Using inhomogeneity to raise the superconducting critical temperature in a two-dimensionalXYmodel

Abstract

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: ${T}_{c}=A\ensuremath{\Upsilon}(0)$. 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.