In the past three decades, quasi-low-dimensional organic materials have attracted intense interests, both experimentally and theoretically. Due to their reduced dimensionality and relatively low carrier concentration, many organic materials exhibit strong electron correlations and numerous instabilities of the normal metallic state. The energy scales of such instabilities are often so low that the ground states can be changed by applying a reasonably strong magnetic field. Therefore, magnetic field is an effective tool for the study of quasi-low-dimensional organic materials. In this thesis, we will investigate two of these magnetic field related phenomena. In the first part, we will present our unified theory of angular magnetoresistance oscillations observed in organic conductors. We will demonstrate that, in spite of the absence of Landau level quantization for open Fermi surfaces in a magnetic field, a new quantum effect - Bragg reflections of electrons moving in the extended Brillouin zone - determines unusual magnetic properties of these materials. We will demonstrate that, at commensurate directions of a magnetic field, the electron motion shows 1D→2D dimensional crossover and leads to strong resistivity minima. We will present an analytic expression for interlayer resistivity, by both linear response formalism and solving the Boltzmann kinetic equation in the extended Brillouin zone. In two limiting cases, our general solution reduces to the results previously obtained for the LMA effects and LNL oscillations. We demonstrate that our theoretical results are in good qualitative and quantitative agreement with the existing measurements of resistivity in (TMTSF)₂ClO₄ conductor. In the second part, we will develop a theory for the recently observed high magnetic field high resistance state in (Per)₂Pt(mnt)₂. We demonstrate that the Pauli spinsplitting effects in a magnetic field improve nesting properties of a realistic quasi-onedimensional electron spectrum. As a result, a high resistance Peierls charge-density wave (CDW) phase is stabilized in high enough magnetic fields in (Per)₂Pt(mnt)₂ conductor. We show that, in low and very high magnetic fields, the Pauli spin-splitting effects lead to a stabilization of a soliton wall superlattice (SWS) CDW phase, which is characterized by periodically arranged soliton and anti-soliton walls. We suggest experimental studies of the predicted first order phase transitions between the Peierls and SWS phases to discover a unique SWS phase. It is important that, in the absence of a magnetic field and in a limit of very high magnetic fields, the suggested model is equivalent to the exactly solvable model of Brazovskii, Dzyaloshinskii, and Kirova.

The formation of new phases close to itinerant electron quantum critical points has been observed experimentally in many compounds. We present a unified analytical model that explains the emergence of new types of phases around itinerant ferromagnetic quantum critical points. The central idea of our analysis is that certain deformations of the Fermi surface enhance the phase-space available for low-energy quantum fluctuations and so self-consistently lower the free energy. Using this quantum order-by-disorder mechanism, we find instabilities towards the formation of a spiral ferromagnet and spin-nematic phase close to an itinerant ferromagnetic quantum critical point. Further, we employ the quantum order-by-disorder mechanism to describe the partially ordered phase of MnSi. Using the simplest model of a Stoner-like helimagnetic transition, we show that quantum fluctuations naturally lead to the formation of an unusual phase near to the putative quantum critical point that shares many of the observed features of the partially ordered phase in MnSi. In particular, we predict an angular dependence of neutron scattering that is in good agreement with neutron-scattering data.

Systems with competing orders are of great interest in condensed matter physics. When two phases have comparable energies, novel interplay effects such can be induced by tuning an appropriate parameter. In this thesis, we study two problems of competing orders - (i) ultracold atom gases with competing superfluidity and Charge Density Wave(CDW) orders, and (ii) low dimensional antiferromagnets with Neel order competing against various disordered ground states. In the first part of the thesis, we study the attractive Hubbard model which could soon be realized in ultracold atom experiments. Close to half-filling, the superfluid ground state competes with a low-lying CDW phase. We study the collective excitations of the superfluid using the Generalized Random Phase Approximation (GRPA) and strong-coupling spin wave analysis. The competing CDW phase manifests as a roton-like excitation. We characterize the collective mode spectrum, setting benchmarks for experiments. We drive competition between orders by imposing superfluid flow. Superflow leads to various instabilities: in particular, we find a dynamical instability associated with CDW order. We also find a novel dynamical incommensurate instability analogous to exciton condensation in semiconductors. In the second part, inspired by experiments on Bi3Mn4O12(NO3)(BMNO), we first study the interlayer dimer state in spin-S bilayer antiferromagnets. At a critical bilayer coupling strength, condensation of triplet excitations leads to Neel order. In describing this transition, bond operator mean field theory suffers from systematic deviations. We bridge these deviations by taking into account corrections arising from higher spin excitations. The interlayer dimer state shows a field induced Neel transition, as seen in BMNO. Our results are relevant to the quantitative modelling of spin-S dimerized systems. We then study the J1−J2 model on the honeycomb lattice with frustrating next-nearest neighbour exchange. For J2>J1/6, quantum and thermal fluctuations lead to ‘lattice nematic’ states. For S=1/2, this lattice nematic takes the form of a valence bond solid. With J2<J1 /6, quantum fluctuations melt Neel order so as to give rise to a field induced Neel transition. This scenario can explain the observed properties of BMNO. We discuss implications for the honeycomb lattice Hubbard model.

Systems with competing orders are of great interest in condensed matter physics. When two phases have comparable energies, novel interplay effects such can be induced by tuning an appropriate parameter. In this thesis, we study two problems of competing orders - (i) ultracold atom gases with competing superfluidity and Charge Density Wave(CDW) orders, and (ii) low dimensional antiferromagnets with Neel order competing against various disordered ground states. In the first part of the thesis, we study the attractive Hubbard model which could soon be realized in ultracold atom experiments. Close to half-filling, the superfluid ground state competes with a low-lying CDW phase. We study the collective excitations of the superfluid using the Generalized Random Phase Approximation (GRPA) and strong-coupling spin wave analysis. The competing CDW phase manifests as a roton-like excitation. We characterize the collective mode spectrum, setting benchmarks for experiments. We drive competition between orders by imposing superfluid flow. Superflow leads to various instabilities: in particular, we find a dynamical instability associated with CDW order. We also find a novel dynamical incommensurate instability analogous to exciton condensation in semiconductors. In the second part, inspired by experiments on Bi3Mn4O12(NO3)(BMNO), we first study the interlayer dimer state in spin-S bilayer antiferromagnets. At a critical bilayer coupling strength, condensation of triplet excitations leads to Neel order. In describing this transition, bond operator mean field theory suffers from systematic deviations. We bridge these deviations by taking into account corrections arising from higher spin excitations. The interlayer dimer state shows a field induced Neel transition, as seen in BMNO. Our results are relevant to the quantitative modelling of spin-S dimerized systems. We then study the J1−J2 model on the honeycomb lattice with frustrating next-nearest neighbour exchange. For J2>J1/6, quantum and thermal fluctuations lead to ‘lattice nematic’ states. For S=1/2, this lattice nematic takes the form of a valence bond solid. With J2<J1 /6, quantum fluctuations melt Neel order so as to give rise to a field induced Neel transition. This scenario can explain the observed properties of BMNO. We discuss implications for the honeycomb lattice Hubbard model.

In a strong magnetic field, the psuedospin chirality of bilayer graphene’s low energy bands results in degenerate, zero energy n=0 and n=1 Landau or- bital states. In this thesis, we find that in addition to endowing states with energetic broadness disorder strongly mixes the zero energy orbitals of the lowest Landau level. We study the dependence of mixing and conductivity on inter-layer bias. Quantum Hall ferromagnetic states emerge when electronic interactions are included at the mean-field level. We study the character of ground states and quasiparticle excitations in the context of orbital degen- eracy and in the presence of interactions with the filled Dirac sea of states. Lastly, we study the effect of interactions in ABA-stacked trilayer graphene, and discover a metal-insulator transition and a separate propensity to break mirror symmetry in certain areas of parameter space. / text

This thesis scrutinizes the condensed matter physics phenomenon known as the fractional quantum Hall effect (FQHE), in particular fractional quantum Hall effects occurring in multicomponent systems. Broadly speaking, the FQHE can be defined as a many-electron quantum phenomenon, driven by strong interactions, that occurs in two-dimensional electron gasses in the presence of a perpendicular external magnetic field (and it is also predicted to occur for any two-dimensional particles, such as confined cold atoms, in an external gauge field). Multicomponent systems are systems where the constituent particles (such as electrons or cold atoms) possess internal degrees of freedom, for instance a spin or valley index. These internal degrees of freedom are often overlooked when modeling the FQHE. Taking into account the multicomponent degree of freedom yields an abundance of possibilities for the intellection of new types of so-called “topological phases of matter”, which are ubiquitously associated with the FQHE. In this thesis several different cases are considered. The first topic discussed herein is a study of phase transitions that can take place between FQHE phases with different net values of their multicomponent degrees of freedom. Examples are phase transitions between phases of different uniform net spin polarization, tunable as a function of certain system parameters. Some significant technical refinements are made to a previous model and comparisons are made with a variety of different experiments. The results are relevant for multicomponent FQHEs occurring in GaAs,AlAs and SiGe semiconductor systems where the electronic structure is confined to two dimensions, as well as in two-dimensional materials such as graphene. The second topic discussed herein is the introduction of the multiparticle multicomponent pseudopotential formalism. This methodology is oriented towards considerably expanding an existing framework for the construction of exactly solvable FQHE models by parameterizing multicomponent interactions. The final topic is the first example application of this new formalism to the construction of an exactly solvable FQHE model.

In this thesis, I present an excitonic approach to treating the coherent dynamics of optically generated charge carriers in semiconductor nanostructures. The main feature of this approach is that it includes exchange interactions and phase space filling effects, which have generally been omitted in previous excitonic treatments of coherent dynamics, so that it can go beyond the low excitation limit. In contrast to the well-known semiconductor Bloch equations, this approach treats intraband correlations without factorization. The excitonic formalism and the obtained excitonic equations are shown to be particularly advantageous in systems where bound excitons dominate the optical response and where intraband correlations play a central role. To demonstrate the application of the excitonic approach, we simulate the coherent carrier dynamics of an optically-excited, updoped AlGaAs superlattice in the presence of a terahertz pulse, where 1s excitonic states as well as higher in-plane excited states are included. We find that gain coefficients greater than 20/cm can be achieved over a tuning range of 3-11THz and that due to the coherent cascading of the carriers down the excitonic Wannier-Stark ladder, the gain coefficients have much higher gain saturation fields than comparable two-level systems. To investigate the effects of phase space filling and exchange interaction on exciton dynamics, we then apply the excitonic formalism to a simple model of a quantum ring as well as a realistic model of a quantum well. For the quantum ring, we have obtained numerical results regarding exciton population and interband polarization. We also compared our excitonic approach to the semiconductor Bloch equations in detail using this simple model. For the quantum well, in addition to the investigation of exciton dynamics, we propose and examine several approximations that can make our excitonic dynamic equations very efficient. The excitonic formalism presented in this thesis is an efficient approach that can be applied in a wide range of systems, which makes it a potential alternative to the standard miconductor Bloch equations for many systems where the intraband correlations are crucial. / Thesis (Ph.D, Physics, Engineering Physics and Astronomy) -- Queen's University, 2008-12-01 18:21:17.181

The purpose of the research contained in this thesis is to allow for the prediction of new structures and properties of crystalline structures due to the application of external pressure by using first-principles numerical computations. The body of the thesis is separated into two primary research projects. The properties of cupric oxide (CuO) have been studied at pressures below 70 GPa, and it has been suggested that it may show room-temperature multiferroics at pressure of 20 to 40 GPa. However, at pressures above these ranges, the properties of CuO have yet to be examined thoroughly. The changes in crystal structure of CuO were examined in these high-pressure ranges. It was predicted that the ambient pressure monoclinic structure changes to a rocksalt structure and CsCl structure at high pressure. Changes in the magnetic ordering were also suggested to occur due to superexchange interactions and Jahn-Teller instabilities arising from the d-orbital electrons. Barium chloride (BaCl) has also been observed, which undergoes a similar structural change due to an s – d transition, and whose structural changes can offer further insight into the transitions observed in CuO. Ammonia borane (NH3BH3) is known to have a crystal structure which contains the molecules in staggered conformation at low pressure. The crystalline structure of NH3BH3 was examined at high pressure, which revealed that the staggered configuration transforms to an eclipsed conformation stabilized by homopolar B–Hδ-∙∙∙ δ-H–B dihydrogen bonds. These bonds are shown to be covalent in nature, comparable in bond strength to conventional hydrogen bonds, and may allow for easier molecular hydrogen formation in hydrogen fuel storage.

We determine the dynamical structure factors of two gapped correlated electron systems, namely the Ising model in a strong transverse field and the two-leg spin-1/2 Heisenberg ladder in the limit of strong rung coupling. We consider the low-temperature limit, employing a variety of analytical and numerical techniques. The coherent modes of single-particle excitations, which are delta functions at zero temperature, are shown to broaden asymmetrically in energy with increasing temperature. Firstly, we apply a low-temperature “resummation” inspired by the Dyson equation to a linked-cluster expansion of the two-leg Heisenberg ladder. We include matrix elements to second order in the interaction between states containing up to two particles. A low-frequency response similar to the “Villain mode” is also observed. Next, we apply a cumulant expansion technique to the transverse field Ising model. We resolve the issue of negative spectral weight caused by double pole in the leading self-energy diagram by including a resummation of terms obtained from the six-point function, demonstrating that the perturbation series in 2n-spin correlation functions can be extended to higher orders. The result generalises to higher dimensions and the analytic calculation is compared to a numerical Pade approximant. We outline the extension of this method to the strong coupling ladder. Finally, we compare the previous results to numerical data obtained by full diagonalisation of finite chains and numerical evaluation of the Pfaffian, a method specific to the transverse field Ising chain. The latter method is used for a phenomenological study of the asymmetric broadening as well as an evaluation of fitting functions for the broadened lineshapes.

Microorganisms have evolved in a low Reynolds number environment and have adapted their behaviour to its viscosity. Here, we consider some features of behaviour observed in microorganisms and use hydrodynamic models to show that these behaviours emerge from physical interactions, including hydrodynamic friction, hydrodynamic interactions and mechanical constraints. Swimming behaviour is affected by surfaces and observations of Vibrio cholerae show that it swims near a surface with two distinct motility modes. We develop a model which shows that friction between pili and the surface gives the two motility modes. The model is extended to study the behaviour of bacteria which are partially attached to a surface. Observations of Shewanella constrained by a surface show several different behaviours. The model shows that different degrees of surface constraint lead to different types of behaviour; the flexibility of the flagellar hook and the torque exerted by the flagellar motor also cause different behaviours. Near surface behaviour is important for understanding the initial stages of biofilm formation. Chlamydomonas swims using synchronous beating of its two flagella. A simple model of Chlamydomonas is developed to study motility and synchronisation. This model shows that the stability of synchronisation is sensitive to the beat pattern. Run-and-tumble behaviour emerges when we include intrinsic noise, without the need for biochemical signalling. The model is also used to show how observed responses of the flagella to light stimuli produce phototaxis. Finally we study hydrodynamic synchronisation of many cilia and consider the stability of metachronal waves in arrays of hydrodynamically coupled cilia. This thesis shows that physical interactions are responsible for many behavioural features and that physical models provide a useful technique for exploring open questions in biology.