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Thesis advisor: Kevin S. Bedell / In 1956, Lev Davidovich Landau put forth his theory on systems of interacting fermions, or fermi liquids. A year later, Viktor Pavlovich Silin described spin waves that such a system of fermions would support. The treatment of the contribution of the molecular field to the spin wave dispersion was a novel aspect of these spin waves. Silin predicted that there would exist a hierarchy of spin waves in a fermi liquid, one for each component of the spherical harmonic expansion of the fermi surface. In 1968, Anthony J. Leggett and Michael J. Rice derived from fermi liquid theory how the behavior of the spin diffusion coefficient of a fermi liquid could be directly experimentally observable via the spin echo effect. Their prediction, that the diffusion coefficient of a fermi liquid would not decay exponentially with temperature, but rather would have a maximum at some non-zero temperature, was a direct consequence of the fermi liquid molecular field and spin wave phenomena, and this was corroborated by experiment in 1971 by Corruccini, et al. A parallel advancement in the theory of fermi liquid spin waves came with the extension of the theory to describe weak ferromagnetic metals. In 1959, Alexei Abrikosov and I. E. Dzyaloshiski put forth a theoretical description of a ferromagnetic fermi liquid. In 2001, Kevin Bedell and Krastan Blagoev showed that a non-trivial contribution to the dispersion of the ferromagnetic current spin wave arises from the necessary consideration of higher harmonic moments in the distortion of the fermi surface from its ground state. In the chapters to follow, the author presents new results for transverse spin waves in a fermi liquid, which arise from a novel ground state of a fermi liquid--one in which an l=1 harmonic distortion exists in the ground state polarization. It is shown that such an instability can lead to spin waves with dispersions that are characterized by a linear dependence on the wave number at long wavelengths, or can lead to spin waves that are characterized by a square root dependence on the wave number at long wavelength. The author also presents new results for spin waves in a fermi liquid that has a spin density wave in its ground state. A spin density wave is characterized by a spiral magnetization in the ground state, and is observed to occur in materials such as MnSi. / Thesis (PhD) — Boston College, 2009. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

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A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. Johannesburg, 2015. / Recently there has been signi cant interest in new types of metals called non-Fermi liquids, which cannot be described by Landau Fermi liquid theory. Landau Fermi liquid theory is a theoretical model used to describe low energy interacting fermions or quasiparticles. There is a growing interest in constructing an e ective eld theory for these types of metals. One of the paradigms to understand these metals is by the use of Wilsonian renormalization group (RG) to study a theoretical toy model consisting of fermions coupled to a gapless order parameter eld. Here we will study fermions coupled to gapless bosons (order parameter) below the upper critical dimension (d = 3). We will treat both fermions and bosons on equal footing and construct an e ective eld theory which only integrates out high momentum modes. Then we compute the one-loop RG ows for the Yukawa coupling and four-Fermi interaction. We will discuss log2 and log3 subleties associated with the one loop RG ows for the four-Fermi interaction and how they can be circumvented.

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Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2007. / Includes bibliographical references (leaves 43-45). Also available in electronic version.

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Thesis advisor: Kevin S. Bedell / One of the many achievements of renowned physicist L.D. Landau was the formulation of Fermi Liquid Theory (FLT). Originally debuted in the 1950s, FLT has seen abundant success in understanding degenerate Fermi systems and is still used today when trying to understand the physics of a new interacting Fermi system. Of its many advantages, FLT excels in explaining why interacting Fermi systems behave like their non-interacting counterparts, and understanding transport phenomena without cumbersome and confusing mathematics. In this work, FLT is applied to systems whose low energy excitations obey the massless Dirac equation; i.e. the energy dispersion is linear in momentum, ε α ρ, as opposed to the normal quadratic, ε α ρ². Such behavior is seen in numerous, seemingly unrelated, materials including graphene, high T[subscript]c superconductors, Weyl semimetals, etc. While each of these materials possesses its own unique properties, it is their low energy behavior that provides the justification for their grouping into one family of materials called Dirac materials (DM). As will be shown, the linear spectrum and massless behavior leads to profound differences from the normal Fermi liquid behavior in both equilibrium and transport phenomena. For example, with mass having no meaning, we see the usual effective mass relation from FLT being replaced by an effective velocity ratio. Additionally, as FLT in d=2 has been poorly studied in the past, and since the most famous DM in graphene is a d=2 system, a thorough analysis of FLT in d=2 is presented. This reduced dimensionality leads to substantial differences including undamped collective modes and altered quasiparticle lifetime. In chapter 3, we apply the Virial theorem to DM and obtain an expression for the total average ground state energy $E=\frac{B}{r_s}$ where $B$ is a constant independent of density and $r_s$ is a dimensionless parameter related to the density of the system: the interparticle spacing $r$ is related to $r_s$ through $r=ar_s$ where $a$ is a characterstic length of the system (for example, in graphene, $a=1.42$ \AA). The expression derived for $E$ is unusual in that it's typically impossible to obtain a closed form for the energy with all interactions included. Additionally, the result allows for easy calculation of various thermodynamic quantities such as the compressibility and chemical potential. From there, we use the Fermi liquid results from the previous chapter and obtain an expression for $B$ in terms of constants and Fermi liquid parameters $F_0^s$ and $F_1^s$. When combined with experimental results for the compressibility, we find that the Fermi liquid parameters are density independent implying a unitary like behavior for DM. In chapter 4, we discuss the alleged universal KSS lower bound in DM. The bound, $\frac{\eta}{s}\geq\frac{\hbar}{4\pi k_B}$, was derived from high energy/string theory considerations and was conjectured to be obeyed by all quantum liquids regardless of density. The bound provides information on the interactions in the quantum liquid being studied and equality indicates a nearly perfect quantum fluid. Since its birth, the bound has been highly studied in various systems, mathematically broken, and poorly experimented on due to the difficult nature of measuring viscosity. First, we provide the first physical example of violation by showing $\frac{\eta}{s}\rightarrow 0$ as $T\rightarrow T_c$ in a unitary Fermi gas. Next, we determine the bound in DM in d=2,3 and show unusual behavior that isn't seen when the bound is calculated for normal Fermi systems. Finally we conclude in chapter 5 and discuss the outlook and other avenues to explore in DM. Specifically, it must be pointed out that the physics of what happens near charge neutrality in DM is still poorly understood. Our work in understanding the Fermi liquid state in DM is necessary in understanding DM as a whole. Such a task is crucial when we consider the potential in DM, experimentally, technologically, and purely for our understanding. / Thesis (PhD) — Boston College, 2020. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

Thesis advisor: Kevin S. Bedell / Landau Fermi-liquid theory was first introduced by L. D. Landau in the effort of understanding the normal state of Fermi systems, where the application of the concept of elementary excitations to the Fermi systems has proved very fruitful in clarifying the physics of strongly correlated quantum systems at low temperatures. In this thesis, I use Landau Fermi-liquid theory to study the transport phenomena of two different correlated quantum liquids: the strongly interacting ultracold Fermi gases and the ferromagnet/normal metal (F/N) junctions. The detailed work is presented in chapter II and chapter III of this thesis, respectively. Chapter I holds the introductory part and the background knowledge of this thesis. In chapter II, I study the transport properties of a Fermi gas with strong attractive interactions close to the unitary limit. In particular, I compute the transport lifetimes of the Fermi gas due to superfluid fluctuations above the BCS transition temperature Tc. To calculate the transport lifetimes I need the scattering amplitudes. The scattering amplitudes are dominated by the superfluid fluctuations at temperatures just above Tc. The normal scattering amplitudes are calculated from the Landau parameters. These Landau parameters are obtained from the local version of the induced interaction model for computing Landau parameters. I also calculate the leading order finite temperature corrections to the various transport lifetimes. A calculation of the spin diffusion coefficient is presented in comparison to the experimental findings. Upon choosing a proper value of F0a, I am able to present a good match between the theoretical result and the experimental measurement, which indicates the presence of the superfluid fluctuations near Tc. Calculations of the viscosity, the viscosity/entropy ratio and the thermal conductivity are also shown in support of the appearance of the superfluid fluctuations. In chapter III, I study the spin transport in the low temperature regime (often referred to as the precession-dominated regime) between a ferromagnetic Fermi liquid (FFL) and a normal metal metallic Fermi liquid (NFL), also known as the (F/N) junction, which is considered as one of the most basic spintronic devices. In particular, I explore the propagation of spin waves and transport of magnetization through the interface of the F/N junction where nonequilibrium spin polarization is created on the normal metal side of the junction by electrical spin injection. I calculate the probable spin wave modes in the precession-dominated regime on both sides of the junction especially on the NFL side where the system is out of equilibrium. Proper boundary conditions at the interface are introduced to establish the transport of the spin properties through the F/N junction. A possible transmission conduction electron spin resonance (CESR) experiment is suggested on the F/N junction to see if the predicted spin wave modes could indeed propagate through the junction. Potential applications based on this novel spin transport feature of the F/N junction are proposed in the end. / Thesis (PhD) — Boston College, 2016. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.