Modeling mesoscopic unconventional superconductors

High-temperature superconducting materials are often experimentally realized as thin films that can be patterned into devices operating in the mesoscopic regime. On this length scale, various finite-size and surface effects heavily influence the nature of the superconducting state, and can induce new ground states with spontaneously broken symmetries. Motivated by the wide technological application of such mesoscopic devices and the many open questions regarding the new emergent ground states, this thesis sets out to study mesoscopic grains. In particular, a recently discovered phase which spontaneously breaks translational and time-reversal symmetries will be studied, referred here to as the "loop-current phase". The aim is to study how this phase responds to magnetic and geometric perturbations. The quasiclassical theory of superconductivity is used to simulate mesoscopic thin-film grains in equilibrium, with a strong emphasis on d-wave superconductors, e.g. the cuprates. The properties of the loop-current phase are cataloged, with an explanation of how and why it occurs. Various phase diagrams are produced, and the magnetic-field dependent thermodynamics is studied. In conclusion, the loop-current phase occurs at pairbreaking interfaces that host quasiparticle midgap states. The phase is associated with a spontaneous superfluid momentum which drives circulating current loops that break continuous translational symmetry, providing an energetically favorable Doppler shift of the midgap states. The phase is found to be robust against external fields in the whole Meissner state, but not against very high fields in the mixed state. The phase is lost when there is a competing effect which significantly broadens the spectrum, e.g. a strong external vector potential. The phase transition is associated with a large jump in the heat capacity, serving as a hallmark for the phase to be observed experimentally. It is predicted that the phase leads to a broadening of the spectrum which is consistent with experimental findings.