In molecules, electronic state transitions can occur via quantum coupling of the states. If the coupling is due to the kinetic energy of the molecular nuclei, then electronic transitions are best represented in the adiabatic frame. If the coupling is instead facilitated through the potential energy of the nuclei, then electronic transitions are better represented in the diabatic frame. In our study, we modeled these latter transitions, called ``nonadiabatic transitions.'' For one nuclear degree of freedom, we modeled the de-excitation of a diatomic molecule. For two nuclear degrees of freedom, we modeled the de-excitation of an ethane-like molecule undergoing cis-trans isomerization. For both cases, we studied the dependence of the de-excitation on the nuclear configuration and potential energy of the molecule. We constructed a numerical model to solve the time-dependent Schr\"{o}dinger Equation for two coupled wave functions. Our algorithm takes full advantage of the sparseness of the numerical system, leading to a final set of equations that is solved recursively using nothing more than the Tridiagonal Algorithm. We observed that the most effective de-excitation occurred when the molecule transitioned from a stable equilibrium configuration to an unstable equilibrium configuration. This same mechanism is known to drive fast electronic transitions in the adiabatic frame. We concluded that while the adiabatic and diabatic frames are strongly opposed physically, the mathematical mechanism driving electronic transitions in the two frames is in some sense the same.

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.

Cette thèse montre de nouveaux résultats sur les supraconducteurs ferromagnétiques UCoGe et URhGe et sur l’ordre caché dans URu2Si2. Le diagramme de phase pression température d’UCoGe a été étudié jusqu’à 10.5 GPa. L’ordre ferromagnétique subsiste jusqu’à la pression critique pc≈1 GPa et la supraconductivité non conventionnelle jusqu’à p = 4 GPa. Les fluctuations magnétiques responsables de la supraconductivité peuvent être réduites par l’application d’un champ magnétique. Les surfaces de Fermi d’UCoGe et d’URhGe ont été mesurées grace aux oscillations quantiques. Quatre poches ont été détectées dans UCoGe, elles subissent une succession de transition de Lifshitz de la surface de Fermi sous champ magnétique. Les poches détectés évoluent continument avec la pression jusqu’à 2.5 GPa, sans montrer de reconstruction de la surface de Fermi à la pression critique pc. Dans URhGe, trois poches lourdes de la surface de Fermi ont aussi été découvertes. Enfin dans la phase d’ordre caché d’URu2Si2, les oscillations quantiques ont révélé une forte anisotropie du facteur gyromagnétique g pour deux poches de la surface de Fermi, qui est comparable à l’anisotropie macroscopique. Cette dernière a été étudiée à partir du champcritique supérieur de la supraconductivité. / This thesis is concentrated on the ferromagnetic superconductors UCoGe and URhGe andon the hidden order state in URu2Si2. In the first part the pressure temperature phase diagram of UCoGe was studied up to 10.5 GPa. Ferromagnetism vanishes at the critical pressure pc≈1 GPa. Unconventional superconductivity and non Fermi liquid behavior can be observed in a broad pressure range around pc. The superconducting upper critical field properties were explained by the suppression of the magnetic fluctuations under field. In the second part the Fermi surfaces of UCoGe and URhGe were investigated by quantum oscillations. In UCoGe four Fermi surface pockets were observed. Under magnetic field successive Lifshitz transitions of the Fermi surface have been detected. The observed Fermi surface pockets in UCoGe evolve smoothly with pressure up to 2.5 GPa and do not show any Fermi surface reconstruction at the critical pressure pc. In URhGe, three heavy Fermi surface pockets were detected by quantum oscillations. In the last part the quantum oscillation study in the hidden order state of URu2Si2 shows a strong g factor anisotropy for two Fermi surface pockets, which is compared to the macroscopic g factor anisotropy extractedfrom the upper critical field study.

Materials in proximity to quantum critical points (QCPs) experience strong fluctuations in the order parameter associated with the transition and often, as a result, display interesting properties. In this dissertation, we have used a variety of experimental probes such as Shubnikov-de Haas quantum oscillations, thermal conductivity and heat capacity, to better understand two such materials — $A_3T_4$Sn$_{13}$ and YFe$_2$Ge$_2$. $A_3T_4$Sn$_{13}$ ($A$ = Ca, Sr; $T$ = Ir, Rh) is a family of quasi-skutterudite superconductors with moderate $T_c$’s between 4 and 8 K. Although the superconductivity is believed to be phonon-mediated with s-wave pairing symmetry, an unusual second-order structural transition makes this material family fascinating to study. Whether this structural transition is a result of three distortions with perpendicular wavevectors resulting in a cubic-to-cubic transformation, or each wavevector acting independently giving rise to cubic-to-tetragonal transformations and formation of twinned domains is a disputed issue. We have measured quantum oscillations in the resistivity of Sr3Ir4Sn13 and compared it to density functional theory (DFT) calculations for both scenarios. Our results strongly suggest that the former interpretation is correct. The structural transition temperature $T^*$ in $A_3T_4$Sn$_{13}$ can be suppressed to zero by tuning with physical or chemical pressure. In (Ca$_x$Sr$_{1−x}$)$_3$Rh$_4$Sn$_13$, the quantum critical point can be accessed purely by chemical substitution at x ~ 0.9. In the vicinity of the QCP, we expect large fluctuations of the order parameter at low temperatures, which for a structural transition could manifest as a structural disorder. We have measured thermal conductivity at temperatures much lower than $T_c$ and found that it is well described by a single power law with suppressed exponents near the QCP. The heat capacity, however, remains ~ $T^3$. After excluding conventional phonon scattering mechanisms, we propose the possibility of intrinsic quasi-static spatial disorder that is related to the structural QCP. YFe$_2$Ge$_2$ is closely linked to the “122” family of iron-based superconductors like KFe$_2$As$_2$, although it has a significantly lower $T_c$ ~ 1 K. It has a rather three-dimensional Fermi surface which closely resembles that of KFe$_2$As$_2$ in the pressure-induced collapsed tetragonal phase. YFe$_2$Ge$_2$ is in proximity to several types of magnetic order which are predicted by DFT calculations to have lower energy than the non-spin polarised case. Even though YFe$_2$Ge$_2$ is non-magnetic, its superconductivity could be strongly affected by magnetic fluctuations. Through a collaboration with researchers at the University of Waterloo, we have measured the thermal conductivity of YFe$_2$Ge$_2$ down to millikelvin temperatures and up to 2.5 T in field. Our results suggest that YFe$_2$Ge$_2$ is a nodal superconductor. This result could assist in the explanation of the unconventional superconductivity in iron-based superconductors.

Transition metal oxides adopt a wide variety of crystal structures and display a diverse range of physical phenomena from Mott insulating states to electron-nematics to unconventional superconductivity. Detailed understanding of these states and how they may be manipulated by structural modifications requires both precise structural knowledge and in-depth physical property measurements using as many techniques over as wide a range of phase space as possible. In the work described in this thesis a range of transition metal oxides were studied using high-resolution powder neutron diffraction and detailed low-temperature physical property measurements. The quaternary barium orthotellurates Ba₂NiTeO₆, Ba₂CuTeO₆ and Ba₂ZnTeO₆ belong to an almost unstudied family of materials. The development of procedures for synthesizing large single crystals has facilitated the investigation of interesting new anisotropic magnetic states in the Cu and Ni systems and the existence of a possible structural phase transition in the Zn-based compound. YMnO₃ is a multiferroic with improper ferrielectricity. The study of the high-temperature structural phases described in this thesis has led to the identification both of the transition path to the ferrielectric state and the identification of an isostructural phase transition within the ferrielectric phase. BiFe₀.₇Mn₀.₃O₃ is also a multiferroic material but with proper ferroelectricity. The investigation of the structural phases of this compound have provided confirmation of the high-temperature phases with the reassignment of the symmetry of the highest-temperature phase which is intriguingly different to that of the unsubstituted material. Finally, an investigation of the electronic structures of the high conductivity delafossites PdCoO₂ and PdCrO₂ using micro-cantilever torque magnetometry measurements of quantum oscillations is described. This has resolved the warping of the Fermi surface of PdCoO₂ and given insights into the complicated Fermi surface of the itinerant antiferromagnet PdCrO₂.

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.

<p> The theoretical treatment of the induced torque problem is discussed, and equations describing the functional form of the torque amplitude are derived on the basis of a model calculation valid in the high field limit. This functional form is applied to a detailed interpretation of the open orbit structure in gallium, cadmium, zinc and copper. </p> <p> An investigation of the open orbit structure in gallium at l.4°K using this technique has yielded direct information on the connectivity of the sixth-band hole surface. This surface supports a k(c)-trajectory for all field directions in the ab plane, except within 0.1° of the a-axis. A k(a)-trajectory of lower conductivity is reported over a 10° range of field direction centred (32°±2°) from the b-axis in the be plane. These data, in addition to the highly anisotropic amplitude and field dependence of the k(c) -trajectory, require that this surface contact the Brillouin zone boundary at both the k(a) -and k(c) -faces. The present data are compared with available models of the sixth band hole surface, and are found to be in excellent agreement with the predictions of recent pseudopotential calculations . The possibility of magnetic breakdown in the k(c)-trajectory for B|| b-axis is discussed. Finally, a non-linear frequency dependence, and an anisotropic non-quadratic field dependence are understood to occur through the long mean free path and short skin depth parameters in gallium at l.4°K. </p> <p> In cadmium, the induced torque amplitude due to the [0001]-open trajectory tends to saturation at high field intensities for all observation directions. This effect is attributed to magnetic breakdown between the first-and secondhand hole surfaces through the spin·-orbit interaction energy 'gap near the H-symmetry point in the AHL plane. This magnetic breakdown effect is analyzed on the basis of a linear chain model and the theoretical curves of Falicov and Sievert. Detailed analysis indicates the possibility of two separate breakdown probabilities across the HL and HA gaps; for <1010> directions , breakdown fields of 10.8 k0e and (as low as) 0.72 k0e are indicated . A similar range of breakdown fields is indicated for all field directions in the (0001) plane. </p> <p> In zinc, the induced torque technique is used to investigate magnetic breakdown effects in the [0001]-trajectory for specific field directions in the basa l plane. These effects are attributed to the onset of partial breakdown between the monster and cap surfaces near the H-symrnetry points, for field intensities above 16 kOe. The linear chain model is shown to be an inappropriate description of breakdown effects in zinc. An onset field of 16 kOe for <1120> is determined; no breakdown is observed along <lOIO> below 20 kOe. In addition, magnetic breakdown effects occurring in the basal orbits of zinc were investigated. The general monotonic rise in torque amplitude with field intensities is fitted to the theoretical expressions of Falicov, Pippard, and Sievert. The giant quantum oscillations arising through coherence-effect modulation of the breakdown probability are shown consistent with earlier data. </p> <p> The technique is applied to a general survey of the various types of open orbits existing in copper, and the general applicability of the sample torque equations to both compensated and uncompensated metals is demonstrated. </p> / Thesis / Doctor of Philosophy (PhD)

Im Rahmen dieser Doktorarbeit werden de Haas-van Alphen-Untersuchungen an den nichtmagnetischen Borkarbidsupraleitern LuNi2B2C und YNi2B2C präsentiert. Aus den Quantenoszillationen in der normalleitenden Phase in Kombination mit Bandstrukturrechnungen konnten Informationen über die verzweigte Fermiflächenarchitektur und über die Elektron-Phonon-Kopplung der Borkarbide gewonnen werden. Die Kopplung ist stark anisotrop und fermiflächenabhängig. Dies spricht für einen Mehrbandmechanismus der Supraleitung in der Materialklasse. Zusätzlich konnten de Haas-van-Alphen-Oszillationen mehrerer Fermiflächen unterhalb von Bc2 tief in der Shubnikov-Phase beobachtet werden. Das Verhalten dieser Oszillationen lässt sich nicht mit bisher bekannten Theorien beschreiben. Allerdings weist das Bestehen der Oszillationen weit unterhalb von Bc2 auf ein Bestehen von elektronischen Zuständen in der Shubnikov-Phase hin.

While the free electron model can often be surprisingly successful in describing properties of solids, there are plenty of materials in which interactions between electrons are too significant to be neglected. These strongly correlated systems sometimes exhibit rather unexpected, unusual and useful phenomena, understanding of which is one of the aims of condensed matter physics. Heat capacity measurements of paramagnetic YFe$_{2}$Ge$_{2}$ give a Sommerfeld coefficient of about 100 mJ mol$^{−1}$ K$^{−2}$, which is about an order of magnitude higher than the value predicted by band structure calculations. This suggests the existence of strong electronic correlations in the compound, potentially due to proximity to an antiferromagnetic quantum critical point (QCP). Existence of the latter is also indicated by the non-Fermi liquid T$^{3/2}$ behaviour of the low temperature resistivity. Below 1.8 K a superconducting phase develops in the material, making it a rare case of a non-pnictide and non-chalcogenide iron based superconductor with the 1-2-2 structure. This thesis describes growth and study of a new generation of high quality YFe$_{2}$Ge$_{2}$ samples with residual resistance ratios reaching 200. Measurements of resistivity, heat capacity and magnetic susceptibility confirm the intrinsic and bulk character of the superconductivity, which is also argued to be of an unconventional nature. In order to test the hypothesis of the nearby QCP, resistance measurements under high pressure of up to 35 kbar have been conducted. Pressure dependence of the critical temperature of the superconductivity has been found to be rather weak. μSR measurements have been performed, but provided limited information due to sample inhomogeneity resulting in a broad distribution of the critical temperature. While the superconductivity is the result of an effective attraction between electrons, under different circumstances the electronic properties of a system can instead be dictated by the Coulomb repulsion. This is the case for another transition metal based compound NiS$_{2}$, which is a Mott insulator. Applying hydrostatic pressure of about 30 kbar brings the material across the Mott metal-insulator transition (MIT) into the metallic phase. We have used the tunnel diode oscillator (TDO) technique to measure quantum oscillations in the metallised state of NiS$_{2}$, making it possible to track the evolution of the principal Fermi surface and the associated effective mass as a function of pressure. New results are presented which access a wider pressure range than previous studies and provide strong evidence that the effective carrier mass diverges close to the Mott MIT, as expected within the Brinkman-Rice scenario and predicted in dynamical mean field theory calculations. Quantum oscillations have been measured at pressures as close to the insulating phase as 33 kbar and as high as 97 kbar. In addition to providing a valuable insight into the mechanism of the Mott MIT, this study has also demonstrated the potential of the TDO technique for studying materials at high pressures.

Materialien mit einer geringen, aber endlichen Zahl an beweglichen Ladungsträgern bieten eine interessante Plattform für die experimentelle Erforschung von niederenergetischen elektronischen Anregungen. Derartige Halbmetalle und Halbleiter mit geringer Bandlücke zeigen starke Effekte in Magnetfeldern, wie z. B. Quantenoszillationen und Magnetwiderstandseffekte, welche ein hilfreiches Werkzeug zur Untersuchung der elektronischen Eigenschaften darstellen. In Kombination mit verschiedenen experimentellen Techniken wie elektrischen und thermischen Transportmessungen, der Anwendung uniaxialer Spannung, und Ultraschallmessungen, kann man umfassende Informationen über die Wechselwirkungen und Symmetriebeziehungen in solch einem Material gewinnen. In letzter Zeit sind vor allem die topologischen Eigenschaften der elektronischen Bänder in den Fokus der Festkörperphysik gerückt, deren Beitrag zu den Transporteigenschaften insbesondere in Halbmetallen und Halbleitern mit geringer Bandlücke zu klären ist. In der vorliegenden Dissertation wurden drei solcher Materialien hinsichtlich ihrer außergewöhnlichen elektronischen Eigenschaften untersucht. In NbP, einem Halbmetall mit komplex geformter, anisotroper Fermi-Fläche, welche aus mehreren räumlich entarteten Taschen besteht, wurden die Effekte der Gitterdeformation untersucht. Die Anwendung uniaxialer Spannung führt zur Brechung der Kristallsymmetrie und damit zur Aufhebung der räumlichen Entartung der Fermi-Taschen, was mittels Analyse der Shubnikov-de Haas-Oszillationen im Magnetwiderstand nachgewiesen werden konnte. Weiterhin konnte durch Messung der im Ultraschall auftretenden Quantenoszillationen eine genaue Untersuchung der Anisotropie der Elektron-Phonon-Wechselwirkung durchgeführt werden. ZrTe5 ist ein aus zweidimensionalen Schichten bestehender Halbleiter mit geringer Bandlücke, welcher kürzlich aufgrund seiner besonderen Niedrigtemperatur-Magnetotransporteigenschaften größere Aufmerksamkeit erfahren hat. So weist ZrTe5 plateau-ähnliche Features im Hall-Widerstand, sowie einen ungewöhnlichen Magnet- und Hall-Widerstand im Quanten-Limit auf. Im Rahmen dieser Arbeit wurde der Effekt uniaxialer Spannung auf diese Transportphänomene untersucht, was dazu beitragen kann, deren bislang umstrittene Ursache aufzuklären. Schließlich wurden die elektrischen und thermischen Magnetotransporteigenschaften von GdPtBi untersucht, einem Halbleiter mit geschlossener Bandlücke, welcher sich durch das Vorliegen starker, lokalisierter magnetischer Momente ausgehend von den 4f-Elektronen des Gd auszeichnet. Es konnte gezeigt werden, dass das Auftreten von Anomalien im elektrischen Magnetotransport, welche ursprünglich den topologischen Eigenschaften der im Magnetfeld gekreuzten elektronischen Bänder zugeschrieben wurden, auch durch magnetische Wechselwirkungen zu erklären ist. Desweiteren konnte durch die Messung magnetfeldabhängiger thermischer Transporteigenschaften das Auftreten von Wechselwirkungen zwischen Phononen und magnetischen Momenten, sowie möglicherweise auch magnetischen Spinwellen, nachgewiesen werden. / Materials with a low, but finite density of charge carriers offer an interesting experimental platform for the investigation of electronic low-energy excitations. Such semimetals and narrow-gap semiconductors exhibit large magnetic-field responses, e.g., quantum oscillations (QOs) and magnetoresistance (MR) effects, that can be used as a powerful tool to study the electronic properties. In combination with experimental techniques such as electrical- and thermal-transport measurements, uniaxial-stress application, and measurement of the ultrasound velocity, a lot can be learned about the interactions and symmetry dependences in the materials. Recently, the topological properties of electronic bands became an important research field in condensed matter physics. Especially in semimetals and narrow-gap semiconductors, it is to be clarified to what extent exotic transport phenomena are related to topological effects. In this thesis, three such materials with intriguing electronic properties have been investigated. In NbP, a semimetal with a complex, anisotropic Fermi surface, consisting of spatially degenerate pockets whose degeneracy is tied to the symmetry of the crystal lattice, the effects of lattice deformation have been studied. Application of uniaxial stress breaks the crystalline symmetries and, thereby, lifts the degeneracy of the Fermi-surface pockets, which could be traced via analyzing Shubnikov-de Haas oscillations in the MR. Furthermore, the measurement of QOs in the ultrasound allowed for a detailed analysis of the anisotropy of the electron-phonon interaction in NbP. ZrTe5 is a layered narrow-gap semiconductor that recently attracted a lot of attention due to its remarkable low-temperature magnetotransport, namely plateau-like features in the Hall resistance as well as unconventionalMRand Hall resistance in the quantum limit. Here, the uniaxial-stress response of those features was investigated as a contribution to clarify their origin, which, to date, remains under discussion. Lastly, the electrical and thermal magnetotransport properties of GdPtBi were studied. GdPtBi is a zero-gap semiconductor that features the presence of large localized magnetic moments stemming from Gd’s 4 𝑓 -electron shell. The occurrence of anomalous features in the electrical MR was previously attributed to the topological properties of magnetic-field induced crossings of the electronic bands. However, in the course of this thesis it could be shown that those features can also be explained by magnetic interactions. Further, the presence of interactions between phonons and magnetic moments, and potentially also between phonons and magnetic spin waves, was demonstrated via measurement of a magnetic-field-dependent thermal resistance.