The intermodulation coefficient of an inhomogeneous superconductor

The high-Tc cuprate superconductors are now believed to be intrinsically inhomogeneous. We develop a theory to describe how this inhomogeneity affects the intermodulation coefficient of such a material. We show that the continuum equations describing intermodulation in a superconducting layer with spatially varying properties are formally equivalent to those describing an inhomogeneous dielectric with a nonzero cubic nonlinearity. Using this formal analogy, we calculate the effect of inhomogeneity on the intermodulation coefficient in a high-Tc material, using several assumptions about the topology of the layer and some simple analytical approximations to treat the nonlinearity. For some topologies, we find that the intermodulation critical supercurrent density JIMD is actually enhanced compared to a homogeneous medium, thereby possibly leading to more desirable material properties. We discuss this result in light of recent spatial mappings of the superconducting energy gap in BSCCO-2212. © 2006 American Institute of Physics. DOI: 10.1063/1.2372729