Resistive Transition of High- $T_{c}$ Superconducting Films With Regular Arrays of $T_{c}$ -Domains Induced by Micro- or Nanofunctionalization

We present numerical simulations of the width and shape of the resistance versus temperature transition, i.e., R(T), under zero external magnetic field, in a high-temperature superconducting film with a regular pattern of local variations of critical temperatures, induced, e.g., by means of micro- or nanofunctionalization. To obtain a realistic R(T), we also take into consideration the widening of the transition due to Gaussian and vortex-antivortex fluctuations, plus the effects of the intrinsic inhomogeneity due to the nonstoichiomety of the dopant ions. We focus mainly on square-lattice patterns and show that they may be used to engineer R(T) transitions broader or narrower than the ones of the parent nonstructured film.