Superconductivity with Unconventional Pair Symmetry in a 2D System with Inherent Gap

We study superconductivity in a 2D system with ``inherent'' gap; semiconducting gap is chosen as a prototypical case. We consider s and d wave pair symmetries, and carry out a mean-field study of the evolution of the order parameter and critical temperature, $T_c$, with varying interaction strength, doping and the inherent gap magnitude. The model 2D system exhibits a rich variety of transition and crossover behavior, including a ``pseudogap-like'' feature. To better understand pair-breaking, we also study phase fluctuations, and compare our calculated Kosterlitz-Thouless temperature, $T_c^{KT}$ with our mean-field $T_c$.