Inhomogeneous superconductors with an order parameter of dx²-y² (d-wave) symmetry are investigated within the Ginzburg-Landau (GL) and Bogoliubov-de Gennes (BdG) formalisms. The inhomogeneities considered in detail are external magnetic fields, twin boundaries, and external currents. The Ginzburg-Landau equations are derived within the context of two microscopic lattice models used to describe the high-temperature superconductors: an extended Hubbard model and the Antiferromagnetic-van Hove model. Analytical results are obtained for the extended Hubbard model at low electron densities and weak to intermediate coupling. The variation of the coefficients in the GL equations with carrier density, temperature, and coupling constants are calculated numerically for both models. The anisotropic higher-order terms in the GL free energy are considered, with emphasis on the consequences for the structures of isolated vortices and the vortex lattice in the mixed-state. Twin boundaries are investigated numerically using the BdG formalism within the context of the extended Hubbard model. The twin boundaries are represented by tetragonal regions of variable width, with a reduced chemical potential. For sufficiently large twin boundary width and change in chemical potential, an induced s-wave component may break time-reversal symmetry at a low temperature T*.$ The temperature T*, and the magnitude of the imaginary component, are found to depend strongly on electron density. The results are compared with recent tunneling and transport measurements. The behaviour of d-wave superconductors in the presence of external currents is investigated numerically for both clean systems and those containing twin boundaries. The current response is studied with emphasis on critical currents and the superfluid density. The effect of the external currents on the subdominant s-wave components is characterized. Comparison is made with recent transport and tunneling measurements.

Doctor of Philosophy (PhD)