Gauge fields and superconductivity in three-dimensional spacetime

• Main Author: Dorey, Nick
• Published: University of Edinburgh 1996
• Subjects: 537.623
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.649655

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 (QED<SUB>3</SUB>) 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-<I>N</I> 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 QED<SUB>3</SUB> 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-<I>T<SUB>c</SUB></I> superconductors La<SUB>2</SUB>CuO<SUB>4</SUB> and YBa<SUB>2</SUB>CuO<SUB>6</SUB>. 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 <I>hc/</I>2<I>e</I> and a two-dimensional Meissner effect. The possible relevance of this model to high-<I>T<SUB>c</SUB></I> superconductivity is discussed and avenues for future investigation are suggested.