DC Transport in Pseudogapped Superconductors: The Role of the Fermi Arcs

We examine the dc conductivity $\sigma$ in a d-wave pseudogapped high $T_c$ superconductor for a range of different hole doping concentrations and temperatures $T$. Our approach is based on treating the cuprates as mid-way between BCS and Bose Einstein condensation and our correlation functions are demonstrably consistent with gauge invariance and the transverse f-sum rule. Studies of the $\omega \rightarrow 0$ dc conductivity below $T_c$ lead to a peak structure (observed experimentally) while above $T_c$ we show that pseudogap effects manifest themselves in the resistivity primarily through a depression in the effective carrier number with decreasing $T$. We discuss related implications for resistivity vs $T > T_c$ experiments and demonstrate that the trends with hole doping are compatible with the data, while the role of the Fermi arcs appears overall to be secondary.