Thesis (Ph.D.)--Kent State University, 2009. / Title from PDF t.p. (viewed Apr. 3, 2010). Advisor: Almut Schroeder. Keywords: non-Fermi liquid, CeNi2Ge2, spin fluctuations, neutron scattering, heavy fermions, quantum critical point. Includes bibliographical references.

In this thesis, we study the low-energy effective theory for the antiferromagnetic quantum critical metal in two dimensions. The theory has been the subject of intense study for more than twenty years, due to the novel physics of non-Fermi liquid metals and its potential relevance to high-temperature superconductors and heavy-fermion compounds. In the first part of the thesis, we present the perturbative study of the theory in 3 minus epsilon space dimensions by extending the earlier one-loop analysis to higher-loop orders. We show that the expansion is not organized by the standard loop expansion, and a two-loop graph becomes as important as one-loop graphs even in the small epsilon limit due to an infrared singularity caused by an emergent quasilocality. This qualitatively changes the nature of the infrared fixed point, and the epsilon expansion is controlled only after the two-loop effect is taken into account. Furthermore, we show that a ratio between velocities emerges as a small parameter, which suppresses a large class of diagrams. We show that the critical exponents do not receive quantum corrections beyond the linear order in epsilon in the limit that the ratio of velocities vanishes. In the second part of the thesis, we present a nonperturbative solution to the theory in two dimensions based on an ansatz that is inspired by the perturbative analysis. Being a strongly coupled theory, it can still be solved reliably in the low-energy limit as quantum fluctuations are organized by the ratio of velocities that dynamically flows to zero in the low-energy limit. We predict the exact critical exponents that govern the universal scaling of physical observables at low temperatures. / Thesis / Doctor of Philosophy (PhD)

Thesis (Ph. D.)--Florida State University, 2003. / Advisor: Dr. Zachary Fisk, Florida State University, College of Art and Sciences, Dept. of Physics. Title and description from dissertation home page (viewed Mar. 2,2004). Includes bibliographical references.

Thesis (Ph.D.)--Kent State University, 2009. / Title from PDF t.p. (viewed April 9, 2010). Advisor: Michael Lee. Includes bibliographical references (p. 97-101).

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references and index.

PhD Thesis / The superconductivity in heavy-fermion compounds, iron pnictides and cuprates has been intensively studied for over thirty years. Amongst some of these materials, the common denominator is the presence of strong antiferromagnetic fluctuations in their normal state, signaling an underlying quantum phase transition between a paramagnetic metal and a metal with antiferromagnetic long-range order. Although the quantum critical point is experimentally inaccessible due to the presence of superconducting order, it determines the physical properties of the normal state of the metal in a wide range of temperatures. In this thesis we study the low-energy theory for the critical metallic state that arises at the aforementioned quantum critical point. We present a nonperturbative study of the theory in spatial dimensions between two and three. We pay special attention to two dimensions where we show that our physical predictions are in qualitative agreement with experiments in electron-doped cuprates. We further develop a field theoretic functional renormalization group scheme that is analytically tractable. It provides a general framework to study the low-energy theory of metallic states with or without a quasiparticle description. Within this formalism we characterize the single-particle properties of the antiferromagnetic quantum critical metal. This allows one to study the superconducting instability triggered by critical antiferromagnetic quantum fluctuations quantitatively. / Thesis / Doctor of Science (PhD)

In this thesis we study the effect of electron-electron interactions on Chiral two-dimensional electron gas (C2DEGs). C2DEGs are a very good description of the low-energy electronic properties of single layer and multilayer graphene systems. The low-energy properties of single layer and multilayer graphene are described by Chiral Hamiltoninans whose band eigenstates have definite chirality. In this thesis we focus on the effect of electron-electron interactions on two of these systems: monolayer and bilayer graphene. In the first half of this thesis we use the massless Dirac Fermion model and random-phase-approximation to study the effect of interactions in graphene sheets. The interplay of graphene's single particle chiral eigenstates along with electron-electron interactions lead to a peculiar supression of spin susceptibility and compressibility, and also to an unusual velocity renormalization. We also report on a theoretical study of the influence of electron-electron interactions on ARPES spectra in graphene. We find that level repulsion between quasiparticle and plasmaron resonances gives rise to a gap-like feature near the Dirac point. In the second half we anticipate interaction driven integer quantum Hall effects in bilayer graphene because of the near-degeneracy of the eight Landau levels which appear near the neutral system Fermi level. We predict that an intra-Landau-level cyclotron resonance signal will appear at some odd-integer filling factors, accompanied by collective modes which are nearly gapless and have approximate q[superscrit 3/2] dispersion. We speculate on the possibility of unusual localization physics associated with these modes. / text

This thesis presents an investigation into quantum many-body systems using both theoretical and innovative computational techniques. It has two parts: an investigation of a new class of materials using established methods, and the development of a new set of methods. First, we use Hartree-Fock calculation to study the moiré Hubbard model that represents the low energy physics of twisted WSe₂ and related materials. In these materials, interaction strength, carrier concentration, and band structure can be controlled by the twist angle and gate voltage. A notable feature is the tunable displacement field, i.e., the gate voltage difference between two layers, leading to a highly tunable van Hove singularity. We calculate the magnetic and metal-insulator phase diagrams and find a reentrant metal-insulator transition controlled by the displacement field. Experimental results for devices with twist angle ∼ 4-5° indicate a similar reentrance, placing these devices in the intermediate coupling regime. Building on this, the next chapter employs dynamical mean field theory (DMFT) to study the moiré Hubbard model, extending our analysis to include temperature-dependent transport behaviors and phase transitions. We observe that the cube-root van Hove singularity 𝜌(𝜀) ∼ |𝜀|⁻¹/³ contributes to strange metal behavior, characterized by a linear temperature-dependent scattering rate and 𝜔/𝑇 scaling. We compare the results to the experimental findings in twisted homobilayer WSe₂ and heterobilayer MoTe₂ /WSe₂. We find that in twisted WSe₂, the continuous metal-insulator transition is driven by a magnetic transition associated with a change of the displacement field that brings the high order van Hove point of degree three to the Fermi level. The proximity to this van Hove point also induces a linear resistivity. In MoTe₂/WSe₂, one has a paramagnetic metal to paramagnetic Mott insulator transition driven by variation of the bandwidth, with the displacement field effects being unimportant. In the third study we use the example of magic angle twisted bilayer graphene (TBG) to study the interplay between correlation and band topology. We construct the Wannier basis for TBG involving two triangular site-centered Wannier functions per unit cell derived from the two flat bands per spin per valley. The two crucial point symmetries 𝐶₂𝑇 and 𝐶₃ act locally on the Wannier functions. The Wannier functions have a power-law tail indicative of topological obstruction, but are mostly localized with most charge density concentrated within a single unit cell. This localization significantly enhances the on-site Coulomb interactions relative to interactions with further neighbors, allowing for more accurate estimation of Hamiltonian parameters using a limited set of Wannier functions. Using DMFT, we show that a mixed position/ momentum space representation can be employed, in which the kinetic energy is expressed in the momentum space basis of non-interacting eigenstates, so that all the topological features are exact and well preserved, while the interaction part may be expressed in position space and inherit convenient locality and symmetry properties from the Wannier functions. Finally, we introduce a novel, data-driven approach to compress the two-particle vertex function. Using PCA and an autoencoder neural network, we achieve significant reductions in complexity while maintaining high fidelity in representing the underlying physics. We demonstrate that a linear PCA not only provides deeper physical insights but also exhibits superior zero-shot generalization compared to more complex nonlinear models. Further, we explore the relationships between different quantum states by identifying principal component subspaces common across known phases. Our analysis reveals that while the vertex functions necessary for describing ferromagnetic states differ significantly from those describing the Fermi liquid state, those required for antiferromagnetic and superconducting states share a common foundation, hinting at their emergence from pre-existing fluctuations in the Fermi liquid state.

Orientador: Guillermo Gerardo Cabrera Oyarzun / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-09-24T19:06:18Z (GMT). No. of bitstreams: 1 Uchoa_Bruno_D.pdf: 3173776 bytes, checksum: bbc84ac454d01ce5ee4aa4ae8b9d5b42 (MD5) Previous issue date: 2004 / Resumo: Investigamos os efeitos macroscópicos de ondas das densidade de carga ( CDW) e da supercondutividade em sistemas organizados em planos que exibem quebra da simetria de inversão da rede (o que permitiria o aparecimento de piezoeletricidade), como nos metais de transição dicalcogenados (TMDs). Partindo da teoria de Ginzburg-Landau com dependência temporal a baixas temperaturas, estudamos como as distorções da rede e os modos coletivos de baixa energia da CDW se acoplam ao parâmetro de ordem supercondutor na presença de campos eletromagnéticos. Demonstramos que a supercondutividade e a piezoeletricidade podem coexistir nesses metais singulares. Além disso, este estudo indica a natureza do ponto crítico quântico entre a fase CDW comensurá.vel e a fase de faixas de carga, observado em função da pressão aplicada. Estes resultados são utilizados para fundamentar um modelo microscópico que unifica a supercondutividade às fases de CDW nos TMDs. Baseados na natureza do acoplamento elétron-fônon e na topologia peculiar da superfície de Fermi, propomos que o gap de CDW tem simetria f e quebra a simetria de inversão da rede na fase disorcida. As quase- partículas da teoria são férmions de Dirac definidos pelas exitações elementares da CDW na vizinhaça dos nós da superfície de Fermi, onde o gap da CDW se fecha. O estado supercondutor é formado pela atração entre férmions de Dirac através de fônons virtuais mediados pelo acoplamento piezoelétrico. Segundo esta teoria, as propriedades de transporte e o tempo de meia-vida das excitações de quase-partícula mostram fortes desvios em relação à teoria do líquido de Fermi / Abstract: We investigate the macroscopic effects of charge density waves (CDW) and superconductivity in layered superconducting systems with broken lattice inversion symmetry (allowing for piezoelectricity) such as two dimensional (2D) transition metal dichalcogenides (TMD). We work with the low temperature time dependent Ginzburg-Landau theory and study the coupling of lattice distortions and low energy CDW collective modes to the superconducting order parameter in the presence of electromagnetic fields. We show that superconductivity and piezoelectricity can coexist in these singular metals. Furthermore, our study indicates the nature of the quantum phase transition between a commensurate CDW phase and the stripe phase that has been observed as a function of applied pressure. These results are used to support a microscopic unified picture with superconductivity and CDW phases in TMD. Based on the nature of the electron-phonon coupling and Fermi surface topology, we propose a f-wave symmetry CDW gap which breakes the lattice inversion symmetry in the distorted phase. The quasiparticles are Dirac fennions defined by the elementary excitations of the CDW in the vicinity of the Fermi surface nodes, where the CDW gap is zero. The superconducting state has its origin in virtual phonon attraction of the Dirac fermions, mediated by the piezoelectric coupling. According to this theory, the transport properties and the quasiparticles life-time show strong deviations from the Fermi liquid theory / Doutorado / Física / Doutor em Ciências

<p>When modelling the collapse of massive stars leading to supernova explosions and the cooling of neutron stars, understanding the microphysical processes, such as the interaction of neutrinos within a dense medium are of vital importance. The interaction of neutrinos with nucleons (neutrons and protons) is altered by the presence of the medium, compared to the same process with free nucleons. Neutrino scattering and production processes may be characterized in terms of the excitations that are created or destroyed in the nuclear medium. One way to analyse the effects of the medium is by using Landau's theory of normal Fermi liquids. This theory gives simple relationships between physical quantities such as the spin susceptibility or the response to a weak interaction probe in terms of Landau parameters, that are measures of the interaction between quasiparticles. One problem when using Landau Fermi liquid theory for nucleon matter is that the interaction has a tensor component. The tensor interaction does not conserve the total spin and, as a consequence, there are generally contributions to long-wavelength response functions from states that have more than one quasiparticle-quasihole pair in the intermediate state. Such contributions cannot be calculated in terms of Landau parameters alone, since in the usual formulation of Landau theory, only singlepair excitations are considered. In this thesis three problems are addressed. First, we obtain bounds on the contributions from more than one quasiparticle-quasihole pair by using sum-rule arguments. Second, we derive expressions for static response functions allowing for the tensor components of the interaction. We analyse which the most important effects are on the static response of nucleon matter, and find that the major contributions comes from renormalization of coupling constants and transitions to states with more than one quasiparticle-quasihole pair. Third, we show how contributions to the dynamical response coming from states containing two quasiparticle-quasihole pairs may be evaluated in terms of Landau theory if one allows for the effect of collisions in the Landau kinetic equation. We consider the case of asymmetric nuclear matter, and our work goes beyond earlier works in that they contain the effects of collisions in addition to those of the mean field.</p>