From non-metal to strange metal at the stripe-percolation transition in La$_{2-x}$Sr$_x$CuO$_4$

The nature of the normal state of cuprate superconductors continues to stimulate considerable speculation. Of particular interest has been the linear temperature dependence of the in-plane resistivity in the low-temperature limit, which violates the prediction for a Fermi liquid. We present measurements of anisotropic resistivity in La$_{2-x}$Sr$_x$CuO$_4$ that confirm the strange-metal behavior for crystals with doped-hole concentration $p=x > p^\ast \sim 0.19$ and contrast with the non-metallic behavior for $p<p^\ast$. We propose that the changes at $p^\ast$ are associated with a first-order transition from doped Mott insulator to conventional metal; the transition appears as a crossover due to intrinsic dopant disorder. We consider results from the literature that support this picture; in particular, we present a simulation of the impact of the disorder on the first-order transition and the doping dependence of stripe correlations. Below $p^\ast$, the strong electronic interactions result in charge and spin stripe correlations that percolate across the CuO$_2$ planes; above $p^\ast$, residual stripe correlations are restricted to isolated puddles. We suggest that the $T$-linear resistivity results from scattering of quasiparticles from antiferromagnetic spin fluctuations within the correlated puddles. This is a modest effect compared to the case at $p<p^\ast$, where there data suggest that there are no coherent quasiparticles in the normal state.