| We discuss various models for inhomogeneities and thermal fluctuations in two-dimensional (2D) superconductors. First, we present Monte Carlo simulations of a 2D site-diluted XY model, in which the XY spins are mobile, and also experience a repulsive interaction. Depending on the strength and range of the repulsion, the spin concentration, and the temperature, spins arrange themselves into a variety of patterns. We study the ways in which those patterns affect the superfluid density of the system. Second, we present a method to study the effects of inhomogeneity, temperature, and magnetic field on electronic properties of a model 2D superconductor. This method involves a combination of a microscopic d-wave Hamiltonian of the BCS type with Monte Carlo simulations of a Ginzburg-Landau free energy functional. We typically assume two types of superconducting regions: alpha, with a small gap and large superfluid density, and beta, with the opposite. In the zero-field, low-temperature case, we find that quenched disorder is crucial in obtaining low and broad peaks on the local density of states (LDOS) spectra on beta regions, similar to those observed in experiments. At finite temperatures, the sharp coherence peaks that exist in the LDOS of a regions below the phase ordering temperature Tc disappear above Tc, although a gap persists in a certain temperature range. At low temperatures, the spectral function exhibits a double peak as a function of energy at wave vector k ≃ (pi, 0) if the areal fraction of beta regions is around 0.5 and if the difference between the gap in the alpha and beta regions is large; a double peak similar to it has been reported in underdoped cuprates. Furthermore, peaks that are sharp at zero temperature become reduced in height, broadened, and shifted toward lower energies with increasing temperature. For systems in a magnetic field at low temperatures, we find that beta regions tend to pin vortices provided that the beta regions have a much lower superfluid density than the a regions. Also we find that the LDOS far from vortex cores shows sharp coherence peaks, while near the cores it shows a large gap, as well as low and broad peaks at energies above the superconducting gap, consistent with experiment. |
