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

Percolative nature of the dc paraconductivity in the cuprate superconductors