Competing Phases in Two-Dimensional Quantum Many-Body Systems

Embargo until
2014-12-01
Date
2013-10-22
Journal Title
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Publisher
Johns Hopkins University
Abstract
Quantum many-body systems exhibit a wide array of possible ordered phases at low temperatures. In this thesis, several such phases and the transitions between them are theoretically studied in the context of recent experimental results. I first present an investigation of fluctuation phenomena in layered superconductors in high magnetic fields. In order to account for the important effects of coupling between layers, which enhances the superconducting fluctuations and allows for a finite-temperature phase transition, a novel expansion in the number of coupled layers is used. This expansion leads to a two-dimensional effective Ginzburg--Landau theory, which allows for a controlled calculation of thermodynamic and transport properties such as magnetization and conductivity. Next, a microscopic mean-field analysis of the recently synthesized mixed-valency material KNi2Se2 is presented. Due to the noninteger number of localized electrons per unit cell and substantial degree of electron interactions, this material exhibits a tendency toward charge ordering, which competes with a heavy-fermion phase exhibiting an enhanced effective electron mass. Beginning from a microscopic Hamiltonian and applying mean-field theory, a reentrant charge-order transition is shown to exist theoretically, in apparent agreement with recent experimental observations. Finally, a renormalization group analysis is applied to the study of competing orders in bilayer graphene. In addition to the previously suggested nematic and antiferromagnetic phases, unconventional superconductivity is shown to arise generically in the presence of a nonzero chemical potential, even for the case where the bare interactions are entirely repulsive. The implications of these results on the general understanding of competition between particle-hole and superconducting orders are discussed in detail.
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Keywords
quantum many-body physics, superconductivity, heavy fermions, bilayer graphene
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