No description available.

Previous studies have suggested that the material graphene might transition into an electron-electron interaction driven, unconventional, time-reversal-symmetry-breaking, (d+id)wave superconducting state upon either significant electron or hole doping, and, in particular, upon doping to the Van Hove singularity. As defects are likely to be introduced in the doping process, we are, in this text, concerned with the effects of defects on this superconducting state near the Van Hove singularity doping. To investigate the effects we use a mean-field treatment of a phenomenological resonant-valence-bond model. We find that the resonant-valence-bond amplitudes, which in the defect free graphene sheet are proportional to the superconducting pairing-potential, are suppressed near the defects, and that the recovery is well described by an exponential, yet anisotropic, recovery. In general, we find that the (d+id)-wave, superconducting state is quite resilient, and that even for strong defects, such as a vacancy, the recovery length is of the order of one lattice constant when extrapolated to weak pairing-potentials; this is compared to a conventional superconducting state of an attractive Hubbard model for which the same decay length is found to be of the order of a half lattice constant. For the defect free graphene sheet the (d+id)-wave state is a completely gapped state. The introduction of vacancies is, however, found to be accompanied by the appearance of midgap states. These states are shown to be localized around the vacancies. In accordance with the nature of this text, we will, for the benefit of students and non-experts, include an introductory section on the fundamental methods and concepts used. It gives a short and hopefully pedagogical introduction to the rudimentary concepts of solid state theory and the microscopic BCS theory of superconductivity.

The most-discussed pairing symmetry in Sr₂RuO₄ is chiral p-wave, pₓ ± p[sub]y, whose degeneracy is protected by the lattice symmetry. When the lattice symmetry is lowered by the application of a symmetry-breaking field, the degeneracy can be lifted, potentially leading to a splitting of the superconducting transition. To lift the degeneracy, the symmetry breaking field used in this study is uniaxial stress. Uniaxial stress generated by a piezo-electric actuator can continuously tune the electronic structure and in situ lower the tetragonal symmetry in Sr₂RuO₄. Previous studies of magnetic susceptibility and resistivity under uniaxial stress have revealed that there is a strong peak in T[sub]c when the stress is applied along the a-axis of Sr₂RuO₄. In addition, it has been proposed that the peak in T[sub]c coincides with a van Hove singularity in the band structure, and measurements of Hc₂ at the maximum T[sub]c indicate the possibility of an even parity condensate for Sr₂RuO₄ at the peak in Tc. In this thesis, the heat capacity approach is used to study the thermodynamic behavior of Sr₂RuO₄ under uniaxial stress applied along the crystallographic a-axis of Sr₂RuO₄. The first thermodynamic evidence for the peak in T[sub]c is obtained, proving that is a bulk property. However, the experimental data show no clear evidence for splitting of the superconducting transition; only one phase transition can be identified within the experimental resolution. The results impose strong constraints on the existence of a second phase transition, i.e. the size of the second heat capacity jump would be small or the second T[sub]c would have to be very close to the first transition. In addition to these results, I will present heat capacity data from the normal state of Sr₂RuO₄. The experimental results indicate that there is an enhancement of specific heat at the peak in T[sub]c, consistent with the existence of the van Hove singularity. The possibility of even parity superconductivity at the maximum T[sub]c has also been investigated. However, the heat capacity measurements are shown to be relatively insensitive to such a change, so it has not been possible to obtain strong and unambiguous evidence for whether it takes place or not.

As a result of the computing power provided by the current technology, computational methods now play an important role in modeling and designing materials at the nanoscale. The focus of this dissertation is two-fold: first, new computational methods to model nanoscale transport are introduced, then state-of-the-art tools based on density functional theory are employed to explore the properties of phosphorene, a novel low dimensional material with great potential for applications in nanotechnology. A Wannier function description of the electron density is combined with a generalized Slater-Koster interpolation technique, enabling the introduction of a new computational method for constructing first-principles model Hamiltonians for electron and hole transport that maintain the density functional theory accuracy at a fraction of the computational cost. As a proof of concept, this new approach is applied to model polythiophene, a polymer ubiquitous in organic photovoltaic devices. A new low dimensional material, phosphorene - a single layer of black phosphorous - the phosphorous analogue of graphene was first isolated in early 2014 and has attracted considerable attention. It is a semiconductor with a sizable band gap, which makes it a perfect candidate for ultrathin transistors. Multi-layer phosphorene transistors have already achieved the highest hole mobility of any two-dimensional material apart from graphene. Phosphorene is prone to oxidation, which can lead to degradation of electrical properties, and eventually structural breakdown. The calculations reported here are some of the first to explore this oxidation and reveal that different types of oxygen defects are readily introduced in the phosphorene lattice, creating electron traps in some situations. These traps are responsible for the non-ambipolar behavior observed by experimental collaborators in air-exposed few-layer black phosphorus devices. Calculation results predict that air exposure of phosphorene creates a new family of two-dimensional oxides, which has been later confirmed by X-ray photoemission measurements. These oxides can form protective coatings for phosphorene and have interesting tunable electronic properties. Finally, Wannier function interpolation has been used to demonstrate that a saddle-point van Hove singularity is present near the phosphorene Fermi energy, as observed in some layered cuprate high temperature superconductors; this leads to an intriguing strain-induced ferromagnetic instability.

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.

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 the repertoire of an experimental condensed matter physicist, the ability to tune continuously through features in the electronic structure and to selectively break point-group symmetries are both valuable techniques. The experimental technique at the heart of this dissertation, uniaxial stress, can do both such things. The thesis will start with a thorough discussion of our new technique, which was continually developed over the course of this work, presenting both its unique capabilities and also some guidance on the best working practices, before moving on to describe results obtained on two different strongly correlated electron materials. The first, Sr2RuO4, is an unconventional superconductor, whose order parameter has long been speculated to be odd-parity. Of interest to us is the close proximity of one of its three Fermi surfaces to a Van Hove singularity (VHs). Our results strongly suggest that we have been able to traverse the VHs, inducing a topological Lifshitz transition. T[sub]c is enhanced by a factor ~2.3 and measurements of H[sub](c2) open the possibility that optimally strained Sr2RuO4 has an even-parity, rather than odd-parity, order parameter. Measurements of the normal state properties show that quasiparticle scattering is increased across all the bands and in all directions, and effects of quantum criticality are observed around the suspected Lifshitz transition. Sr3Ru2O7 has a metamagnetic quantum critical endpoint, which in highly pure samples is masked by a novel phase. Weak in-plane magnetic fields are well-known to induce strong resistive anisotropy in the novel phase, leading to speculation that a spontaneous, electronically driven lowering of symmetry occurs. Using magnetic susceptibility and resistivity measurements we can show that in-plane anisotropic strain also reveals the strong susceptibility to electronic anisotropy. However, the phase diagram that these pressure measurements reveal is consistent only with large but finite susceptibility, and not with spontaneous symmetry reduction.

Although band theory is about a century old, it remains relevant today as a tool for the treatment of electrons in solids. The confluence of mathematical ideas like geometry and topology with band theory has proven to be a ripe avenue for research in the past few decades. The importance of Fermi surface geometry, especially in conjunction with electronic correlation, has been well recognized. One particular thread in this direction is probing the occurrence of non-trivial Fermi surface geometry, and its influence on macroscopic properties of materials. A notable example of exotic Fermi surface geometry arises from singular points of the dispersion, and these have been known since 1953. The investigation into these was reignited recently, culminating in the work presented in this thesis. In this dissertation, I investigate two broad categories of singular points in bands. At a singular point, either the dispersion or the Fermi surface fail to be smooth. This may cause distinct signatures in transport and spectroscopic properties when the singular point occurs close to the Fermi level. In the two dimensional setting, I classify using catastrophe theory, the point singularities arising from higher order saddles of the dispersion. These are the more exclusive cousins of the regular van Hove saddle that cause, among other things, a power law divergence in the density of states. The role of lattice symmetries in aiding or preventing the occurrence of these singularities is also carefully explored. In the case of three dimensional bands, I investigate the spectroscopic properties of the nodal point singularity, arising from a linear band crossing. In particular, I determine the distinct signature of nodal points in the analytic, momentum resolved, joint density of states (JDOS) and the numerically calculated resonant inelastic x-ray scattering (RIXS) spectrum, within the fast collision approximation that ignores core hole effects. The results presented here will be the stepping stone towards a careful future calculation, incorporating the potential edge singularity effects through core hole potential. Such a calculation may be directly comparable with ongoing experiments.