Percolative nature of the dc paraconductivity in the cuprate superconductors

We present an investigation of the planar direct-current (dc) paraconductivity of the model cuprate material HgBa${}_2$CuO${}_{4+\delta }$ in the underdoped part of the phase diagram. The simple quadratic temperature-dependence of the Fermi-liquid normal-state resistivity enables us to extract the paraconductivity above the macroscopic $T_c$ with great accuracy. The paraconductivity exhibits unusual exponential temperature dependence, with a characteristic temperature scale that is distinct from $T_c$. In the entire temperature range where it is discernable, the paraconductivity is quantitatively explained by a simple superconducting percolation model, which implies that underlying gap disorder dominates the emergence of superconductivity.