Competing orders in s-wave and p-wave superconductors
Li, Qi, 1976-
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Li, Qi, 1976-
This dissertation investigates the interplay between, and the possible coexistence of, magnetic and superconducting order in metals. We start with studying the electromagnetic properties of s-wave superconductors near a ferromagnetic instability. By using a generalized Ginzburg-Landau theory and scaling arguments, we show that competition between magnetic order and superconducting order can change the scaling of observables. For instance, the exponent for the temperature dependence of the critical current can deviate from the Ginzburg-Landau value of 3/2. These results may be relevant to understanding the observed behavior of MgCNi 3 . We then study the nature of the superconductor-to-normal-metal transition in p-wave superconductors. Although the phase transition is continuous at a mean- field level, a more careful renormalization-group analysis in conjunction with large-n expansion techniques strongly suggest that the transition is first order. This conclusion is the same as for s-wave superconductors, where these techniques also predict a first-order transition. In p-wave superconductors, topological excitations known as skyrmions are known to exist in addition to the more common vortices. In the third part of this dissertation, we study the properties of skyrmion lattices in an external magnetic field. We propose iv experiments to distinguish vortex lattices from skyrmion lattices by means of their melting curves and their μSR signatures.