Using inhomogeneity to raise the superconducting critical temperature in a two-dimensional XY model

Superconductors with low superfluid density are often dominated by phase fluctuations of the order parameter. In this regime, their physics may be described by XY models. The transition temperature T_c of such models is of the same order as the zero-temperature phase stiffness (helicity modulus), a long-wavelength property of the system: T_c=AΥ(0). However, the constant A is a nonuniversal number, depending on dimensionality and the degree of inhomogeneity. In this Brief Report, we discuss strategies for maximizing A for two-dimensional XY models; that is, how to maximize the transition temperature with respect to the zero-temperature, long-wavelength properties. We find that a framework type of inhomogeneity can increase the transition temperature significantly. For comparison, we present similar results for Ising models.