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Title: Gauge fields and superconductivity in three-dimensional spacetime
Author: Dorey, Nick
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 1996
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The analogy between the BCS theory of superconductivity and chiral symmetry breaking in QCD is reviewed and the Nambu-Jona-Lasinio model is introduced as a paradigm for both these phenomena. In Part I, the properties of quantum electrodynamics in (2+1)-dimensional spacetime (QED3) are investigated in detail. After describing the symmetry structure of the theory, the finite-temperature photon propagator is calculated at leading order in the large-N expansion and the effective attraction between static test charges is derived. The bound-state spectrum of the theory is discussed and the dynamical generation of a fermion mass is investigated analytically. The analysis of QED3 concludes with an approximate treatment of the symmetry restoration transition, including a numerical solution of the finite-temperature gap equation. Part II begins with a brief review of the phenomenology of the quasi-planar high-Tc superconductors La2CuO4 and YBa2CuO6. The two-dimensional Heisenberg antiferromagnet is introduced as a microscopic description of these materials and the nonlinear σ-model is derived as a long-wavelength limited in the undoped case. Following Shankar, the dynamics of holes in the antiferromagnet is modelled by coupling two species of Grassmann fields to the σ-model action. The long-wavelength limit of this system is found to be a 'pseudo-relativistic' quantum field theory of Dirac fermions interacting with an abelian gauge field. The results of Part I are applied to demonstrate the dynamical generation of a fermion mass, which corresponds to the opening of a superconducting gap in the 'quasi-hole' spectrum. The long-wavelength theory exhibits type-II superconductivity without parity or time-reversal symmetry violation, flux quantization with quantum hc/2e and a two-dimensional Meissner effect. The possible relevance of this model to high-Tc superconductivity is discussed and avenues for future investigation are suggested.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available