<p> A study of the Fermi surface of mercury has been carried out using cyclotron resonance and magnetoresistance techniques. Oscillations of the microwave surface impedance, which have been identified as quantum oscillations, have appeared at high magnetic field strengths, and a study of these oscillations has added more information about the Fermi surface. </p> <p> The results of these experiments are compared with two models of the Fermi surface, the nearly-free-electron model, and the relativistic-augmented-plane-wave model. The relativistic-augmented-plane-wave model was found to require only small modifications to be consistent with the data. </p> / Thesis / Doctor of Philosophy (PhD)

<p> Under certain conditions, an induced torque measurement is a measure of the ratio of the resistivity to the square of the Hall constant. Induced torque measurements can be directly related to the connectivity of the Fermi surface.</p> <p> A modulation technique for measuring induced torque is justifield theoretically, and an instrument employing this technique is characterized. Operational limitations on parameters such as sample resistivity and modulation rate are specified. A new procedure is proposed to extract more information from induced torque measurements. This procedure would allow the measurement of resistivity and Hall constant of ellipsoidal samples. The procedure is untested but appears to be feasible.</p> <p> Observations of the induced torque of Hg3-δAsF6 show that the Fermi surface supports an open orbit in one direction. This is discussed in the context of a model (Razavi et al., 1979), which has Fermi surface cylinders of common direction. This is based on conduction in Hg chain directions, which lie in only two directions. At magnetic fields greater than 3.0 Tesla, magnetic breakdown is observed. A Brillouin zone constructed using Hg chain symmetry and crystal parameters yields reciprocal lattice vectors compatible with the observed magnetic breakdown. The model is confirmed but a refinement is needed to allow an undulation of the Fermi surface cylinders.</p> / Thesis / Master of Science (MSc)

<p> The energy bands and Fermi surface of mercury have been calculated using local and non-local pseudopotentials. The non-local pseudopotentials were an approximation in which the repulsive potentials of the outer atomic core states were explicitly represented by non-local projection operators. </p> <p> A search was made for the regions of parameter space where the pseudopotential generated a Fermi surface having a good fit to the experimental magneto-acoustic calipers and de Haas-van Alphen extremal cross sectional areas. </p> <p> De Haas-van Alphen frequencies and cyclotron masses were calculated for symmetry planes using a local pseudopotential. </p> <p> General questions of pseudopotential theory, the symmetry of the energy bands, the occurrence of degeneracies, and the influence of spin-orbit coupling are also considered. </p> / Thesis / Doctor of Philosophy (PhD)

<p> The galvanomagnetic properties and shape of the Fermi surface of copper single crystals containing different density of dislocations have been studied experimentally and theoretically through magnetoresistivity measurement and using effective medium theory respectively. </p> <p> In experiments, two crystallographic orientations of copper single crystal samples with tensile axis parallel to < 100 > and < 541 > have been plastically strained to various stress levels to introduce different density Nd of dislocations. The experimental data of angle and field-dependent magnetoresistivity measured at temperature T = 2K and in the magnetic filed up to 9 Tesla show that dislocations influence substantially the galvanomagnetic properties of copper crystal samples in the open, extended and closed orbit crystallographic orientations. The results reveal that the pure samples with resistivity ratio RR equal to or larger than 151 show quadratic dependence of transverse magnetoresistivity as a function of the magnetic field in the open-orbit orientation, which changes to linear variation of magnetoresistivity with magnetic fields in highly deformed samples with RR smaller than 138. A quadratic dependence of transverse magnetoresistivity as a function of the magnetic field is significantly suppressed as the density of dislocations increases. The magnetoresistivity decrease with the increase of the density of dislocations was also observed in the closed-orbit crystallographic orientation. Such effect is independent upon the type of dislocations introduced to the crystal lattice.</p> <p> Measurements of the de Hass-van Alphen effect in plastically deformed copper single crystals have been carried out with torque magnetometer and AC susceptibility options of Quantum Design PPMS-9 system. The oscillation frequencies for the extremal orbits normal to the principal crystallographic directions are obtained through Fourier transform of torque versus inversed field characteristics. By comparing these frequencies with the analogous frequencies obtained for undeformed copper crystals, the changes in the cross-sectional area of the Fermi surface corresponding to the extremal orbits are obtained and the shape of the dislocation-distorted Fermi surface is postulated based on measurements performed.</p> <p> The effective-medium approximation and Green's function method are applied to model the magnetoresistivity data and to gain insight into the fundamental material properties responsible for the observed magnetoresistivity behavior. The effective magnetoresistivity calculated using a self-consistent method shows a good agreement with the experimental results.</p> / Thesis / Doctor of Philosophy (PhD)

<p> Field modulation techniques were used to observe the de Haas-van Alphen effect in magnetic fields up to 5.5 tesla and at temperatures below 1.1°K. A data acquisition system recorded on magnetic tape the large amount of data necessary for computer fourier analysis of the oscillations. All of the orbits predicted by Keeton and Loucks' model of the Fermi surface of mercury were at least tentatively identified. The data on the β, τ and α orbits were in essential agreement with previous work. The γ and X-face orbits were also investigated in some detail, while tentative identification was made of the μ and T-face orbits. When the data permitted, the areas were fitted to ellipsoids or hyperboloids of revolution by a least squares calculation.</p> <p> A search was made for modifications to the de Haas-van Alphen theory due to phonons. Accurate torque de Haas-van Alphen amplitude measurements were taken as a function of temperature and magnetic field. The analysis of the results revealed no systematic dependence of either the cyclotron effective mass or the Dingle temperature on temperature from 1.25°K to 4.2°K or on magnetic field from 1.5 tesla to 2.3 tesla. Thus no effects due to phonons were observed.</p> <p> A method of observing the open orbits in metallic single crystals was developed and used to observe the open orbits in mercury. The method utilized the eddy currents induced in the sample by the rotation of a magnetic field. This provided a signal which was dependent on the conductivity in the plane perpendicular to the open orbit. The torque amplitude, which indicated the number of open orbit carriers, was used to detect the angular range of the bands of open orbits in mercury. The method was experimentally simple since no special sample geometry was necessary and no electrical connections to the sample were needed.</p> / Thesis / Doctor of Philosophy (PhD)

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.

In dieser Doktorarbeit wurde die elektronische Struktur von konventionellen und unkonventionellen Supraleitern untersucht. Das Ziel dieser Arbeit war es, die dHvA Parameter zu berechnen und mit experimentellen Daten zu vergleichen. Mit Hilfe des Bandstrukturprogrammes FPLO, welches auf der DFT basiert, untersuchten wir Diboride (MgB$_2$ und TaB$_2$) und schwere Fermionenverbindungen (CeMIn$_5$ und PuMGa$_5$, M=Co, Rh, und Ir) innerhalb der LSD-Näherung. / In this thesis theoretical study of the electronic structure of conventional and unconventional superconductor compounds was carried out. The goal was to calculate the dHvA parameters in comparison with available experimental data. By means of FPLO band structure code based on DFT within LSDA we investigated diborides (MgB$_2$ and TaB$_2$) and heavy fermion compounds (CeMIn$_5$ and PuMGa$_5$, M=Co, Rh, and Ir).

The aim of this thesis was to identify topologically protected states in the materials SnTe and Fe3Sn2. Such states are currently receiving a large amount of interest due to their applications for spintronic devices. Recently SnTe was discovered to be a crystalline topological insulator, a state of matter where its surface is highly conducting while the bulk remains insulating. However detection of these surface states is difficult using transport measurements, since the bulk is not totally insulating but still contains a large number of free carriers. SnTe undergoes a rhombohedral structural distortion on cooling caused by a soft transverse optic phonon, with the exact Tc strongly dependent on the carrier concentration. The distortion acts to lower crystal symmetry removing some of the symmetries that protect the surface state. Single crystal samples displaying the structural transition were grown and investigated using inelastic X-ray scattering to measure the phonon softening previously reported by other authors. The soft phonon was seen to recover again after distortion indicative of a 2nd order ferroelectric transition. This is the first reported discovery of the recovery showing the distortion is ferroelectric in nature. Shubnikov de Haas quantum oscillations were measured to study the Fermi surface under ambient and high hydrostatic pressure conditions. A distortion of the Fermi surface caused by the structural transition was evident, resulting in 4 distinct oscillation frequencies. However at applied pressures above 6 kbar, the transition was suppressed and only 1 oscillation measured. A two component Hall response also becomes apparent under high pressure. The possible origin of this and its relation to possible surface states is discussed. The anomalous Hall effect was also measured in the ferromagnet Fe3Sn2 which has a bilayer Kagome structure. Previous measurements on polycrystalline Fe3Sn2 suggested a non-collinear spin rotation from the spins pointing along the c-axis at high temperature to lying in the a-b plane below 80 K. A spin glass phase is then expected below 80 K. Single crystal magnetisation measurements carried out in this thesis show the spins are in the a-b plane at high temperatures and begin to display a ferromagnetic component along the c-axis approaching 80 K. The difference is accounted for by considering the demagnetising factor in the plate shaped single crystals. For this temperature range an applied field along the c-direction however rotates the moments towards c. At intermediate fields there are strong features evident in both the anomalous Hall effect and magnetoresistance. These features may be due to a topological Hall effect caused by a non-collinear spin structure. The possible existence of Skyrmion excitations was also recently discussed theoretically in Fe3Sn2. Our data is more suggestive of static Skyrmions known to cause topological Hall effects in MnSi.

The interplay of partially filled d- or f-electron shells with conduction-band electrons is a key ingredient in new rare-earth transition-metal compounds for the emergence of unusual electronic and magnetic properties. Among which unconventional superconductivity is one of the most studied. Despite many years of intensive experimental investigations and plenty promising theoretical models, unconventional superconductivity still remains hotly debated a very rich topic. One of the fundamental unsolved problems for condensed-matter physicists is the mechanism that causes the electrons to form anisotropic superconductivity. Since electrons in the vicinity of the Fermi level are primarily responsible for superconductivity, in order to better understand the mechanism giving rise to this phenomenon and the origin of complex forces between correlated electrons, knowledge of the Fermi surface and band selective effective mass is essential. Of the many techniques used to study electronic band-structure properties, measurements of quantum oscillations in the magnetization, so-called de Haas-van Alphen (dHvA) effect, in combination with band-structure calculations is the traditional proven tool for studying Fermi-surface topology and quasiparticle effective mass. In the present work, electronic structure and Fermi-surface properties of Ybsubstituted heavy fermion superconductor CeCoIn5 and iron based ternary phosphides LaFe2P2 and CeFe2P2 have been investigated by means of dHvA measurements. For these measurements, capacitive cantilever-torque magnetometry was utilized. In Ce1−xYbxCoIn5, the evolution of the Fermi surface and effective mass was studied as a function of Yb concentration. The observed topology change is consistent with what is expected from the band-structure calculations. For a small Yb concentration, x = 0.1, the band-structure topology and the effective masses remain nearly unchanged compared to CeCoIn5. This contrasts clearly modified Fermi surfaces and light, almost unrenormalized effective masses for x = 0.2 and above. For LaFe2P2 and CeFe2P2, the obtained effective masses are light. Good agreement between the calculated and measured dHvA frequencies was identified only for LaFe2P2. However, for CeFe2P2 strong disagreement was observed. Moreover, different CeFe2P2 single crystals reveal different experimental results. In order to reconcile the results of the dHvA measurements and density-functional-theory calculations more work is necessary.

In dieser Doktorarbeit wurde die elektronische Struktur von konventionellen und unkonventionellen Supraleitern untersucht. Das Ziel dieser Arbeit war es, die dHvA Parameter zu berechnen und mit experimentellen Daten zu vergleichen. Mit Hilfe des Bandstrukturprogrammes FPLO, welches auf der DFT basiert, untersuchten wir Diboride (MgB$_2$ und TaB$_2$) und schwere Fermionenverbindungen (CeMIn$_5$ und PuMGa$_5$, M=Co, Rh, und Ir) innerhalb der LSD-Näherung. / In this thesis theoretical study of the electronic structure of conventional and unconventional superconductor compounds was carried out. The goal was to calculate the dHvA parameters in comparison with available experimental data. By means of FPLO band structure code based on DFT within LSDA we investigated diborides (MgB$_2$ and TaB$_2$) and heavy fermion compounds (CeMIn$_5$ and PuMGa$_5$, M=Co, Rh, and Ir).