Strain-induced structural change and nearly-commensurate diffuse scattering in the model high-temperature superconductor HgBa${}_2$CuO${}_{4+\delta }$

We investigate the strain response of underdoped HgBa${}_2$CuO${}_{4+\delta }$ (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 ${\nu }_{ba}$=0.16 and ${\nu }_{ca}$=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 which 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 four 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.