Pervasive symmetry-lowering nanoscale structural fluctuations in the cuprate La$_{2-x}$Sr$_{x}$CuO$_{4}$

The cuprate superconductors are among the most widely studied quantum materials, yet there remain fundamental open questions regarding their electronic properties and the role of the structural degrees of freedom. Recent neutron and x-ray scattering measurements uncovered exponential scaling with temperature of the strength of orthorhombic fluctuations in the tetragonal phase of $La_{2-x}Sr_xCuO_4$ and $Tl_2Ba_2CuO_{6+y}$, unusual behavior that closely resembles prior results for the emergence of superconducting fluctuations, and that points to a common origin rooted in inherent correlated structural inhomogeneity. Here we extend the measurements of $La_{2-x}Sr_xCuO_4$ to higher temperatures in the parent compound (x=0) and to optimal doping (x=0.155), and we furthermore investigate the effects of in-situ in-plane uniaxial stress. Our neutron scattering result for undoped $La_2CuO_4$ complement prior x-ray data and reveal that the structural fluctuations persist to the maximum experimental temperature of nearly 1000K, i.e., to a significant fraction of the melting point. At this temperature, the spatial correlation length extracted from the momentum-space data is still about three lattice constants. The neutron scattering experiment enables quasistatic discrimination and reveals that the response is increasingly dynamic at higher temperatures. We also find that uniaxial stress up to 500 MPa along the tetragonal [110] direction, which corresponds to a strain of about 0.2%, does not significantly alter this robust behavior. Overall, these results support the notion that subtle, underlying inhomogeneity underpins the cuprate phase diagram. Finally, we uncover (for x=0.2) low-energy structural fluctuations at a nominally forbidden reflection. While the origin of these fluctuations is not clear, they might be related to the presence of extended defects such as dislocations or stacking faults.