Absence of inflation symmetric commensurate states in inflation symmetric networks

Abstract

In this paper we present measurements of the normal-to superconducting phase boundary T c (H) for three different networks possessing inflation symmetry. Fluxoid quantization constraints induce the formation of a lattice of fluxoid quanta for any non-zero perpendicular magnetic field, and at particular fields, T c (H) exhibits cusp-like structure indicating that the lattice is commensurate with the underlying network geometry. For inflation symmetric netrvorks studied in the past, all commensurate states have always been related to the inflation symmetry. In the three networks studied here, none of the commensurate phase boundary structure derives from the inflation symmetry. We propose that this structure can instead be understood by considering the Fourier transform of the network geometry and that the transform actually provides a more universal prescription for the identification of commensurate states. The relevance of the transform (as opposed to the inflation symmetry) in determining commensurate states in two dimensions is consistent with analytical work performed for one dimensional systems