Title: Emergence of superconductivity in the cuprates via a universal percolation process,
Abstract: A pivotal step toward understanding unconventional superconductors would be
to decipher how superconductivity emerges from the unusual normal state upon
cooling. In the cuprates, traces of superconducting pairing appear above the
macroscopic transition temperature $T_c$, yet extensive investigation has led
to disparate conclusions. The main difficulty has been the separation of
superconducting contributions from complex normal state behaviour. Here we
avoid this problem by measuring the nonlinear conductivity, an observable that
is zero in the normal state. We uncover for several representative cuprates
that the nonlinear conductivity vanishes exponentially above $T_c$, both with
temperature and magnetic field, and exhibits temperature-scaling characterized
by a nearly universal scale $T_0$. Attempts to model the response with the
frequently evoked Ginzburg-Landau theory are unsuccessful. Instead, our
findings are captured by a simple percolation model that can also explain other
properties of the cuprates. We thus resolve a long-standing conundrum by
showing that the emergence of superconductivity in the cuprates is dominated by
their inherent inhomogeneity.