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In this dissertation, we examine quantum ferromagnets and determine various effects of the magnetic Goldstone modes or "magnons'' in these systems. Firstly, we calculate the magnon contribution to the transport relaxation rate of conduction electrons in metallic ferromagnets and find that at asymptotically low temperatures, the contribution behaves as T^2 exp(-T_0/T) and not as T^2 predicted previously. To perform these calculations, we derive and use a very general effective theory for metallic ferromagnets. This activation barrier-like behavior is due to the fact that spin waves only couple electrons from different Stoner subbands that arise from the splitting of the conduction band in presence of a nonzero magnetization. The T^2 behavior is found to be valid only in a pre-asymptotic temperature window. The temperature scale T_0 is the energy of the least energetic ferromagnon that couples electrons of different spins. Second, we discuss magnon-induced long-range correlation functions in quantum magnets. In the ordered phases of both classical ferromagnets and antiferromagnets, the long-range correlations induced by the magnons lead to a singular wavenumber dependence of the longitudinal order-parameter susceptibility in spatial dimensions 2<d<4. We investigate the quantum analog of this singularity using a nonlinear sigma model. In a quantum antiferromagnet at $T=0$, a weaker nonanalytic behavior is obtained, which is consistent with power counting. The analogous result for a quantum ferromagnet is absent if the magnon damping is neglected. This is due to the lack of magnon number fluctuations in the quantum ferromagnetic ground state. Magnon damping due to quenched disorder restores the expected nonanalyticity. Finally, we use an effective field theory for clean, strongly interacting electron systems to calculate the magnon contribution to the density of states, the longitudinal magnetic susceptibility and the conductivity in an itinerant ferromagnet. Utilizing a loop expansion that does not assume the electron-electron interaction to be a small parameter, we obtain the leading nonanalytic corrections to the Stoner saddle-point results for these observables, as functions of the frequency and wavenumber in the hydrodynamic limit. The dissertation includes previously published and unpublished co-authored material.

Ce travail de thèse présente un nouvel ordre magnétique dans l'énigmatique phase de pseudo-gap des cuprates supraconducteurs à haute température critique. L'étude des composés YBa2Cu3O6+δ, HgBa2CuO4+δ et La1.92Sr0.08CuO4 par diffusion élastique de neutrons polarisés a permis de mettre en évidence un paramètre d'ordre magnétique en dessous d'une température comparable à celle de l'ouverture du pseudo-gap de ces systèmes. Nous avons également montré pour la première fois l'existence dans la famille HgBa2CuO4+δ de deux modes collectifs magnétiques associés à la phase de pseudo-gap. Tous ces résultats indiquent qu'à l'ouverture du pseudo-gap est associée une vraie transition de phase, avec un paramètre d'ordre magnétique et une symétrie brisée: la symétrie par renversement du temps. Il est toutefois important de noter que la symétrie de translation du réseau est préservée: on parle alors d'ordre à Q=0. Dans le système YBa2Cu3O6+δ, nous avons établi que lorsque l'on s'approche du composé parent, ou lorsque l'on introduit des impuretés telles que du Zn, les fluctuations de spin incommensurables autour du vecteur d'onde antiferromagnétique (QAF) se développent au détriment du nouvel ordre à Q=0. De manière similaire, nous avons pu mettre en évidence une interaction entre l'instabilité magnétique autour de QAF et le nouvel ordre à Q=0 dans La1.92Sr0.08CuO4. L'ensemble de ces résultats apporte une pièce maitresse au puzzle que représente toujours la supraconductivité à haute température critique, malgré 25 ans de recherche.

<p>Using field theoretical methods models of strongly correlated electrons have been investigated. Application to electronic structure calculations has been made.</p><p>In this thesis an attempt is made to build a bridge between first-principle band structure calculations and a theory of systems with strongly correlated electrons, by making use of perturbation theory from the atomic limit. Analyzing the total non-relativistic Hamiltonian leads to the basic model of strongly correlated systems, the Hubbard-Anderson model. In this thesis these basic models have been tested. Conclusions on delocalization and many-body aspects have been extracted from the solutions. Specifically for the lanthanides a separation of the f-system into two subsystems has resolved the discrepancy between calculated equilibrium volumes and experimental ones. The calculations are done within the Hubbard-I approximation, where it is possible to define renormalized fermion operators. The calculation is a true many-body calculation.</p><p>Using perturbation theory a set of self consistent equations has been formulated, and solved, for praseodymium metal using the periodical Anderson model. The solution shows a self consistent decrease of the Hubbard U, and delocalization of the f-shell, when crucial parameters of the model are changed. The most salient feature of the models for strongly correlated electrons is the transfer of spectral weight from one energy region to another by adjusting pressure or other external parameters. The effects come from kinematic interactions that are important for strongly correlated systems.</p><p>Investigations of the degenerate Hubbard model applied to the metal to insulator transition has also been made. When the degeneracy is considered, the transition to the metallic state occurs at smaller Coulomb energies. </p><p>The validity of the Fermi liquid description for strongly correlated electrons has also been studied. The results show that the general behavior of the Fermi liquid state is quite robust.</p>

Using field theoretical methods models of strongly correlated electrons have been investigated. Application to electronic structure calculations has been made. In this thesis an attempt is made to build a bridge between first-principle band structure calculations and a theory of systems with strongly correlated electrons, by making use of perturbation theory from the atomic limit. Analyzing the total non-relativistic Hamiltonian leads to the basic model of strongly correlated systems, the Hubbard-Anderson model. In this thesis these basic models have been tested. Conclusions on delocalization and many-body aspects have been extracted from the solutions. Specifically for the lanthanides a separation of the f-system into two subsystems has resolved the discrepancy between calculated equilibrium volumes and experimental ones. The calculations are done within the Hubbard-I approximation, where it is possible to define renormalized fermion operators. The calculation is a true many-body calculation. Using perturbation theory a set of self consistent equations has been formulated, and solved, for praseodymium metal using the periodical Anderson model. The solution shows a self consistent decrease of the Hubbard U, and delocalization of the f-shell, when crucial parameters of the model are changed. The most salient feature of the models for strongly correlated electrons is the transfer of spectral weight from one energy region to another by adjusting pressure or other external parameters. The effects come from kinematic interactions that are important for strongly correlated systems. Investigations of the degenerate Hubbard model applied to the metal to insulator transition has also been made. When the degeneracy is considered, the transition to the metallic state occurs at smaller Coulomb energies. The validity of the Fermi liquid description for strongly correlated electrons has also been studied. The results show that the general behavior of the Fermi liquid state is quite robust.

Studies on strongly correlated electron systems over decades have allowed physicists to discover unusual properties such as spin density waves, ferromagnetic and antiferromagnetic states with unusual ordering of spins and orbitals, and Mott insulating states, to name a few. In this thesis, the focus will be on the specific heat property of these materials exhibiting novel electronic ground states in the presence and absence of a field. The purpose of these measurements is to characterize the phase transitions into these states and the low energy excitations in these states. From measurements at the phase transitions, one can learn about the amount of order involved [i.e. entropy: ΔS = ∫Δc p/T dT], while measurements at low temperatures illuminate the excitation spectrum. In order to study the thermodynamic properties of the materials at their phase transitions, a high sensitive technique, ac-calorimetry was used. The ac-calorimeter, workhorse of our low dimensional materials lab, is based on modulating the power that heats the sample and measuring the temperature oscillations of the sample around its mean value. The in-house ac-calorimetry set up in our lab has the capability to produce a quasi-continuous readout of heat capacity as a function of temperature. A variety of single crystals were investigated using this technique and a few among them are discussed in my thesis. Since many of the crystals that are studied by our group are magnetically active, it becomes useful for us to also study them in the presence of a moderate to high magnetic field. This motivated me to design, develop, and build a heat capacity probe that would enable us to study the crystals in the presence of non-zero magnetic fields and at low temperatures. The probe helped us not only to revisit some of the studied materials and to draw firm conclusions on the previous results but also is vital in exploring the untouched territory of novel materials at high magnetic fields (~ 14 T).

In the first part of this work, we describe a theory of the ground states and charge gaps in the fractional quantum Hall states of graphene. The theory relies on knowledge of these properties for filling fractions smaller than one. Then, by the application of two mapping rules, one is able to obtain these properties for fractional quantum Hall states at arbitrary fillings, by conceiving the quantum Hall ferromagnets as vacua on which correlated electrons or correlated holes are added. The predicted charge gaps and phase transitions between different fractional quantum Hall states are in good agreement with recent experiments. In the second part, we investigate the low energy theory for the neutral Landau level of bilayer graphene. We closely analyze the way different terms in the Hamiltonian transform under the action of particle-hole conjugation symmetries, and identify several terms that are relevant in explaining the lack of such symmetry in experiments. Combining an accurate parametrization of the electronic structure of bilayer graphene with a systematic account of the impact of screening we are able to explain the absence of particle-hole symmetry reported in recent experiments. We also study the energetics of fractional quantum Hall states with coherence between n=0 and n=1 cyclotron quantum numbers, and obtain a general formula to map the two-point correlation function from their well-known counterparts made from only n=0 quantum numbers. Bilayer graphene has the potential for realizing these states which have no analogue in other two-dimensional electron systems such as Gallium Arsenide. We apply this formula to describe the properties of the n=0/n=1 coherent Laughlin state which displays nematic correlations. / text

Strong electron correlation lies at the root of many quantum collective phenomena observed in solids, including high Tc superconductivity. Theoretically, the problem of many interacting electrons is difficult to treat, however, and a microscopic understanding of strongly correlated systems remains one of the foremost challenges in modern physics. A particularly clean realisation of this general problem is found in magnetic systems, where theory and experiment are both well developed and complementary. The role of the chemist in this endeavour is to provide model experimental systems to both inspire new developments in theory and to confirm existing predictions. This thesis aims to demonstrate aspects of both synthesis and physical characterisation of such model systems, with particular emphasis on materials which exhibit unusual quantum ground states due to a combination of reduced dimensionality, low spin, and geometric frustration. Four materials are considered: The first among these is a new material, KTi(SO4)2·(H2O), which was prepared using a hydrothermal route, and characterised by magnetic susceptibility, specific heat, and high field magnetisation measurements. Fitting exact diagonalisation and series expansion results to these data imply that KTi(SO4)2·(H2O)is a long-sought experimental realization of the S = 1/2 Heisenberg frustrated (J1 − J2) chain model in the dimerised regime of the phase diagram. The anhydrous analogue of KTi(SO4)2·(H2O), KTi(SO4)2, was also investigated, and found by magnetic neutron scattering to exemplify the S = 1/2 Heisenberg anisotropic triangular lattice model in the 1D chain limit. The final two materials discussed are the naturally occurring minerals volborthite and herbertsmithite, both thought to realise the S = 1/2 Heisenberg kagome antiferromagnet model. Diffuse and inelastic magnetic neutron scattering experiments, however, indicate that the kagome physics are partially destroyed by defects in the former and lattice distortion in the latter.

Thesis advisor: Ziqiang Wang / Exotic phases and associated phase transitions in low dimensions have been a fascinating frontier and a driving force in modern condensed matter physics since the 80s. Due to strong correlation effect, they are beyond the description of mean-field theory based on a single-particle picture and Landau's symmetry-breaking theory of phase transitions. These new phases of matter require new physical quantities to characterize them and new languages to describe them. This thesis is devoted to the study on exotic phases of correlated electrons in two spatial dimensions. We present the following efforts in understanding two-dimensional exotic phases: (1) Using Zn vertex algebra, we give a complete classification and characterization of different one-component fractional quantum Hall (FQH) states, including their ground state properties and quasiparticles. (2) In terms of a non-unitary transformation, we obtain the exact form of statistical interactions between composite fermions in the lowest Landau level (LLL) with v=1/(2m), m=1,2... By studying the pairing instability of composite fermions we theoretically explains recently observed FQHE in LLL with v=1/2,1/4. (3) We classify different Z2 spin liquids (SLs) on kagome lattice in Schwinger-fermion representation using projective symmetry group (PSG). We propose one most promising candidate for the numerically discovered SL state in nearest-neighbor Heisenberg model on kagome lattice}. (4) By analyzing different Z2 spin liquids on honeycomb lattice within PSG classification, we find out the nature of the gapped SL phase in honeycomb lattice Hubbard model, labeled sublattice pairing state (SPS) in Schwinger-fermion representation. We also identify the neighboring magnetic phase of SPS as a chiral-antiferromagnetic (CAF) phase and analyze the continuous phase transition between SPS and CAF phase. For the first time we identify a SL called 0-flux state in Schwinger-boson representation with one (SPS) in Schwinger-fermion representation by a duality transformation. (5) We show that when certain non-collinear magnetic order coexists in a singlet nodal superconductor, there will be Majorana bound states in vortex cores/on the edges of the superconductor. This proposal opens a window for discovering Majorana fermions in strongly correlated electrons. (6) Motivated by recent numerical discovery of fractionalized phases in topological flat bands, we construct wavefunctions for spin-polarized fractional Chern insulators (FCI) and time reversal symmetric fractional topological insulators (FTI) by parton approach. We show that lattice symmetries give rise to different FCI/FTI states even with the same filling fraction. For the first time we construct FTI wavefunctions in the absence of spin conservation which preserve all lattice symmetries. The constructed wavefunctions also set up the framework for future variational Monte Carlo simulations. / Thesis (PhD) — Boston College, 2011. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

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.