Recent studies of the transition metal dichalcogenide niobium diselenide have led to debate in the scientific community regarding the mechanism of the charge density wave (CDW) instability in this material. Moreover, whether or not CDW boosts or competes with superconductivity (SC) is still unknown, as there are experimental measurements which supports both scenarios. Motivated by these measurements we study the interplay of charge density modulations and superconductivity in the context of the Bogoliubov de-Gennes (BdG) equations formulated on a tight-binding lattice. As the BdG equations require large numerical demand, software which utilizes parallel algorithms have been developed to solve these equations directly and numerically. Calculations were performed on a large-scale Beowulf-class PC cluster at the University of Saskatchewan.<p> We first study the effects of inhomogeneity on nanoscale superconductors due to the presence of surfaces or a single impurity deposited in the sample. It is illustrated that CDW can coexist with SC in a finite-size s-wave superconductor. Our calculations show that a weak impurity potential can lead to significant suppression of the superconducting order parameter, more so than a strong impurity. In particular, in a nanoscale d-wave superconductor with strong electron-phonon coupling, the scattering by a weakly attractive impurity can nearly kill superconductivity over the entire sample.<p> Calculations for periodic systems also show that CDW can coexist with s-wave superconductivity. In order to identify the cause of the CDW instability, the BdG equations have been generalized to include the next-nearest neighbour hopping integral. It is shown that the CDW state is strongly affected by the magnitude of the next-nearest neighbour hopping, while superconductivity is not. The difference between the CDW and SC states is a result of the anomalous, or off-diagonal, coupling between particle and hole components of quasiparticle excitations. The Fermi surface is changed as next-nearest neighbour hopping is varied; in particular, the perfect nesting and coincidence of the nesting vectors and the vectors connecting van Hove singularities (vHs) for zero next-nearest neighbor hopping is destroyed, and vHs move away from the Fermi energy. It is found that within our one-band tight-binding model with isotropic s-wave superconductivity, CDW and SC can coexist only for vanishing nearest neighbor hopping and for non-zero hopping, the homogeneous SC state always has the lowest ground-state energy. Furthermore, we find in our model that as the magnitude of the next-nearest neighbor hopping parameter increases, the main cause of the divergence in the dielectric response accompanying the CDW transition changes from nesting to the vHs mechanism proposed by Rice and Scott. It is still an open question as to the origin of CDW and its interplay with SC in multiple-band, anisotropic superconductors such as niobium diselenide, for which fundamental theory is lacking. The work presented in this thesis demonstrates the possible coexistence of charge density waves and superconductivity, and provides insight into the mechanism of electronic instability causing charge density waves.

In this thesis, we study an isolated vortex in an s-wave superconductor by solving the Bogoliubov-de Gennes equations self-consistently on a disc. We calculate the order parameter and supercurrent profiles, as well as the distribution of quasiparticle states. In contrast to quasi-classical treatments, the ratio Δ∞/EF between the order parameter and the Fermi energy is not assumed negligible. We study a regime where this ratio is on the order of 10-1, relevant to high-temperature superconductors. In this regime, we find a Friedel-like oscillation in the order parameter profile at low temperatures. This oscillation is attributed to an increased level spacing of the quasiparticle states, causing a decrease of the number of states present inside the superconducting energy gap. The results are in good agreement with previously published works. In future studies, the method used in this thesis will be generalized to d-wave superconductors. / I detta examensarbete studeras en ensam virvel i en s-vågssupraledare genom att självkonsistent lösa Bogoliubov och de Gennes' ekvationer på en cylinderskiva. Vi beräknar ordningsparameter- och superströmsprofiler, samt fördelningen av kvasipartikeltillstånd. Till skillnad från i kvasiklassiska metoder så antas inte kvoten Δ∞/EF mellan ordningsparametern och Fermi-energin vara negligerbar. Vi studerar en regim där denna kvot är av storleksordningen 10-1, vilket är fallet i högtemperatur-supraledare. Vid låga temperaturer finner vi i denna regim en Friedelliknande oscillation i ordningsparameterprofilen. Denna oscillations förklaras genom att separationen mellan kvasipartikeltillstånd ökar, vilket får som effekt att färre tillstånd ryms innanför det supraledande energigapet. Våra resultat överensstämmer väl med tidigare publicerade artikler. I framtida studier kommer metoden vi använder i detta examensarbete att generaliseras till d-vågssupraledare.

<p>This thesis focuses on the fluctuation in the switching current $I_s$ of superconducting Al nanowires. We discovered that the maximum current which nanowires can support is limited by a single phase slip at low temperature. </p><p>Al superconducting nanowires less than 10 nm wide were fabricated based on a MBE grown InP ridge template in an edge-on geometry. The method utilizes a special substrate featuring a high standing 8nm-wide InP ridge. A thin layer of Al was evaporated on the substrate and Al on the ridge formed nanowires.</p><p>The fluctuation effects starts to dominate in the nanowire due to reduced energy barrier. One of such effects is the phase slip. The phase slip is a topological event, during which the superconducting phase between two superconducting electrodes changes by $2\pi$. The phase slip broadens the normal-superconducting transition. Part of the nanowire becomes normal during the phase slip and forms a normal core. The normal core generates heat and causes the premature switching in superconducting nanowires.</p><p></p><p>The nanowire becomes superconducting below the critical temperature $T_c$. The superconducting-normal transition was studied in the thesis. The transition of nanowires with superconducting leads qualitatively fits the thermally activated phase slip (TAPS) theory. On the other hand, the transition of the nanowires with normal leads showed a resistive tail due to the inverse-proximity effect.</p><p>The nanowire switches from the superconducting state to the normal state as the current is increased. Ideally, the maximum current is set by a pair-breaking mechanism, by which the kinetic energy of quasi-particles exceeds the bonding energy of Cooper pairs. This is called the critical current, $I_c$. In practice, the measured maximum current, called the switching current $I_s$, cannot reach $I_c$ because of the phase slip.</p><p>$I_s$ shows stochasticity due to the phase slip. For the nanowires with superconducting leads, the average $I_s$ approximately follows but falls below $I_c$. The fluctuation in $I_s$ shows non-monotonic behavior, in contrast to other studies. The fluctuation first increases and then decreases rapidly with increasing temperature. The fluctuation behavior is consistent with a scenario where the switch is triggered by a single phase slip at low temperature while by multiple phase slips at higher temperature. Thermal activation of phase slips appears dominant at most temperatures. However, in the thinnest nanowire, the saturation of the fluctuation at low temperature indicates that the phase slips by macroscopic quantum tunneling.</p><p>The superconducting nanowires with normal leads were also studied. One of the distinctive properties of our nanowire (the critical field of 1D nanowire is 10 times larger than that of a 2D superconducting film) allowed us to study the same nanowire with different leads (superconducting or normal). Both the average $I_s$ and the fluctuation in $I_s$ differed qualitatively depending on whether the leads were superconducting or normal. The temperature dependence of the average $I_s$ followed the $I_c$ of the Josephson junction instead of the phenomenological pair-breaking $I_c$. The difference was found to depend on both the temperature (close to $T_c$ or 0) and the length (shorter or longer than the charge imbalance length). Our study also showed that nonlinear current-voltage (IV) curves were observed due to the inverse-proximity effect.</p> / Dissertation

Bi2Rh3Se2 have been known as a charge-density-wave (CDW) superconductor, where the superconducting critical temperature Tc and the CDW phase transition are about 0.7 K and 250 K, respectively. Since there has no definite proof that the anomaly at around 250 K comes from charge-density-wave, we wished to provide another evidence to study whether the superconductor had the properties of CDW by electric resistivity measurements applied different pressures. Bi2Rh3Se2 was prepared by using the solid state reaction method and heating in the quartz tube. After the sample was synthesized, the quality was identified by XRD, MPMS, and specific heat probe. With the confirmation of the above-mentioned measurements, we can determine the sample¡¦s quality is good. Furthermore, temperature-dependent resistivity (2-340 K) under pressure (up to 22.23 kbar) on the ternary superconductor Bi2Rh3Se2 are performed to study the possible coexistence of CDW and superconductivity. Interestingly, the resistive anomaly occurred at Ts~250 K, is shifted to higher temperature with increasing pressure. This experimental finding is not consistent with a traditional CDW transition. Moreover, the temperature-dependent Transmission Electron Microscopy (TEM) electron diffraction is evident a structural phase transition from space group ¡§C1 2/m 1¡¨ (Ts > 250 K) to ¡§P1 2/m 1¡¨ (Ts < 250 K). Finally, We do the Co doping to make sure the effects of chemical pressure on this phase transition. The results are opposite to imposed by physical pressure that the transition is shift to lower temperature with more Co inside the sample.

In this work the interactions between neighboring superconducting thin film and ferromagnetic structures, i.e. superconductor-ferromagnet hybrid systems, were studied. A type-II superconducting thin film (Pb82Bi12), was deposited in close proximity to various ferromagnetic structures. These magnetic structures include: (i) alternating iron-brass shims of 275 mu m period, (ii) an array of 4 mu m wide Co stripes with smaller period (9 mu m), (iii) a square array of 50nm diameter, high aspect ratio (5-7) Ni rods with 250nm period. Measurements of critical transport current (IC), resistance (RH(T)) and second critical field (HC2) are reported. A variety of novel effects (enhancement of (IC) and (HC2), matching field effect, field compensation effect, and large hysteresis) are also reported. Using measurements on thin superconducting films atop a Co stripe array with a 9 mu m period, a superconductor-ferromagnet hybrid device (a mechanical superconducting persistent switch) is proposed. In addition, scanning Hall probe microscopy (SHPM) and other imaging techniques were used to characterize the magnetic properties of the systems mentioned. The SHPM was also used to acquire B-H and M-H curves. An additional sharp magnetic needle and electromagnetic coil assembly intended for micromanipulation of small magnetic particles and individual cells was also characterized.

In spite of the failures to find an ultimate theory of unconventional superconductivity, after many years of research the scientific community possesses a considerable store of theoretical knowledge about the problem. Over time, the focus is gradually shifted from finding a theoretical description of an experimentally observed phenomenon to distinguishing between multiple models that offer comparably reasonable descriptions. From the point of view of an experimentalist, this means that any qualitative under-standing of an experimental observation would no longer suffice. Instead, the empha-sis in the experimental research should be shifted to accurate quantification of obser-vations, which becomes possible only if the results available from all the available ex-perimental methods are connected together by the theoretical glue. Among the meth-ods that are to be unified, ARPES plays a central role. The reason for this is that it gives access to the single-particle excitation spectrum of the material as a function of both momentum and energy with very high resolution. Other experimental techniques, such as inelastic neutron scattering (INS), Raman spectroscopy, or the newly estab-lished Fourier-transform scanning tunneling spectroscopy (FT-STS) probe more com-plicated two-particle spectra of the electrons and up to now can not achieve the mo-mentum resolution comparable with that of ARPES. Such reasoning serves as the mo-tivation for the present work, in which some steps are done towards understanding the anomalous effects observed in the single-particle excitation spectra of cuprates and relating the ARPES technique to other experimental methods. First, the electronic properties of BSCCO are considered — the superconducting cuprate most studied by surface-sensitive methods. The recent progress in un-derstanding the electronic structure of this material is reported, focusing mainly on the many-body effects (renormalization) and their manifestation in the ARPES spectra. The main result of this part of the work is a model of the Green’s function that is later used for calculating the two-particle excitation spectrum. Then, the matrix element effects in the photoemission spectra of cuprates are discussed. After a general introduction to the problem, the thesis focuses on the recently discovered anomalous behavior of the ARPES spectra that partially originates from the momentum-dependent photoemission matrix element. The momentum- and excitation energy dependence of the anomalous high-energy dispersion, termed “waterfalls”, is covered in full detail. Understanding the role of the matrix element effects in this phenomenon proves crucial, as they obstruct the view of the underlying excitation spectrum that is of indisputable interest. Finally, the work describes the relation of ARPES with other experimental methods, with the special focus on the INS spectroscopy. For the optimally doped bilayer Bi-based cuprate, the renormalized two-particle correlation function in the superconducting state is calculated from ARPES data within an itinerant model based on the random phase approximation (RPA). The results are compared with the experimental INS data on BSCCO and YBCO. The calculation is based on numerical models for the normal and anomalous Green’s functions fitted to the experimental single-particle spectra. The renormalization is taken into account both in the single-particle Green’s function by means of the self-energy, and in the two-particle correlation function by RPA. Additionally, two other applications of the same approach are briefly sketched: the relation of ARPES to FT-STS, and the nesting properties of Fermi surfaces in two-dimensional charge density wave systems.

This thesis represents a systematic study of electronic structure of the modulation-free Pb-doped Bi2212 superconducting cuprates with respect to interlayer coupling done by using the angle-resolved photoemission spectroscopy (ARPES), which is a leading technique in the experimental investigation of the single particle excitations in solids. The results presented in this work indicate a very different origin for the observed complex spectra lineshape. Specifically, the peak-dip-hump lineshape can be easily understood in terms of the superposition of spectral features due to bilayer band splitting, namely the splitting of the CuO2 plane derived electronic structure in bonding and antibonding bands due to the interlayer coupling of CuO2 bilayer blocks within the unit cell of Bi2212. By performing experiments at synchrotron beamlines where the energy of the incoming photons can be tuned over a very broad range, the detailed matrix elements energy dependence for both bonding and antibonding bands was determined. This gave the opportunity to study the electronic properties these two bands separately. For the first time, it was proved that the superconducting gap has the same value and symmetry for both bands. Furthermore, having recognized and sorted out the bilayer splitting effects, it became possible to identify more subtle effects hidden in the details of the ARPES lineshapes. On underdoped samples an &amp;quot;intrinsic&amp;quot; peak-dip-hump structure due to the interaction between electrons and a bosonic mode was observed. Studying the doping, temperature, and momentum dependence of the photoemission spectra it was established that: the mode has a characteristic energy of 38-40 meV and causes strong renormalization of the electronic structure only in the superconducting state; the electron-mode coupling is maximal around the (?à,0) point in momentum space and is strongly doping dependent (being greatly enhanced in the underdoped regime). From the above, it was concluded that the bosonic mode must correspond to the sharp magnetic resonance mode observed in inelastic neutron scattering experiments, and that this coupling is relevant to superconductivity and the pairing mechanism in the cuprates.

Nous avons mesuré la durée de vie de l'etat supraconducteur d'une jonction Josephson<br />polarisée en courant et shuntée par un circuit microonde se comportant comme une ligne à echos electromagnetiques. En faisant varier in situ la longueur de cette ligne, nous pouvons ajuster le temps d'aller-retour de ces echos. A basse température (T=20mK), la jonction transite hors de l'état supraconducteur par effet tunnel quantique macroscopique. Nous montrons que cet effet tunnel est fortement attenué si le temps d'aller-retour des<br />échos est inférieur à un nouveau temps caractéristique de l'effet tunnel, différent du temps de vie. Nous interprétons ce nouveau temps caracteristique comme le temps moyen passé par la particule sous la barrière de potentiel lors de sa sortie du puits. A plus haute<br />température (T=1K), la jonction transite hors de l'état supraconducteur par activation thermique. Dans ce regime, le taux de sortie varie de façon oscillatoire en fonction de la longueur de la ligne. Nous interprétons ce phenomène comme la manifestation des oscillations<br />effectuées par la différence de phase de la jonction dans l'état supraconducteur juste avant la transition vers l'état dissipatif, ces oscillations etant entretenues par les fluctuations thermiques.

Cette thèse a permis le développement et l'optimisation de jonctions Josephson SNS (Supraconducteur–métal Normal–Supraconducteur) à électrodes NbN et barrière TaxN de haute résistivité. On a montré une bonne reproductibilité des propriétés des couches TaxN en fonction des paramètres du dépôt. Les tricouches NbN/TaxN/NbN présentent la température critique élevée attendue (16K). Les jonctions présentent une dépendance claire du produit RnIc (courant Josephson x résistance normale, indicateur de la fréquence Josephson maximale) en fonction de la pression d'azote dans le dépôt. On a ainsi obtenu sur des collections de jonctions des produits RnIc très élevés, jusqu'à 3,74mV à 4,2K pour des densités de courant critique Jc voisines de 15kA/cm2. Les jonctions présentent les comportements Josephson attendus, (diffraction de Fraunhofer et marches de Shapiro) jusqu'à 14K. La dépendance du Jc des jonctions en fonction de la température a été interpolée en utilisant le modèle des jonctions SNS longues dans la limite sale, donnant une longueur de cohérence du métal normal autour de 3,8nm à 4,2K. Nous avons enfin étudié un procédé de fabrication multiniveaux adapté aux circuits RSFQ (Rapid Single Flux Quantum), comprenant un plan de masse commun et des résistances de polarisation. Pour conclure, nous avons montré la supériorité de performances des jonctions NbN/TaxN/NbN sur les jonctions actuelles en niobium et leur intérêt pour réaliser des circuits numériques RSFQ compacts. En effet ces jonctions s'affranchissent des résistances d'amortissement des jonctions Nb, et peuvent fonctionner jusqu'à des fréquences d'horloge supérieures à 150 GHz et jusqu'à 10K (contre 50 GHz en Nb à 4,2K).

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