKT) critical behavior. BKT transitions are expected and have been observed for superﬂuid [40] and superconducting two dimensional systems [41]. Although our data do not prove the occurrence of a BKT transition, the consistency of our resistance curves with the BKT behavior suggests that our ﬁlms are 2 dimensional (2D). In the BKT scenario, the correlation length above T_BKT behaves as:

ξ˜= ˜ξ0exp 1

2bt^−1/2

with t = T

T_BKT −1 , (2.8)

whereξ˜0 and b are material-dependent but temperature-independent parameters.

Invoking dynamic scaling, the resistance R scales in D = 2 as R = ˜ξ^−z^cl where z_cl is the dynamic critical exponent of the classical dynamics for simple diﬀusion:

zcl = 2 [11]. Combining these formulae we obtain R=R₀exp −bt^−1/2

. To avoid the need for determiningR₀, we note that:

dln(R) dT

_−2/3

=

2TBKT

b

_2/3 T TBKT −1

. (2.9)

This equation implies a linear relation between(d ln(R)/dT)^−2/3andT, crossing the temperature axis atT_BKT. This relation has been observed in our very under-doped samples as shown in Fig.2.14.

The estimation of the induced carrier density, following the procedure described in section 2.3 allows us to relate Δn2D to the modulation of the critical temperature ΔTBKT. As shown in Figure 2.15, we observe the following linear relation between Δn_2D and ΔT_BKT for four diﬀerent samples:

ΔT_BKT = 1.3·10⁻¹³ [K cm²] Δn_2D . (2.10) ΔT_BKT ∝ Δn_2D means that zν¯= 1, signature of a QSI transition occurring in 2D (see section 2.1.2, Eq.2.1).

To go one step further, we tried to relate the change in TBKT to a change in the penetration depth. To do so, we used resistance measurements in magnetic ﬁeld to access the penetration depth.

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Figure 2.14: (dln(R)/dT)⁻²^/³versusT at various gate voltages. The solid lines indicate the BKT behavior, as described by Eq.2.9. TBKT is determined by the condition(dln(R)/dT)⁻²^/³(T) = 0.

(sample 1)

The magnetic phase diagram

Unlike type I superconductors which completely repel magnetic field lines, in a type II superconductor, for some magnetic field and temperature conditions, it is energetically favorable to let some magnetic flux penetrate in the form of so-called

“vortices”. Vortices possess a “core” in the normal state (i.e. not superconducting) of a radius roughly given byξ, the superconducting coherence length. The magnetic ﬁeld penetrates into the material over a length λ, the London penetration depth.

Supercurrents (currents in the SC state) around the core of the vortex screen the ﬁeld over a distance λ. A moving vortex dissipates energy leading to a ﬁnite resistance.

The vortex state can be a solid or a liquid depending on several parameters, including vortex density, disorder, dimensionality, etc. This is a very complex subject which has been studied in details (see for instance [42]).

The vortex structure depends upon the temperature and magnetic field. It is thus natural to study the magnetic field versus temperature phase diagram that has been determined both experimentally and theoretically, and that is sketched in Fig.2.16. [42] At low temperature and low magnetic field, the SC is in the Meiss- ner state (below H_c1(T)) and completely expels the magnetic field. At higher field, but moderate temperature, vortices are generated but are in a “vortex solid” state.

They can arrange themselves in a lattice in clean materials, or are solidiﬁed as a

“glass” in disordered materials. At high enough temperature, the vortex solid melts

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Figure 2.15: Variation of TBKT, ΔTBKT, as a function of the change in areal carrier density Δn2D. The inset showsTBKT as a function of gate voltageVG for the same samples.

and becomes a “vortex liquid”. Finally, the normal state is reached for high enough temperature or magnetic ﬁeld, above the Hc2(T) line. In HTS, this transition is smeared out by ﬂuctuations.

In the liquid phase, the resistance is due to vortex ﬂow. In the case of a low density vortex liquid and low current density, the resistivity ρ is thermally activated with an activation energy U [42] :

ρ(H, T) =ρnexp

−U(H, T) kBT

. (2.11)

Close toTc,U(H, T) = 2U0(H) (1−T/Tc) [43].

In a 2D lattice, the energy U is associated with the unbinding of dislocation pairs [44–46]:

U0(H) = − Φ²₀d

16π²μ0λ²(0)ln a₀

ξab(0)

=− Φ²₀d

32π²μ0λ²(0) ln(H) +K , (2.12) wherea₀ =

3Φ₀/(√

2H)is the mean vortex-vortex distance andξ_abis the coherence length. As one will see, this relation can be used to estimate the London penetration depth.

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Figure 2.16: Schematic simpliﬁed magnetic ﬁeld vs. temperature phase diagram. See text for details. Adapted from Ref. [42].

Activation Energies and the “Uemura relation”

Because the relation between Δn2D and the superfluid density ns is not straight- forward [38], the in-plane penetration depth λab which is related to the superfluid density by n_s ∝ λ⁻²_ab has been evaluated from the analysis of the vortex activation energies. U can be extracted from Arrhenius plots of the resistivity. The behavior follows indeed the expected activated behavior ln(R) ∝ 1/T: the inset of Fig.2.17 shows the relationship between resistivity and the temperature in a 0.1 T magnetic field for different gate voltages. IfU(T)∝(1−T/Tc), the slope of the Arrhenius plot is directly−2U0. Fig.2.17 reveals the expected dependenceU0 ∝ln(H). Such a dependence is only expected for a 2D SC and has previously been observed [45,47–51], while in 3D, one expects U0 ∝H^−1/2 [42].

Fig.2.18(a) shows the relation between dU₀/dln(H) ∝ 1/λ²(0) and T_BKT. As can be seen, the relation is linear althoughTBKT vanishes for a non-zero1/λ²(0). Going one step further, using Eq.2.12, one can estimate λ and compare the data obtained here to the data collected by Uemura [13]. Fig.2.18(b) shows T_BKT versus 1/λ²(0) and the universal relation (solid line) expected between TBKT and 1/λ²(0). The slope is very close to what is expected although the TBKT are shifted. Note that other criteria for T_c (e.g: T at which R(T) equals some very low resistivity value) would shift the curve. In Fig.2.18(c) our data are plotted along with the Uemura data.

It has to be noted that the universal relation between TBKT and 1/λ²(0) implies that the slope dT_BKT/d(1/λ²(0))is given. This is indeed what we observe here. We

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Figure 2.17: U0/kB vs. H for diﬀerent applied voltages for the sample 1. A linear relation betweenU0andlog(H)is observed with a slope which depends on the applied electric ﬁeld. Inset:

log(ρ)as a function of 1/T for sample 2 and for three different electrical fields at0.1T. The zero temperature activation energy U0 at a given applied electrical field is obtained from the slope of the Arrhenius plot.

will see in chapter 4 that at high vortex-antivortex densities, the situation is more complex.

It is also interesting to look at the relation between the induced normal state carriers Δn2D and the superﬂuid density ns. The superﬂuid density is related to λ(0) by [15, 41]:

1

λ²(0) = μ0e² m^∗ ns .

It is thus possible to compare the changes in superfluid density (3D) with the induced charges. Looking at the relation between the relative changes ofn_2D and the changes in d·ns (or 1/λ²(0)) as shown on Fig.2.19, one finds that only 40% of the carriers seem to condense. To get this value, we tookd= 12Å andm^∗ = 4.5me [13,52]. The condensation of only a fraction of the induced carriers has also been concluded in Ref. [38] where X-ray absorption spectroscopy was used to study field effect doping.

Conclusions

Our field effect measurements on thin NBCO films allowed us to show that:

ΔTBKT ∝Δn2D ∝Δ 1 λ²_ab(0) ,

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Figure 2.18: (a)TBKT as a function of−d(U0/kB)/d(ln(H))which is proportional to1/λ²(0) and shows a qualitative agreement with the Uemura law. (sample 1) (b)TBKT as a function of 1/λ²(0). Same data as (a) but assuming that Eq.2.12 applies to our system. (c) Uemura plot:

Tc as a function of 1/λ²(0). The straight lines in plots (b) and (c) are illustrating the universal relation betweenTBKT and1/λ²(0), the red/light gray squares are the data (b), the dots are the data from Uemura’s paper (YBa₂Cu₃O₇₋δ data are in blue/dark gray).

signaling a QSI transition occurring in 2D. Since the anisotropy of NBCO at optimal doping is of the order of ∼ 7 [8], our data suggest a 3D to 2D crossover as one is progressively under-doping the system. We ﬁnd a quantitative agreement with the original Uemura relation. Finally, we observed that probably only a fraction (∼40%) of the induced charges condenses.

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Figure 2.19: Change in sheet superﬂuid density Δnsd (left axis) andΔ1/λ²(0) (right axis) as a function of the induced areal charge density Δn₂D. The slope indicates that only 40% of the carriers condense (see text for details).

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Chapter 3 Ferroelectric Field Eﬀect on Nb-doped SrTiO ₃

3.1 Nb-doped SrTiO

₃

: a Superconductor with a Very Low Carrier Concentration

Strontium titanate is one of the most used substrate in the oxide community. Besides this useful role, it is also a material with very rich properties.

Pure SrTiO₃ (STO) is a band insulator with a band gap of∼ 3.2eV. It has several subtle structural phase transitions, the most well known being the cubic to tetragonal one at around 105 K [34, 53]. It has a very large dielectric constant, even at 300 K of about 300 which increases by two orders of magnitude to ∼10 000 at 4 K (see Fig.2.12). The material is nearly ferroelectric and known as a “quantum para- electric” [36]. Its dielectric constant also presents a large “tunability”, meaning that it is changing a lot as a function of an applied electric ﬁeld. In our experiments, we typically measure a drop of one order of magnitude as an external ﬁeld of about 1 MV/m at 4 K is applied (see Fig.2.12). This tunability nearly disappears at high temperature and drops down to∼5% for 2 MV/m at 77 K.

STO can easily be doped and turned to a semiconductor, a metal and even a superconductor [54]. Bulk properties have been studied extensively in the sixties. There are three current ways to dope STO: oxygen reduction [55–57], Ti⁴⁺ substitution by Nb⁵⁺ [55, 56], and Sr²⁺ substitution by La³⁺. In each case one obtains an n type doping. As the doping goes from10¹⁷ to10¹⁸cm⁻³, the conductivity changes by ﬁve orders of magnitude as shown on Fig.3.1(a) (reproduced from [58]). The mobility is a function of the carrier concentration, but is also sensitive to the kind of dopant (see Fig.3.1(b)).

Doped SrTiO₃ is superconducting for carrier concentration between7×10¹⁸ and4× 27

Oxide superconducting thin films and interfaces studied using field effect

Thesis

Reference

Oxide superconducting thin films and interfaces studied using field effect

Oxide Superconducting Thin Films and Interfaces Studied using Field

Eﬀect

Contents

Résumé en Français

Chapter 1 Introduction

Chapter 2

A Field Eﬀect Study of Under-Doped NdBa 2 Cu 3 O 7−δ Thin Films near the Quantum Phase Transition

2.1 A Short Introduction to High Temperature Su- perconductivity

2.1.1 Structure of NdBa

Cu

O

2.1.2 Phase Diagram

2.2 Thin Films Preparation

2.3 The Field Eﬀect Technique

2.4 Modulation of the Superconducting Properties by Field Eﬀect

Chapter 3

Ferroelectric Field Eﬀect on Nb-doped SrTiO 3

3.1 Nb-doped SrTiO

: a Superconductor with a Very Low Carrier Concentration

A Field Eﬀect Study of Under-Doped NdBa ₂ Cu ₃ O _7−δ Thin Films near the Quantum Phase Transition

Ferroelectric Field Eﬀect on Nb-doped SrTiO ₃