Evidence for unusual superconducting correlations coexisting with stripe order in La_1.875Ba_0.125CuO₄

We present new x-ray and neutron-scattering measurements of stripe order in La_1.875Ba_0.125CuO₄, along with low-field susceptibility, thermal conductivity, and specific-heat data. We compare these with previously reported results for resistivity and thermopower. Temperature-dependent features indicating transitions (or crossovers) are correlated among the various experimental quantities. Taking into account recent spectroscopic studies, we argue that the most likely interpretation of the complete collection of results is that an unusual form of two-dimensional superconducting correlations appears together with the onset of spin-stripe order. Recent theoretical proposals for a sinusoidally modulated superconducting state compatible with stripe order provide an intriguing explanation of our results and motivate further experimental tests. We also discuss evidence for one-dimensional pairing correlations that appear together with the charge order. With regard to the overall phenomenology, we consider the degree to which similar behavior may have been observed in other cuprates and describe possible connections to various puzzling phenomena in cuprate superconductors.