Strain-induced structural change and nearly-commensurate diffuse scattering in the model high-temperature superconductor HgBa$_{2}$ CuO$_{4+δ}$

We investigate the strain response of underdoped HgBa$_2$⁢CuO$_{4+𝛿}$ (Hg1201), by synchrotron X-ray diffraction and corresponding simulations of thermal diffuse scattering. The compression in the crystallographic 𝑎 direction leads to relatively small expansion in the 𝑏 and 𝑐 directions, with Poisson ratios 𝜈$_{ba}$=0.16 and 𝜈$_{ca}$=0.11, respectively. However, the Cu-O distance in the 𝑐 direction exhibits a notable 0.9% increase at 1.1% 𝑎-axis compression. We further find strain-induced diffuse scattering that corresponds to a new type of two-dimensional charge correlation. Interestingly, this signal is insensitive to the onset of superconductivity and instead corresponds to a short-range, nearly commensurate modulation with a wave vector close to (0.5,0,0) and a correlation length of approximately 4 unit cells. It closely resembles the charge order theoretically predicted in the phase diagram of the spin-liquid model with resonating valence bonds on a square lattice.