Strongly correlated metals are known to give rise to a variety of exotic states. In particular, if a system is tuned towards a quantum critical point, new ordered phases may arise. Sr₃Ru₂O₇ is a quasi-two dimensional metal in which field-tuned quantum criticality has been observed. In very pure single crystals of this material, a phase with unusual transport properties forms in the vicinity of its quantum critical point. Upon the application of a small in-plane field, electrical resistivity becomes anisotropic, a phenomenon which has led to the naming of this phase as an `electron nematic'. The subject of this thesis is a study of the electrical transport in high purity crystals of Sr₃Ru₂O₇. We modified an adiabatic demagnetisation refrigerator to create the conditions by which the entire temperature-field phase diagram can be explored. In particular, this allowed us to access the crossover between the low-temperature Fermi liquid and the quantum critical region. We also installed a triple axis `vector magnet' with which the applied magnetic field vector can be continuously rotated within the anisotropic phase. We conclude that the low- and high-field Fermi liquid properties have a complex dependence on magnetic field and temperature, but that a simple multiple band model can account for some of these effects, and reconcile the measured specific heat, dHvA quasiparticle masses and transport co-efficients. At high temperatures, we observe similarities between the apparent resistive scattering rate at critical tuning and those observed in other quantum critical systems and in elemental metals. Finally, the anisotropic phase measurements confirm previous reports and demonstrate behaviour consistent with an Ising-nematic, with the anisotropy aligned along either of the principal crystal axes. Our observations are consistent with the presence of a large number of domains within the anisotropic phase, and conclude that scattering from domain walls is likely to contribute strongly to the large measured anisotropy.

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Thesis (Ph.D.)--Mississippi State University. Department of Physics and Astronomy. / Title from title screen. Includes bibliographical references.

We investigate the electronic band structure of device relevant GaInNAs/GaAs multiple quantum wells (MQWs) and veitical-cavity surface-emitting laser (VCSEL) structures. We report photo-modulated reflectance (PR) studies under applied pressure and variable temperature that probe the influence of N-related states on the electronic structure of dilute nitrogen (N) III-V MQWs. The pressure and temperature dependence of the intersubband transitions within the MQWs is reduced by addition of N. By matching our experimental results with a theoretical model important predictions for the ground-state electron effective mass and conduction band offset as a function of N and pressure are made. We present results of angle- and temperature-dependent electro-reflectance (ER) measurements on a dilute-N GaInNAs VCSEL and show that these explain how the corresponding VCSEL device can operate over a such a wide range of temperatures. We argue that intrinsic properties of dilute-N QWs provide novel ways to design laser devices, especially in the crucial telecommunication range of wavelengths. We show how non-destructive ER and PR measurements can be used, in order to estimate the QW transition energy when it is coupled with the cavity mode (CM). The energy of the main exciton is determined by monitoring the amplitude and the phase of the PR spectra. The ER measurements are presented on the GaInNAs VCSEL described in the previous paragraph. Furthermore we present a growth characterisation study on a representative InGaAs/GaAs/AlAs/AlGaAs as-grown VCSEL structure, using PR spectroscopy as a function of position on a non-uniform wafer. We also show how temperature dependent PR and the appropriate lineshape model can be used to obtain a full picture of the relative movements between the gain and the CM over the full range of temperature. This information allows calculating the material gain in the temperature range of interest, independent from the effect of the CM and also provides an alternative method for characterising the growth, which can be applied to uniform wafers. PR and non-destructive ER can be used to identify regions suitable for fabrication into devices. For this reason modulation spectroscopy can be very useful for industry to reject wafers where good alignment between the CM and the QW does not occur and can thus save on the time consuming and expensive fabrication procedures.

We use spectroscopy to study infrared optoelectronic inter and intraband semiconductor carrier dynamics. The overall aim of this thesis was to study both III-V and Pb chalcogenide material systems in order to show their future potential use in infrared emitters. The effects of bandstructure engineering have been studied in the output characteristics of mid-IR III-V laser diodes to show which processes (defects, radiative, Auger and phonon) dominate and whether non-radiative processes can be suppressed. A new three-beam pump probe experiment was used to investigate interband recombination directly in passive materials. Experiments on PbSe and theory for non-parabolic near-mirror bands and non-degenerate statistics were in good agreement. Comparisons with HgCdTe showed a reduction in the Auger coefficient of 1-2 orders of magnitude in the PbSe. Using Landau confinement to model spatial confinement in quantum dots (QDs) "phonon bottlenecking" was studied. The results obtained from pump probe and cyclotron resonance saturation measurements showed a clear suppression in the cooling of carriers when Landau level separation was not resonant with LO phonon energy. When a bulk laser diode was placed in a magnetic field to produce a quasi quantum wire device the resulting enhanced differential gain and reduced Auger recombination lowered Ith by 30%. This result showed many peaks in the light output which occurred when the LO phonon energy was a multiple of the Landau level separation. This showed for the first time evidence of the phonon bottleneck in a working laser device. A new technique called time resolved optically detected cyclotron resonance, was used as a precursor to finding the earner dynamics within a spatially confined quantum dot. By moving to the case of a spatial QD using an optically detected intraband resonance it was possible to measure the energy separation interband levels and conduction and valence sublevels within the dot simultaneously. Furthermore this technique has been shown that the inhomogeneous broadening of the photoluminescence spectrum is not purely affected by just size and composition. We suggest that other processes such as state occupancy, In roughing, and exciton binding energies may account for the extra energy.

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.

Light is electromagnetic radiation that could be shown in a spectrum with a wide range of wavelengths. Blackbody radiation is a type of thermal radiation and is an important topic to explore due to it being an ideal body that materials’ properties are often described in comparison to it. Therefore, it helps in understanding how materials behave on the quantum level. One must understand its interaction with light spectrum and how electron excitation happens. Thus, concepts such as Planck’s law, energy quantization and band theory will be discussed to try to grasp of how light interacts with materials.

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