Thesis advisor: Vidya Madhavan / <p>It has been more than two decades since the first high temperature superconductor was discovered. In this time there has been tremendous progress in understanding these materials both theoretically and experimentally. Some important questions however remain to be answered; one of them is the temperature dependence of the superconducting gap which is in turn tied to question of the origin of the pseudogap and its connection with superconductivity.</p> <p> In this thesis, we present detailed Scanning Tunneling Microscopy (STM) spectroscopic studies of an electron doped superconductor, Pr<subscript>0.88</subscript>LaCe<subscript>0.12</subscript>CuO<subscript>4-&#948;</subscript> (PLCCO). The electron doped compounds form an interesting venue for STM studies for many reasons. In the hole-doped materials, especially in the underdoped side of the phase diagram, there is mounting evidence of a second gap that survives to high temperatures (high temperature pseudogap) that may have a different origin from superconductivity. This complicates studies of the temperature dependence of the superconducting gap in these materials. In PLCCO however, there is little evidence for a high temperature pseudogap potentially allowing us to address the question of the temperature evolution of the superconducting gap without the complication of a second gap. Secondly, the low T<subscript>c</subscript> of the optimally doped materials makes it easily accessible to temperature dependent STM studies. Finally, while hole-doped materials have been extensively studied by scanning tunneling microscopy (STM), there have been no detailed STM spectroscopic studies on the electron doped compounds. </p> <p> In the first part of the thesis, we investigate the effect of temperature on the superconducting gap of optimally doped PLCCO with T<subscript>c</subscript> = 24K. STM spectroscopy data is analyzed to obtain the gap as a function of temperature from 5K to 35K. The gap is parameterized with a d-wave form and the STM spectra are fit at each temperature to extract the gap value. A plot of this gap value as a function of temperature shows clear deviations from what is expected from BCS theory. We find that similar to the hole-doped superconductors a fraction of the surface still shows a gap above T<subscript>c</subscript>. The implications of our finding to the pseudogap phase are discussed.</p> <p> In the second part of the thesis, STM spectra are analyzed to determine the effect of impurities or vacancies on the local density of states. Electron doped superconductors require a post-annealing process to induce superconductivity. It is claimed that Cu vacancies in the CuO<subscript>2</subscript> planes which suppress superconductivity are healed by this process. This implies that for the same doping, a sample with higher T<subscript>c</subscript> should have fewer impurities compared to a sample with lower T<subscript>c</subscript>. We studied two PLCCO samples with 12% Ce doping; one with higher T<subscript>c</subscript> (24K) and the other with lower T<subscript>c</subscript> (21K). Through quasiparticle scattering study we find that there are more impurities in 21K samples than 24K sample, consistent with the picture of Cu vacancies in as grown samples. Finally, we present a discussion of the bosonic modes observed in the STM spectra and their connection to the spin excitations measured by neutron scattering.</p> / Thesis (PhD) — Boston College, 2009. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

Cette thèse est consacrée à l'étude mathématique de quelques modèles suggérés par la théorie de la supraconductivité. Plus spécifiquement, nous étudions le modèle de Ginzburg-Landau simplifié (sans champ magnétique) en présence de condition de type Dirichlet ou du type degrés prescrits. Dans une première partie nous traitons le problème d'existence de minimiseurs locaux dans un domaine multiplement connexe du plan pour des conditions de type degrés prescrits. La deuxième partie traite l'effet d'un terme de chevillage dans l'énergie de Ginzburg-Landau (GL) bi-dimensionnelle en imposant une condition de type Dirichlet. Cette partie se décompose en trois chapitres. On commence par l'étude d'un terme de chevillage qui est étagé et qui prend une valeur différente de 1 uniquement en un nombre fixe de sous domaines (aussi appelés inclusions) dont la taille tend vers zéro. Dans le chapitre suivant, nous considérons le cas d'un terme de chevillage sans hypothèse de structure particulière dans le cas où la donnée au bord est de degré nul. Dans le dernier chapitre de la deuxième partie, nous traitons le cas d'un terme de chevillage étagé et uniformément distribué avec une condition de type Dirichlet de degré non nul. On montre que la vorticité est quantifiée et localisée dans les inclusions. La dernière partie s'intéresse à l'effet d'un terme de chevillage étagé dans un domaine tridimensionnel avec une condition de Dirichlet. Les résultats préliminaires que nous présentons permettent d'appréhender la manière dont les filaments de vorticité sont "tordus" par l'effet du terme de chevillage / This thesis is devoted to the mathematical study of some models suggested by the theory of the superconductivity. More specifically, we consider the simplified model of Ginzburg-Landau (without magnetic field) in presence of a Dirichlet or a degree condition. In the first part we treat the existence problem of local minimizers in a multiply connected domain of the plan with prescribed degrees conditions. In the second part, we discuss the effect of a pinning term in the two-dimensional Ginzburg-Landau functional. This part is divided in three chapters. We first consider the situation of a pinning term (depending on the Ginzburg-Landau parameter) which is a simple function and takes a value different to 1 only in a fixed number of subdomains (also called inclusions) whose size tends to zero. We prove that, considering a Dirichlet condition with a non zero degree, the vorticity is quantized and localized inside the inclusions. In the second chapter, we consider the situation of a pinning term without specific structure. We imposed a Dirichlet boundary condition with a null degree. In the last chapter of the second part, we deal with the case of a simple and uniformly distributed pinning term. We impose a Dirichlet boundary condition with a non zero degree. The last part deals with the effect of a simple pinning term (independent of the Ginzburg-Landau parameter) in the three-dimensional Ginzburg-Landau functional. The preliminary results we present allow to understand how the vorticity lines are bent under the effect of the pinning term

We report a systematic investigation of the local electronic, magnetic, and superconducting properties of the new iron-based high temperature superconductor Ba(Fe(1-x)Co(x)As(2) (x = 0, 0.02 , 0.04, 0.082) through the measurement of 75As and 59Co NMR (Nuclear Magnetic Resonance) lineshapes, Knight shift (K), and spinlattice relaxation rate ( 1/ T1) . The 75As NMR lineshape of the undoped parent compound splits into two sets due to discrete values of hyperfine magnetic field B(c)(hf)= ±1.32 Tesla below the magnetic ordering temperature to the SDW (Spin Density Wave) state, TSDW. In contrast, for lightly Co doped samples with x=0.02 and 0.04, the 75As and 59Co lineshapes become broad and featureless below Tsnw , indicating that the ground state is no longer the commensurate SDW ordered state. The observed lineshape is consistent with an incommensurate SDW ordered state, or a commensurate state with large distribution of hyperfine field Bhf. In the optimally doped superconductor with x = 0.082 (Tc = 22 K) , we observe two types of As sites and three types of Co sites, respectively, as expected from a binomial distribution of Co dopants. We found no evidence for induced localized moments in the vicinity of Co dopants. This finding is in remarkable contrast with the case of Zn or Ni doped high Tc cuprates, and suggests that the fundamental physics of iron-based superconductors is different from that of cu prates. The temperature dependences of 75,59K and 75,59 (1/T1T) at both 75As and 59Co sites show that Ba(Fe(1-x)Co(x))(2)As(2) exhibits spin pseudo-gap like behavior down to ~100 K for a broad Co concentration range. Below ~100 K , we observe the enhancement of residual antiferromagnetic spin fluctuations associated with inter-band spin excitations between the hole and electron Fermi surfaces even for x= 0.082. This effect is suppressed in the overdoped sample with x= 0.099, and Tc decreases. Therefore, we suggest that antiferromagnetic spin fluctuations play a crucial role in the superconducting mechanism of Ba(Fe(1-x)Co(x))(2)As(2) . We also demonstrate that the superconductivity arises from a novel electronic state with spin susceptibility Xs ~ constant and in-plane resistivity P(ab)~T, which is not consistent with canonical Fermi-liquid behavior. / Thesis / Doctor of Philosophy (PhD)