La compréhension de la dissipation dans l'état supraconducteur est l'une des clefs de l'émergence de la technologie supraconductrice. Dans le cadre particulier des couches minces, cette thèse décrit le passage de l'état supraconducteur vers l'état normal sous l'effet d'un courant de transport, et ses possibles implications technologiques. Un régime d'écoulement visqueux de vortex (flux flow) suivi par un brusque saut vers l'état normal est tout d'abord identifié et discuté dans des films de niobium. Il est également montré, dans ces couches minces, l'influence des surfaces sur la dynamique des vortex. La transition vers l'état normal de films d'YBaCuO permet ensuite de vérifier le haut potentiel des supraconducteurs comme limiteurs de courant alternatif ou continu. Il est enfin démontré que de tels systèmes peuvent récupérer leur état supraconducteur sous courant.

The work described in this thesis uses oxygen NMR to probe the electronic system of rare earth co-doped La_{2-x}Sr_xCuO_4, the prototypical high temperature superconducting cuprate (HTSC). Oxygen NMR turns out to be a powerful tool for this purpose. The nucleus is located directly inside the CuO_2 planes. It has a spin of 5/2 and a quadrupole moment and therefore can probe both, interactions with the magnetic hyperfine field as well as interactions through the electric field gradient of the crystal. Furthermore, the spin lattice relaxation time T_1 and the spin spin relaxation time T_2 contain information about the dynamics of these interactions. Such a link between the spin and charge structures in high temperature superconductors has been elusive until today. Instead, there are magnetic probes such as neutron scattering and muSR that provide evidence for a modulation of the spin structure and static magnetic moments, respectively, and charge probes like STM that reveal inhomogeneous doping distributions in the CuO_2 planes. In either case, inhomogeneities in the spin and charge system seem to be typical for HTSCs. Whereas the spin and charge modulations are believed to be dynamic in the superconducting compounds, they become static at low temperatures in Eu doped La_{2-x}Sr_xCuO_4, where superconductivity is suppressed. As could be demonstrated here, evidence for such a spin and charge separation, that often revealed stunning similarities to the spin ladder compounds, is apparent in almost all measured NMR parameters. / In dieser Arbeit werden Sauerstoff NMR Untersuchungen der elektronischen Struktur von Selten-Erd dotiertem La_{2-x}Sr_xCuO_4, dem prototypischen Hochtemperatursupraleiter (HTSL), vorgestellt. Sauerstoff NMR ist zu diesem Zweck besonders gut geeignet. Der Kern befindet sich innerhalb der Kupferoxid-Ebenen. Er hat einen Spin von 5/2 und ein Quadrupolmoment. Damit lassen sich Wechselwirkungen mit dem magnetischen Hyperfeinfeld der Cu-Atome sowie Wechselwirkungen mit dem elektrischen Feldgradienten des Kristalls untersuchen. Des Weiteren geben die Spin-Gitter-Relaxationszeit T_1 sowie die Spin-Spin-Relaxationszeit T_2 Aufschluss über die Dynamik dieser beiden Wechselwirkungen. Eine Verbindung zwischen der Spin- und Ladungsordnung gibt es in den HTSL bisher nicht. Statt dessen haben magnetische Messmethoden wie Neutronenstreuung oder muSR Aussagen über die magnetische Ordnung geliefert. Unabhängig davon liefern Messmethoden wie STM nur Informationen über eine Ladungsordnung oder inhomogene Ladungsverteilungen. Inhomogenitäten der Spins und Ladungen scheinen aber typisch für die HTSL zu sein. Man vermutet, dass diese Inhomogenitäten dynamisch in den supraleitenden Verbindungen sind, während sie in Eu dotiertem La_{2-x}Sr_xCuO_4 bei tiefen Temperaturen statisch werden und die Supraleitung unterdrücken. In dieser Arbeit wird gezeigt, dass sich diese Ladungs- und Spininhomogenitäten in vielen Parametern der NMR Spektren bemerkbar machen.

This thesis presents a theoretical study of Bose-Einstein condensates in a doublering trap. In particular, we determine the ground states of the condensate in the double-ring trap that arise from the interplay of quantum tunnelling and the trap’s rotation. The trap geometry is a concentric ring system, where the inner ring is of smaller radius than the outer ring and both lie in the same two-dimensional plane. Due to the difference in radii between the inner and outer rings, the angular momentum that minimises the kinetic energy of a condensate when confined in the individual rings is different at most frequencies. This preference is in direct competition with the tunnel coupling of the rings which favours the same angular momentum states being occupied in both rings. Our calculations show that at low tunnel coupling ground state solutions exist where the expectation value of angular momentum per atom in each ring differs by approximately an integer multiple. The energy of these solutions is minimised by maintaining a uniform phase difference around most of the ring, and introducing a Josephson vortex between the inner and outer rings. A Josephson vortex is identified by a 2p step in the relative phase between the two rings, and accounts for one quantum of circulation. We discuss similarities and differences between Josephson vortices in cold-atom systems and in superconducting Josephson junctions. Josephson vortices are actuated by a sudden change in the trapping potential. After this change Josephson vortices rotate around the double-ring system at a different frequency to the rotation of the double-ring potential. Numerical studies of the dependence of the velocity on the ground state tunnel coupling and interaction strength are presented. An analytical theory of the Josephson vortex dynamics is also presented which is consistent with our numerical results.

This thesis presents a theoretical study of Bose-Einstein condensates in a doublering trap. In particular, we determine the ground states of the condensate in the double-ring trap that arise from the interplay of quantum tunnelling and the trap’s rotation. The trap geometry is a concentric ring system, where the inner ring is of smaller radius than the outer ring and both lie in the same two-dimensional plane. Due to the difference in radii between the inner and outer rings, the angular momentum that minimises the kinetic energy of a condensate when confined in the individual rings is different at most frequencies. This preference is in direct competition with the tunnel coupling of the rings which favours the same angular momentum states being occupied in both rings. Our calculations show that at low tunnel coupling ground state solutions exist where the expectation value of angular momentum per atom in each ring differs by approximately an integer multiple. The energy of these solutions is minimised by maintaining a uniform phase difference around most of the ring, and introducing a Josephson vortex between the inner and outer rings. A Josephson vortex is identified by a 2p step in the relative phase between the two rings, and accounts for one quantum of circulation. We discuss similarities and differences between Josephson vortices in cold-atom systems and in superconducting Josephson junctions. Josephson vortices are actuated by a sudden change in the trapping potential. After this change Josephson vortices rotate around the double-ring system at a different frequency to the rotation of the double-ring potential. Numerical studies of the dependence of the velocity on the ground state tunnel coupling and interaction strength are presented. An analytical theory of the Josephson vortex dynamics is also presented which is consistent with our numerical results.

This thesis presents a theoretical study of Bose-Einstein condensates in a doublering trap. In particular, we determine the ground states of the condensate in the double-ring trap that arise from the interplay of quantum tunnelling and the trap’s rotation. The trap geometry is a concentric ring system, where the inner ring is of smaller radius than the outer ring and both lie in the same two-dimensional plane. Due to the difference in radii between the inner and outer rings, the angular momentum that minimises the kinetic energy of a condensate when confined in the individual rings is different at most frequencies. This preference is in direct competition with the tunnel coupling of the rings which favours the same angular momentum states being occupied in both rings. Our calculations show that at low tunnel coupling ground state solutions exist where the expectation value of angular momentum per atom in each ring differs by approximately an integer multiple. The energy of these solutions is minimised by maintaining a uniform phase difference around most of the ring, and introducing a Josephson vortex between the inner and outer rings. A Josephson vortex is identified by a 2p step in the relative phase between the two rings, and accounts for one quantum of circulation. We discuss similarities and differences between Josephson vortices in cold-atom systems and in superconducting Josephson junctions. Josephson vortices are actuated by a sudden change in the trapping potential. After this change Josephson vortices rotate around the double-ring system at a different frequency to the rotation of the double-ring potential. Numerical studies of the dependence of the velocity on the ground state tunnel coupling and interaction strength are presented. An analytical theory of the Josephson vortex dynamics is also presented which is consistent with our numerical results.

The study of cuprate high-temperature superconductors has undergone a recent resurgence due to the discovery of charge order in several families of cuprate materials. While its existence is now well established, little is known about its microscopic origins or its relationship to high-temperature superconductivity and the pseudogap. The aim of the research presented in this thesis is to address these questions. In this thesis I will report on the use of spectroscopic-imaging scanning tunnelling microscopy (SI-STM) to visualise the short-ranged charge density wave (CDW) in Bi₂Sr₂CaCu₂O₈₊ₓ and NaxCa₂₋ₓCuO₂Cl₂. Building on previous measurements of the intra unit-cell electronic structure of cuprates, I introduce sub-lattice segregated SISTM to individually address the atomic sub-lattices in the CuO₂ plane with spatial phase sensitivity. Using this technique I establish that the CDW in Bi₂Sr₂CaCu₂O₈+x and NaxCa₂₋ₓCuO₂Cl₂ has a previously unobserved d-symmetry form factor, where a breaking of rotational symmetry within the unit cell is modulated periodically in space. Towards identifying a mechanism of CDW formation, I establish that the amplitude of CDW modulations in the electronic structure are maximal at the pseudogap energy-scale and that these modulations exhibit a spatial phase difference of π between filled and empty states. Together with the doping evolution of the CDW wave-vector this highlights the role of the low-energy electronic structure of the pseudogap regime in CDW formation. To elucidate the relationship between the CDW and the superconducting condensate I will introduce nanometer resolution scanned Josephson tunnelling microscopy (SJTM). In this approach the Cooper pair (Josephson) tunnelling current between a Bi₂Sr₂CaCu₂O₈₊ₓ sample and a scan-able Bi₂Sr₂CaCu₂O₈₊ₓ nano-flake STM tip is used to directly visualise the superconducting condensate. I will report the observation of a periodic modulation in the Cooper pair condensate at the same wave-vector as the CDW, the first direct detection of a periodically modulating condensate in any superconductor.

In this thesis, the electronic properties in superconducting LiFeAs single crystal are investigated using low temperature scanning tunneling microscopy and spectroscopy (STM/S) at various temperatures. For this purpose, the differential conductance (dI/dV) measured by STS which is directly proportional to the local density of states (LDOS) of the sample to the sub-atomic precision, is used together with the topography information. The dI/dV spectra within the ±1 V energy range reveal a characteristic feature at around -350 mV to -400 mV in stoichiometric LiFeAs. This feature seems to be a universal property among all the Fe-based high temperature superconductors, because it is also found in Fe0.965Se1.035 and NaFe0.975Co0.025As single crystals at the energy of -210 mV and -200 mV, respectively. The temperature dependent spectroscopy data averaged over a spatially fixed clean area of 2 nm × 2 nm are successfully executed between 5 K and 20 K. The two distinct superconducting phases with critical temperatures Tc = 16 K and 18 K are observed. In addition, the distance between the dip position outside the superconducting gap and the superconducting coherence peak in the spectra remains temperature independent which confirms that it is not connected to an antiferromagnetic (AFM) spin resonance. The temperature dependent spectra have been measured between 5 K and 61 K within the energy range of ±100 mV as well. The hump structure at 42 mV tends to disappear around 60 K from unknown origin. The temperature dependent quasiparticle interference (QPI) has been studied within the temperature range between 6.7 K and 25 K and analyzed by the Fourier transformation of the measured spectroscopic maps. The dispersion plots in momentum space as a function of temperature show an enhancement of QPI intensity (±5.5 mV) within the superconducting gap at the Fermi level at 6.7 K near q ~ 0. This is interpreted on the basis of Andreev bound state. In both polarities outside of this, a depletion of QPI intensity is noticed between 5.5 mV and around 9 mV. At positive energies, the QPI intensity becomes very rich above 9 mV. The size of the enhanced QPI intensity near the Fermi level, and the edge of the rich QPI intensity beyond 9 mV are found to behave like superconducting order parameter with rising of temperature. Furthermore, an energy mode peaked at around 14 mV appears in the integrated QPI intensity below superconducting Tc (6.7 K). This is consistent with the observed peak at 1st derivative of the dI/dV spectra. In both of these cases, such 14 mV peak is suppressed at normal state (25 K). This mode is therefore directly related to superconductivity in LiFeAs. The off-stoichiometric LiFeAs single crystal with superconducting Tc of 6.5 K has a 10 mV rigid band shift of the Fermi level towards electron doping. The absence of the rich QPI intensity between 9 mV and 17 mV is found compared to the stoichiometric LiFeAs, and hence the 14 mV mode is absent here. This brings us to conclude once more time that such 14 mV energy mode is relevant for superconductivity in LiFeAs.

The experimental discovery of graphene in 2004 has opened up a new research field in the direction of atomically thin two-dimensional layered materials for exploration of many fundamental research problems and technological applications. The charge carriers in graphene are massless Dirac fermions due to which they exhibit absence of localization, thereby giving rise to huge intrinsic mobilities and ballistic transport even at room temperatures. But it was observed that the extrinsic disorder and intrinsic structural disorder can significantly influence the transport in graphene films. This thesis focuses on three different aspects of graphene -disorder, magnetism and proximity-induced superconductivity. We have reported conductance fluctuations-based transport studies to investigate these aspects as they provide more detailed information than what can be obtained from the standard transport measurements. Even though these conductivity fluctuations pose a serious bottleneck for various applications, they can also yield useful insights into the various scattering mechanisms and the symmetry properties of graphene. In the first half of the thesis, we describe the measurement of low frequency 1/f noise in large area polycrystalline graphene films to understand the role of grain boundaries in charge carrier transmission in graphene. TEM studies on the low and high angled GBs formed in these graphene samples showed that they form distinct disordered regions of varying widths depending on the tilt angle of the GBs. At low temperatures, the 1/f noise measurements indicated spontaneous breaking of time reversal symmetry across graphene grain boundaries which suggests the magnetic nature of these grain boundaries. In the second half of the thesis, we will concentrate on the universal conductance fluctuations (UCF) in graphene which is the manifestation of quantum interference phenomena at low temperatures. We find that the absolute magnitude of the UCF is directly related to various symmetry-breaking disorder present in graphene. We also discuss how the UCF can be used to study the nature of proximity-induced superconducting correlations in graphene. In the end, we have proposed new device schemes for the integration of ferromagnetic and superconducting materials with graphene.

In this thesis, the electronic properties in superconducting LiFeAs single crystal are investigated using low temperature scanning tunneling microscopy and spectroscopy (STM/S) at various temperatures. For this purpose, the differential conductance (dI/dV) measured by STS which is directly proportional to the local density of states (LDOS) of the sample to the sub-atomic precision, is used together with the topography information. The dI/dV spectra within the ±1 V energy range reveal a characteristic feature at around -350 mV to -400 mV in stoichiometric LiFeAs. This feature seems to be a universal property among all the Fe-based high temperature superconductors, because it is also found in Fe0.965Se1.035 and NaFe0.975Co0.025As single crystals at the energy of -210 mV and -200 mV, respectively. The temperature dependent spectroscopy data averaged over a spatially fixed clean area of 2 nm × 2 nm are successfully executed between 5 K and 20 K. The two distinct superconducting phases with critical temperatures Tc = 16 K and 18 K are observed. In addition, the distance between the dip position outside the superconducting gap and the superconducting coherence peak in the spectra remains temperature independent which confirms that it is not connected to an antiferromagnetic (AFM) spin resonance. The temperature dependent spectra have been measured between 5 K and 61 K within the energy range of ±100 mV as well. The hump structure at 42 mV tends to disappear around 60 K from unknown origin. The temperature dependent quasiparticle interference (QPI) has been studied within the temperature range between 6.7 K and 25 K and analyzed by the Fourier transformation of the measured spectroscopic maps. The dispersion plots in momentum space as a function of temperature show an enhancement of QPI intensity (±5.5 mV) within the superconducting gap at the Fermi level at 6.7 K near q ~ 0. This is interpreted on the basis of Andreev bound state. In both polarities outside of this, a depletion of QPI intensity is noticed between 5.5 mV and around 9 mV. At positive energies, the QPI intensity becomes very rich above 9 mV. The size of the enhanced QPI intensity near the Fermi level, and the edge of the rich QPI intensity beyond 9 mV are found to behave like superconducting order parameter with rising of temperature. Furthermore, an energy mode peaked at around 14 mV appears in the integrated QPI intensity below superconducting Tc (6.7 K). This is consistent with the observed peak at 1st derivative of the dI/dV spectra. In both of these cases, such 14 mV peak is suppressed at normal state (25 K). This mode is therefore directly related to superconductivity in LiFeAs. The off-stoichiometric LiFeAs single crystal with superconducting Tc of 6.5 K has a 10 mV rigid band shift of the Fermi level towards electron doping. The absence of the rich QPI intensity between 9 mV and 17 mV is found compared to the stoichiometric LiFeAs, and hence the 14 mV mode is absent here. This brings us to conclude once more time that such 14 mV energy mode is relevant for superconductivity in LiFeAs.

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