Superconductivity in magnesium diboride (MgB2) was first discovered in 2001. It is unique in that it has two superconducting gaps. The transition temperature of 39 K exceeded the maximum transition temperature thought to be possible through phonon mediated superconductivity. Through the study of MgB2, a general paradigm is being formulated to describe multi-gap superconductors. The paradigm includes inter-band and intra-band scattering between the gaps which can cause a smearing of the gap parameter over a distribution instead of a single value. Although each gap is individually thought to be well described by the BCS theory, the interaction between the two gaps causes complications in describing the overall superconducting properties of MgB2. The focus of this work was to lay the groundwork for an MgB2-based Josephson junction technology. This includes improving on a previously established baseline for all-MgB2 Josephson junctions, utilizing the Josephson Effect to experimentally verify a model pertaining to the two-gap nature of MgB2, specifically the magnetic penetration depth, and designing, fabricating, and testing multi-junction devices and circuits. The experiments in this work included fabrication of Josephson Junctions, DC superconducting quantum interference devices (SQUIDs), Josephson junction arrays, and a rapid single flux quantum (RSFQ) circuit. The junctions were all made utilizing the hybrid physical-chemical vapor deposition method, with an MgO sputtered barrier. The current process consists of three superconducting layers which are patterned using standard UV photolithography and etched with Ar ion milling. There were SQUIDS made with sensitivity to magnetic fields parallel to the film surface, which were used to measure the inductance of MgB2 microstrips. This inductance was used in design of more complicated devices as well as in calculating the magnetic penetration depth of MgB2, found to be about 40 nm at low temperature, in good agreement with a previously published theoretical model. Planar-type DC SQUIDs were also made to present the feasibility of the technology for application purposes. The large voltage modulation of over 500 μV at 15 K for these devices along with operation up to 37 K shows that MgB2 is a potential replacement for low temperature devices. The junction series arrays were fabricated with 100 junctions of equal size to present the ever-increasing robustness of the technology. The devices served well to measure the large property spread associated with these junctions and have been well established as a diagnostic tool for improving this spread. The culmination of this work was a basic RSFQ toggle flip flop circuit. A DC measurement of these circuits yielded digital operation up to 180 GHz at low temperature and about 63 GHz at 20 K. This is not yet near the potential limit of MgB2 established by the value of the superconducting gap parameters, but a huge success in showing that MgB2 is a viable option for pursuing superconducting digital electronics suitable for low power, cryogen-free operation. / Physics

No / We consider two distant mesoscopic SQUID rings, approximated with two-level systems, interacting with two-mode microwaves. The Hamiltonian of the system is used to calculate its time evolution. The cases with microwaves which at t = 0 are in separable states (classically correlated) or entangled states (quantum mechanically correlated) are studied. It is shown that the Josephson currents in the two SQUID rings are also correlated.

Dans cette thèse intitulé "Dynamique quantique de la phase et de la charge dans des chaînes des jonctionsJosephson", une étude expérimentale et une description théorique des effets quantiques des phases et descharges dans les chaînes de jonctions Josephson est présenté.La dynamique des chaînes de jonctions est dominé par deux échelles d'energie: l'energie Josephsonrelié a la superposition des fonctions d'ondes de deux électrodes et l'energie de charge relié a l'énergieélectrostatique des charges sur les deux électrodes. La réalisation d'un état quasi-classique de la chargenécessite une énergie de charge importante pour diminuer lesfluctuation quantique de la charge. En plus,le temps de relaxations de la jonctions dois être augmenté par un environnement a haute impédance.Un état de charges localisé a été réalisé sur une jonctions Josephson dans un environnement inductiveréalisé par une chaîne de jonction Josephson. L'état de charge localisé se manifeste par l'apparition d'undomaine a haute résistances dans les caractéristques courant-tension.Une chaînes des jonctions n'est pas une inductances parfaite. Des résonances electro-magnétique lié a lacapacité vers la masse des îlots supra-conducteurs altèrent la localisation de charge.Une characterisation des effets de pertes et des non-lineartés de ces résonances a été effectué. / In this thesis entitled ' Quantum phase and charge dynamics in Josephson junction chains ' an experimental study and theoretical description of quantum effects of phases and charges in chains of Josephsonjunctions is presented.The dynamics of Josephson junction chains are dominated by two different energy scales: the Josephsonenergy, which is related to the overlap of the superconducting wave functions of the two superconductorsforming the junction and the charging energy that is related to the electrostatic energy of the Cooper-pairs on the islands. The realization of a well-defined charge state on a Josephson junction requires a highcharging energy to suppress the quantumfluctuations of the charge. In addition, the charge relaxationtimes must be increased by inserting the junction in a high impedance environment.We have realized such a well-defined charge state on a Josephson junction in an inductive environmentthat is formed by a Josephson junction chain. The localized charge state manifest itself by the appearanceof a high resistive regime in the current-voltage characteristic.A Josephson junction chain is however not a perfect inductor. Electromagnetic resonances related withthe finite ground capacitance of the superconducting islands influence the charge localization.We have characterized the effect of losses and nonlinearities on the electromagnetic resonances of Josephson junction chains in microwave spectroscopy measurements.

Cette thèse poursuit deux directions dans le domaine des isolants et supraconducteurs topologiques.Dans la première partie de la thèse nous étudions des isolants en deux dimensions sur réseau, présentant un effet Hall quantique anormal (c'est-à-dire en l'absence d'un champ magnétique externe), induit par la présence d'un flux magnétique inhomogène dans la maille. Le système possède des phase isolantes caractérisés par un invariant topologique, le nombre de Chern, qui est lié à la conductance portée par le bord états. Nous montrons que les modèles à deux bandes admettent des phase à nombre de Chern arbitraire, ou, de façon équivalente, un nombre arbitraire d'états de bord, quand on augmente la portée des couplages sur réseau. Cette compréhension est rendue possible grâce à la démonstration d'une formule montrant que le nombre de Chern d'une bande dépend de certains propriétés d'un ensemble discret de points dans la zone de Brillouin, les points de Dirac en l'absence du gap. Ces idées sont rendues plus concrètes dans l'étude du modèle de Haldane et dans la création d'un modèle artificiel avec cinq phases de Chern dont les états de bord sont déterminés en détail. La deuxième partie de la thèse porte sur les supraconducteurs topologiques unidimensionnels qui exhibent des états exotiques d'énergie zéro: les états liés de Majorana. Nous étudions ici la présence de fermions de Majorana dans des fils de semiconducteurs à fort couplage spin-orbite sous l’effet de proximité d'un supraconducteur d'onde s. Nous montrons que la polarisation de spin des degrés de liberté électroniques dans la fonction d'onde Majorana dépend du poids relatif du couplage spin-orbite Dresselhaus et Rashba. Nous étudions également les fermions de Majorana dans des jonctions linéaires longues supraconducteur-normal et supraconducteur-normal-supraconducteur (SNS) où ils apparaissent comme des états étendus dans la jonction normale. En outre, la géométrie d'anneaux peut être mise en correspondance avec une jonction SNS, et, sous l'action de gradients dans la phase supraconductrice, des fermions Majorana étendus se forment encore à l'intérieur du fil normal. Enfin, un modèle à deux bandes avec des fermions de Majorana multiples est traité. Nous démontrons que les jonctions Josephson construites à partir de ce modèle maintiennent l'une des signatures remarquables des fermions de Majorana, à savoir la périodicité 4π de l'effet Josephson fractionnaire. / This thesis follows two threads in the field of topological insulators and superconductors. The first part of the thesis is devoted to the study of two-dimensional quantum anomalous Hall insulators on a lattice, in the absence of an external magnetic flux, but induced by an inhomogeneous flux in the unit cell. The system possesses several gapped phases characterized by a topological invariant, the Chern number, that is related to the conductance carried by the edge states. Here we show that two-band models admit an arbitrary large number of Chern phases or, equivalently, an arbitrary number of edge states, by adding hopping between distant neighbor sites. This result is based on a formula proving that the Chern number of a band depends on certain properties of a finite set of points in the Brillouin zone, i.e. the Dirac points for the gapless system. These ideas are made more concrete in the study of a modified Haldane model, and also by creating an artificial model with five Chern phases, whose edge states are determined in detail. The second part of the thesis focuses on one-dimensional topological superconductors with exotic zero-energy edge states: the Majorana bound states. Here we investigate the presence of Majorana fermions in spin-orbit coupled semiconducting wire in proximity to an s-wave superconductor. We show that the spin-polarization of the electronic degrees of freedom in the Majorana wave function depends on the relative weight of Dresselhaus and Rashba spin-orbit couplings. We also investigate Majorana fermions in linear superconductor-normal and long superconductor-normal-superconductor (SNS) junctions where they appear as extended states in the normal junction. Furthermore, ring geometries can be mapped to an SNS junction, and, we have shown that under the action of superconducting phases gradients, extended Majorana fermions can form again inside the normal wire. Finally a two-band model with multiple Majorana fermions is treated and we show that Josephson junctions built from this model maintain the 4π periodicity for the fractional Josephson effect, one of Majorana fermions signatures.

This thesis presents the results of an experimental study on single-charge effects in nanoscale Josephson junctions and Cooper pair transistors (CPTs). In nanoscale Josephson junctions the charging energy EC becomes significant at sub-Kelvin temperatures and single-charge effects, such as the Coulomb blockade of Cooper pair tunneling, influence the transport properties. In order to observe charging effects in a single Josephson junction, the impedance of the electromagnetic environment surrounding the junction has to be larger than the quantum resistance (RQ=h/4e2≈6.45kΩ). In this work the high impedance environment is obtained by biasing the sample under test (single Josephson junction or CPT) with four one-dimensional Josephson junction arrays having SQUID geometry. The advantage of this configuration is the possibility of tuning in situ the effective impedance of the electromagnetic environment. By applying a magnetic field perpendicular to the SQUID loops, the Josephson energy EJ of the SQUIDs is suppressed, resulting in an increase of the measured zero bias resistance of the arrays of several orders of magnitude (104< R0 (Ω) <109). This bias method enables the measurement of the same sample in environments with different impedance. As the impedance of the environment is increased, the current-voltage characteristics (IVCs) of the single Josephson junction and of the CPT show a well defined Coulomb blockade feature with a region of negative differential resistance, signature of the coherent tunneling of single Cooper pairs. The measured IVCs of a single Josephson junction with SQUID geometry in the high impedance environment show a qualitative agreement with the Bloch band theory as the EJ/EC ratio of the junction is tuned with the magnetic field. We also studied a single nontunable Josephson junction with strong coupling (EJ/EC > 1), where the exact dual of the overdamped Josephson effect is realized, resulting in a dual shape of the IVC, where the roles of current and voltage are exchanged. Here, we make for the first time a detailed quantitative comparison with a theory which includes the effect of fluctuations due to the finite temperature of the environment. The measurements on CPTs in the high impedance environment showed that the Coulomb blockade voltage is modulated periodically by the gate-induced charge. The gate-voltage dependence of the CPT changes from e-periodic to 2e-periodic as the impedance of the environment is increased. The high impedance environment reduces quasiparticle tunneling rates, thereby restoring the even parity of the CPT island. This behavior suggests that high impedance leads can be used to effectively suppress quasiparticle poisoning. / QC 20100928

Ce manuscrit de thèse aborde les propriétés de transport hors-équilibre des systèmes mésoscopiques supra-conducteurs. Cette étude se décline en deux volets : i) la signature des fermions de Majorana dans les jonctionsJosephson topologiques, et ii) les corrélations du courant dans les jonctions Josephson tri-terminales.Les fermions de Majorana apparaissent aux bords d’un supraconducteur topologique. Lorsque deux supra-conducteurs topologiques sont reliés pour former une jonction Josephson, les états de Majorana d’énergie nullede part et d’autre de jonction forment un état lié d’Andreev. Puisque cet état porteur du supercourant est4π-périodique vis-à-vis de la différence de phase supraconductrice, il a été spéculé un effet Josephson fraction-naire en présence d’une tension de polarisation. On montre qu’une vitesse de phase finie induit un couplagedynamique entre l’état lié et le continuum des états au dessus de l’amplitude du gap supraconducteur. Ce cou-plage intrinsèque constitue un mécanisme inévitable qui altère l’effet Josephson fractionnaire. On discute, enfonction des paramètres du circuit, les signatures expérimentales pertinentes de l’effet Josephson fractionnaire :l’effet pair-impair dans les marches de Shapiro et l’émergence d’un pic à la fréquence fractionnaire dans la den-sité spectrale du bruit en courant. D’autres manifestations de ces états d’énergie nulle dans la caractéristiquecourant-tension, sous l’amplitude du paramètre d’ordre supraconducteur, sont également exposés.Dans un second temps sont abordées les fluctuations du courant dissipatif dans les jonctions Josephsontri-terminales. On montre que, les corrélations croisées du courant peuvent être positives et amplifiées dans unrégime cohérent. Ces résultats ouvrent la possibilité à des études plus élaborées sur l’enchevêtrement quantiquedans ces systèmes. / This PhD thesis manuscript deals with the non equilibrium transport properties of superconducting meso-scopic systems. This study declines in two shutters : i) signatures of Majorana fermions in topological Josephsonjunctions and ii) current-current correlations in three-terminal Josephson junctions.Majorana fermions appears at the boundaries of topological superconductors. When two topological su-perconductors are connected to form a Josephson junction, the zero-energy Majorana bound states localizedon either side of the junction form an Andreev bound state. As this current carrying state is 4π-periodic inthe superconducting phase difference, it was speculated that, at finite dc bias voltage, the junction exhibits afractional Josephson effect. We show that any finite phase velocity induces a dynamic coupling between thebound state and the continuum of states above the superconducting gap amplitude. This intrinsic couplingprovides an unavoidable mechanism that alters the fractional Josephson effect. We discuss, in terms of thecircuit parameters, signatures of the fractional Josephson effect that could be relevant for current experimen-tal investigations : the even-odd effect in Shapiro steps and the emergence of a peak at fractional Josephsonfrequency in the current noise spectrum. Furthermore, other manifestations of the Majorana bound states onthe subgap current-voltage characteristic are discussed.In a second step, we discuss the dissipative current fluctuations in three terminal Josephson junctions. Weshow that, current-current cross correlations can be positive and amplified in a coherent regime. This findingopens the possibility for further investigations on quantum entanglement in those systems

Nous utilisons un microscope combinant microscopie à force atomique (AFM) et microscopie à effet tunnel (STM) à très basse température (~100 mK) afin d'étudier des nanocircuits mésoscopiques. Pour effectuer l'AFM dans ces conditions, nous utilisons un diapason en quartz recouvert de deux électrodes sur l'une desquelles est collée la pointe. Lorsque le diapason vibre on peut alors localiser en AFM un échantillon conducteur sur un substrat isolant, puis stopper les vibration pour réaliser des spectroscopies tunnel le long de la partie conductrice. Nous utilisons des pointes de platine-iridium ce qui nous permet de mesurer la densité d'états électronique locale. Nous nous sommes intéressés aux jonctions Josephson hybrides composées d'un îlot d'environ 1 µm de métal normal (cuivre) séparant deux supraconducteurs (aluminium). Ces échantillons sont réalisées par lithographie électronique et évaporation sous angle.Les courbes courant-tension de ces jonctions deviennent hystérétiques à très basse température ce qui est vraisemblablement dû à la dissipation thermique dans la partie normale. Nous avons pu localiser de manière fiable des échantillons uniques et effectuer simultanément des mesures en transport et des spectroscopies locales. Nous avons vu que la densité d'états du supraconducteur varie continuement à proximité du métal normal. Nous avons également observé un chauffage du supraconducteur avec le courant traversant la jonction. La mesure de la densité d'états du supraconducteur permet alors d'estimer la température électronique dans l'échantillon. La comparaison avec notre modèle thermique montre que l'énergie thermique produite dans le métal normal semble être évacuée mieux que prévu. / We use a microscope combining atomic force microscopy (AFM) and scanning tunneling microscopy (STM) at very low temperature (~100 mK) to study mesoscopic nanocircuits. To perform AFM measurements, we use quartz tuning forks covered with metallic electrodes on which we glue the tip. By using the tuning fork as a dynamic force sensor, we can localize the sample. Then, switching off the oscillation, we can perform local spectroscopies along the conductive part. We use platinum-iridium coated tips to measure the local density of states. This work is focused on hybrid Josephson junctions composed of a normal metal (copper) island of approximately 1 µm separating two superconductors (aluminium). These samples are made by electronic lithography and shadow evaporation.The current-voltage characteristics of these junctions become hysteretic at very low temperature because of thermal dissipation in the normal part. We achieved the localization of a unique sample and performed simultaneously transport measurements and local spectroscopies. We observed that the density of states of the superconductor varies continuously close to the normal metal. We also observed heating in the superconductor when the junction is current biased. The measure of the density of states of the superconductors gives an estimation of the electronic temperature in the sample. The comparison with our thermal model shows that the energy produced in the normal metal seems to be evacuated better than expected.

La jonction Josephson (JJ) est le composé de base de nombreux circuits électroniques supraconducteurs (SQUID, détecteurs d’ondes millimétriques, logique RSFQ). Avec la découverte des supraconducteurs HTc (à haute température critique), d’intenses recherches ont été entreprises pour réaliser des JJ fonctionnant à la température de l’azote liquide (77 K) permettant l’utilisation d’une cryogénie compacte. Toutefois, la complexité de ces matériaux a longtemps rendu difficile le développement d’une technologie viable et simple à mettre en œuvre. Parmi les méthodes de fabrication de jonctions, celle utilisant l’irradiation par faisceau d’ions a atteint un niveau de maturité suffisamment important pour pouvoir envisager la production de circuits comportant plusieurs milliers de JJ à HTc.Le but de ma thèse repose sur la fabrication, la caractérisation et l’étude des propriétés électromagnétiques de réseaux de jonctions Josephson réalisés dans des films minces d’YBa2Cu3O7-d. par la méthode d’irradiation ionique. / The Josephson junction (JJ) is the basis of many compound superconducting electronic circuits (SQUID detectors millimeter wave RSFQ logic). With the discovery of HTS superconductors (high critical temperature), intensive research has been undertaken to make JJ operating at the temperature of liquid nitrogen (77 K) allowing the use of a compact cryogenics. However, the complexity of these materials has long hampered the development of a viable technology and simple to implement. Among the junctions manufacturing methods, one using the ion beam irradiation has reached a sufficiently high degree of maturity to be able to envisage the production of circuits having thousands of JJ to HTS.The aim of my thesis is based on the fabrication, characterization and study of the electromagnetic properties of Josephson arrays achieved in thin films of YBa2Cu3O7-d. by the ion irradiation method.

No description available.

Continued pursuit of better superconducting devices and an understanding of how the focused ion beam evolves in a complex material are the primary motivations behind this work. The materials of interest are MgB2 and Co-doped Ba122. Superconducting properties of MgB2 were discovered in 2001. It is the first superconductor recognized as a multigap superconductor. Owing to its high Tc of ~39K, electronic circuits based on this material are expected to operate at a much higher temperature (~25 K) than low-temperature superconductors, using compact cryocoolers. Co-doped Ba122 is also a multigap superconductor which belongs to Fe-based superconductor (FeSC) family. The undoped Ba122 compound is a metal exhibiting antiferromagnetism which coexists with superconducting phase up to a certain doping level. The optimally electron-doped BaFe2As2 exhibits the transition temperature Tc of ~21 K which corresponds to the top of the “dome” in the phase diagram. While the Fe-based SC may not signify a particular advance in terms of practical applications, many unique aspects make them worth studying. In particular, the superconducting gap symmetry and structures which appear to be quite different from family to family and not yet fully understood. We report on investigating the normal-state, and superconducting properties of Co-doped BaFe2As2 and MgB2 thin films irradiated at room temperature using a 30-keV focused He+ ion beam in helium ion microscope (HIM). R-T measurement was carried out to extract the dose dependence for Tc and resistivity p0 of the irradiated region. We observed an increase in p0 and a decrease in Tc down to complete suppression of superconductivity for both materials, although the trend of the changes was quite different. In addition, for Ba122, the data for ΔTc ⁄ Tc0 versus measured change in resistivity favors s± over s++ symmetry. Using TRIM software, the projected range and the damage density distribution of the He+ ions were tracked in the samples. Single track irradiation sites for MgB2 sample were characterized using FIB extraction/TEM. The TEM micrographs reveal the subsurface damage density contours that evolve with increasing dose. The Josephson effect is a unique phenomenon that gives direct access to the phase difference �� of the macroscopic wave functions that describe the superconducting state. Josephson junction is also appealing for engineering application in superconducting electronics. Having found the dose at which complete suppression of Tc occurs from the first part of the study, a fabrication process was developed to produce planar Josephson junctions from MgB2 and Co-doped Ba122. The Josephson coupling across the barrier for both materials was observed. MgB2 Josephson junctions showed resistivity shunted junction (RSJ) I-V curve with excellent uniformity and reproducibility. We have also demonstrated tens of planar MgB2 Josephson junctions operating coherently in series arrays. 60 Josephson junction series arrays successfully developed with less than 4% spread in critical current at 12 K. Under microwave radiation, flat giant Shapiro steps up to 150 μA width appear at voltages Vn=NnΦ0f, where N is the number of junction in the array, �� is an integer representing Shapiro step index, and f is the applied microwave frequency. The uniformity and close spacing of JJs in the arrays are significantly better than MgB2 multi-junction devices made by other techniques. It has been a huge success in showing the feasibility of this technology for pursuing superconducting digital electronics, Josephson voltage standards and arbitrary function generators in particular, in MgB2 with ≥ 20K operating temperature. / Physics