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This thesis addresses the tunnelling of charge carriers in different materials. First looking at the simplest case of electron tunnelling in metals at zero, then finite temperature, the current is obtained using the Fermi-Dirac golden rule and then the conductance is obtained. This is extended to take into account the spatial dependence of one of the metals being a tip since experimentally this is done by scanning tunnelling microscopy where a tip traces over the surface of a sample. The next step is to look at tunnelling between a metal and a semiconductor, again the current is found. Semiconductors can be doped and the effect this has on tunnelling is examined. Next superconductors are introduced. The purpose of my research has been to look at the tunnelling spectra of high-temperature superconducting cuprates for both extrinsic (metal-superconductor) and intrinsic (superconductor-superconductor) tunnelling. The main features seen experimentally with cuprate tunnelling are identified and then a theory capable of explaining these features is discussed. The theory is compared to experimental results and we find good agreement.

Thesis advisor: Ziqiang Wang / One of the most unconventional electronic states in high transition temperature cuprate superconductors is the pseudogap state. In the temperature versus doping phase diagram, the pseudogap state straddles across the antiferromagnetic (AF) state near half filling and the superconducting (SC) dome on the hole doped side above the transition temperature Tc. The relationship between the pseudogap state and these two well known states - the AF state and the SC state is believed to be very important for understanding superconductivity and the emergent quantum electronic matter in doped Mott insulators. The pseudogap is characterized by the emergence of a soft gap in the single-particle excitation spectrum in the normal state in the temperature range between Tc and a characteristic temperature T*, i.e. Tc < T < T*. The most puzzling feature of the pseudogap is the nodal-antinodal dichotomy. Observed by ARPES in momentum space, the Fermi surface is gapped out in the antinodal region leaving a Fermi arc of gapless excitations near the nodes. Whether the pseudogap is an incoherent superconducting gap (onegap scenario) or it is a different gap governed by other mechanisms, other than superconductivity, (two-gap scenario) is still under debate. In this thesis I study the particle-particle channel and the particle-hole channel of the valence bond fluctuations away from half filling. Based on a strong-coupling analysis of the t-J model, I argue that the superexchange interaction J induced incommensurate bond centered density wave order is the driving mechanism for the pseudogap state. Low energy density of states (DOS) are eliminated by multiple incommensurate scatterings in the antinodal region at the Fermi level. I show that the interplay between the incommensurate bond centered d-wave density wave instability and the intrinsic electronic inhomogeneity in real cuprate materials is responsible for the observed pseudogap phenomena. Utilizing the spatially unrestricted Gutzwiller approximation, I show that the off-stoichiometric doping induced electrostatic disorder pins the low-energy d-wave bond density fluctuations, resulting in a VBG phase. The antinodal Fermi surface (FS) sections are gapped out, giving rise to a genuine normal state Fermi arc. The length of the Fermi arc shrinks with underdoping below the temperature T* determined by thermal filling of the antinodal pseudogap. Below Tc, the d-wave superconducting gap due to singlet pairing coexists and competes with the VBG pseudogap. The spatial, momentum, temperature and doping dependence of these two gaps are consistent with recent ARPES and STM observations in underdoped and chemically substituted cuprates. The temperature versus doping phase diagram captures the salient properties of the pseudogap phenomena and provides theoretical support for the two-gap scenario. In addition to resolving the complexities of the quantum electronic states in hole-doped cuprates, my unified theory elucidates the important role of the interplay between the strong electronic correlation and the intrinsic electronic disorder in doped transition metal oxides. / Thesis (PhD) — Boston College, 2011. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

Thesis advisor: Kevin S. Bedell / We investigate the structure of the equation of state of finite nuclear matter by examining the nature of isospin dependence in the (a)symmetry energy term. In particular, we include in the description of the binding energy fourth-order dependence with respect to the asymmetry factor, (N-Z)/A, and the regime of the l=0 Landau parameter, F0´ , is required to be less than –1. This modified equation predicts a minimum binding energy where N&#8800;Z, in addition to the standard symmetric minimum when N=Z. Results with the new asymmetry energy term are compared with experimental binding and symmetry energies from standard semi-empirical mass formulas. Importantly, this method reveals one possible mechanism for producing the phenomenon of neutron excess which is seen in physical nuclei. / Thesis (BS) — Boston College, 2004. / Submitted to: Boston College. College of Arts and Sciences. / Discipline: Physics. / Discipline: College Honors Program.

Nodal semimetals host either degenerate points (Dirac/Weyl points) or lines whose band topology in Brillouin zone can be classified either as trivial (normal nodal semimetals) or non trivial (topological nodal semimetals). This thesis investigates the electronic structure of two different categories of topological nodal semimetals probed by angleresolved photoemission spectroscopy (ARPES): The first material is Indium Bismuth (InBi). InBi is a semimetal with simple tetragonal structure with P4/nmm space group. This space group is predicted to host protected nodal lines along the perpendicular momentum direction at the high symmetry lines of the Brillouin zone boundary even under strong spin-orbit coupling (SOC) situation. As a semimetal with two heavy elements, InBi is a suitable candidate to test the prediction. The investigation by ARPES demonstrates not only that InBi hosts the nodal line in the presence of strong SOC, it also shows the signature of type-II Dirac crossing along the perpendicular momentum direction from the center of Brillouin zone. However, as the nodal line observed is trivial in nature, there is no exotic drumhead surface states observed in this material. This finding demonstrates that Dirac crossings can be protected in a non-symmorphic space group. The second material is NbIrTe₄ which is a semimetal that breaks inversion symmetry predicted to host only four Weyl points. This simplest configuration is confirmed by the measurement from the top and bottom surface of NbIrTe₄ showing only a pair of Fermi arcs each. Furthermore, it is found that the Fermi arc connectivity on the bottom surface experiences re-wiring as it evolves from Weyl points energy to the ARPES Fermi energy level. This change is attributed to the hybridisation between the surface and the bulk states as their projection lie within the vicinity of each other. The finding in this work demonstrates that although Fermi arcs are guaranteed in Weyl semimetals, their shape and connectivity are not protected and may be altered accordingly.

Fermi surface, the locus in momentum space of gapless low-energy excitations, is a concept of fundamental importance in solid state physics. Electronic properties of a material are determined by the long-lived low-energy excitations near the Fermi surface. Conventionally, Fermi surface is understood as a property exclusive to a metallic state, contoured by electronic bands crossed by the Fermi level, although there has been a continuing effort in searching for Fermi surface outside the conventional description. In this thesis, techniques developed to prepare high-quality single crystals of SmB$_6$ and YBa$_2$Cu$_3$O$_{6+x}$ (abbreviated as YBCO$_{6+x}$ hereinafter) are described. By utilising measurement techniques of exceptional sensitivity and exploring a wide range of temperatures, magnetic fields, and electrical currents, we found signatures of unconventional Fermi surfaces beyond the traditional description in these strongly correlated electronic systems. SmB$_6$ is a classic example of Kondo insulators whose insulating behaviour arises due to strong correlation between the itinerant $d$-electrons and localised $f$-electrons. The peculiar resistivity plateau onsets below 4 K has been a decades-long puzzle whose origin has been recently proposed as the manifestation of topological conducting surface states. We found that the insulating behaviour in electrical transport is robust against magnetic fields up to 45 T, while prominent quantum oscillations in magnetisation are observed above 10 T. Angular dependence of the quantum oscillations revealed a three-dimensional characteristics with an absolute amplitude consistent with a bulk origin, and temperature dependence showed a surprising departure from the conventional Lifshitz-Kosevich formalism. Complementary thermodynamic measurements showed results consistent with a Fermi surface originating from neutral itinerant low-energy excitations at low temperatures. Theoretical proposals of the unconventional ground state uncovered by our measurements in SmB$_6$ are discussed. YBCO$_{6+x}$ is a high-temperature superconductor with a maximum $T_{\rm c}$ of 93.5 K and the cleanest member in the family of copper-oxide, or {\it cuprate}, superconductors. The correct description of electronic ground state in the enigmatic pseudogap regime, where the antinodal density of states are suppressed below a characteristic temperature $T^*$ above $T_{\rm c}$, has been a subject of active debates. While the quantum oscillations observed in underdoped YBCO$_{6+x}$ have been predominately interpreted as a property of the normal state where the superconducting parameter is completely suppressed at $\approx$ 23 T, we made the discovery that YBCO$_{6.55}$ exhibits zero resistivity up to 45 T when a low electrical current is used, consistent with the observation of a hysteresis loop in magnetisation. Quantum oscillations in the underdoped YBCO$_{6+x}$ are thus seen to coexist with $d$-wave superconductivity. Characteristics of the quantum oscillations are consistent with an isolated Fermi pocket reconstructed by a charge density wave order parameter and unaccompanied by significant background density of states, suggesting the antinodal density of states is completely gapped out by a strong order parameter involving pairing correlations, potentially in addition to the other order parameters. Transport measurements performed over a wide doping range show signatures consistent with pairing correlations that persist up to the pseudogap temperature $T^*$. The surprising observation of quantum oscillations in insulating SmB$_6$ and superconducting YBCO$_{6+x}$ demonstrates a possible new paradigm of a Fermi surface without a conventional Fermi liquid. A new theoretical framework outside the realm of Fermi liquid theory may be needed to discuss the physics in these strongly correlated materials with enticing electronic properties.

The main topic of this thesis is analysis of an unidentified Galactic TeV gamma-ray source, MGRO J1908+06, discovered by Milagro instrument in 2007. We analyzed 54 hours of observational data from the Very Energetic Radiation Imaging Telescope Array System (VERITAS), a ground-based gamma-ray observatory in southern Arizona comprised of an array of four Cherenkov Telescopes that reconstructs the energy and direction of astrophysical gamma-rays by imaging Cherenkov light emitted by energetic particles in air showers produced by the primary gamma-rays. MGRO J1908+06 is located between a supernova remnant SNR G40.5-0.5 and a young, energetic pulsar PSR J1907+0602. We studied the energy dependent morphology of the TeV emission from the source and measured the source extent and spectrum. The source extends well past the boundary of the SNR and is not correlated with strong radio continuum or molecular line emission which likely excludes an origin for the emission as solely due to the SNR. While emission in the 0.5-1.25 TeV band was centered around the pulsar, higher energy emission was observed near the supernova remnant. This morphology is opposite that observed in other pulsar wind nebulae. We proposed two models for the high energy emission located well away from the pulsar but close to the SNR: (1) shock acceleration at the shock front created by an interaction between the pulsar wind and the dense gas at the edge of the SNR or (2) molecular clouds around the SNR provides seed photons with energies higher than those from Cosmic Microwave Backgrounds for inverse Compton scattering. The former model can be tested by looking for molecular emission lines that trace shocks and by measuring the pulsar velocity. In addition, we investigated the gamma-ray emission from the nova explosion of V407 Cygni that occurred in March 2010. The Fermi-LAT observed this event in the energy range of E >100 MeV. The origins of the gamma-ray emission that the Fermi-LAT team proposed are either protons (hadronic model) or electrons (leptonic model), both of which were accelerated at the nova shock via the Fermi acceleration mechanism. We did not consider their leptonic model because no TeV gamma-ray emission is predicted. Their hadronic model can generate TeV gamma-rays with the modeled parameters. We found no evidence for TeV emission. We showed that with the flux upper limit calculated using the VERITAS data imposes constraints on the extension of the proton spectrum at high energies.

We conduct a comprehensive and systematic study of the Fermi-Pasta-Ulam (FPU) model using both equilibrium and non-equilibrium molecular dynamics simulations, with the aim being to explain the cause of the anomalous energy-transport behaviour in the model. In the equilibrium scenario, our motivation stems from the lack of a complete understanding of the effects of initial conditions on the energy dissipation among Fourier modes. We also critically reconsider the ????probes' that had been widely used to quantitatively describe the types of energy sharing in a system, and then decide on a preferred choice to be used in our equilibrium study. We establish, from strong numerical evidence, that there exists a critical energy density of approximately 0:1, above which the energy dissipation among the modes becomes independent of initial conditions and system parameters, and that the full equipartition of mode energy is never attained in the FPU model. We report, for the first time, the violation of particle positions in the FPU model at high energies, where the particles are found to pass through one another. In the non-equilibrium scenario, we critically review the Nos???Se-Hoover algorithm thermostatting method largely used by other works, and identify its weaknesses. We also review some other alternative methods and decide on the most appropriate one to be implemented throughout our work. We confirm the divergence of the thermal conductivity of the FPU model as the chain length increases, and that kfpu [symbol] No.41, in agreement with other works. Our study further shows that there exists an upper limit of the anharmonicity in the FPU model, and that any attempt to increase the strength of this anharmonicity will not succeed. We also introduce elastic collisions into the original FPU model and find that the Modified model (FPUC) still exhibits anomalous thermal conductivity. We conclude that a one-dimensional FPU-type model with ????only' nearest-neighbour interaction, regardless of being soft or hard, does not exhibit a finite thermal conductivity as the system size increases, due to the non-chaotic nature of its microscopic dynamics, the origin of which we are unable to account for. Finally, we briefly outline possible research directions.

Le satellite Fermi a été lancé le 11 juin 2008, avec à son bord le Large Area Telescope (LAT). Le LAT est un télescope sensible au rayonnement gamma de 20 MeV à plus de 300 GeV. Au début de l'activité de Fermi, neuf pulsars jeunes et énergétiques étaient connus dans le domaine gamma. Le nombre de détections de pulsars par le LAT prédit avant lancement était de plusieurs dizaines au moins. Le LAT permettait également l'étude des pulsars milliseconde (MSPs), jamais détectés avec certitude à très haute énergie jusqu'alors. Cette thèse aborde dans un premier temps la campagne de chronométrie des pulsars émetteurs radio et/ou X, candidats à la détection par le LAT, en collaboration avec les grands radiotélescopes et télescopes X. Cette campagne a permis la recherche de signaux gamma pulsés avec une grande sensibilité. En outre, la plupart des MSPs galactiques ont été suivis dans le cadre de cette campagne, sans biais de sélection a priori sur cette population d'étoiles. Pour la première fois, des pulsations ont été détectées pour huit MSPs galactiques au-dessus de 100 MeV. Quelques bons candidats à une détection prochaine apparaissent. Une recherche similaire a été conduite pour des MSPs d'amas globulaires, sans succès à présent. L'analyse des courbes de lumière et des propriétés spectrales des huit MSPs détectés révèle que leur rayonnement gamma est relativement similaire à celui des pulsars ordinaires, et est vraisemblablement produit dans la magnétosphère externe. Cette découverte suggère que certaines sources non identifiées sont des MSPs, pour l'instant inconnus.