New ground states in unconventional superconductors

The properties of unconventional superconductors have recently been the subject of much theoretical inquiry, since both the high-T$\sb{c}$ and heavy fermion superconductors may have unconventional order parameters. The term unconventional refers to order parameters having a lower degree of symmetry than the normal state lattice. Such systems may therefore break rotational, time reversal and translational symmetry, leading to a variety of novel effects. This thesis is devoted to the detailed analysis of one such effect. In particular, we show how an unconventional superconductor, in zero applied field, can be subject to a magnetic instability, yielding a new ground state which breaks both translational and time reversal symmetry. From our analytic calculations we will make predictions about the form of the new ground state, and the qualitative features of the H $-$ T phase diagram. We continue our consideration of this system by performing global minimizations of the Ginzburg-Landau functional via the method of simulated annealing. This technique allows us to study the detailed form of the order parameter and magnetic field both with and without an applied field. We will present the results of these minimizations, and discuss to what degree they support our analytic work. Finally, we will present the results of microscopic calculations of the Ginzburg-Landau parameters using the weak coupling quasiclassical theory, including the effects of impurity scattering. The results of these calculations will be discussed in conjunction with the physical feasibility of our instability conditions