Inhomogeneity of charge-density-wave order and quenched disorder in a high-Tc superconductor

It has recently been established that the high-transition-temperature (high-Tc) superconducting state coexists with short-range charge-density-wave order1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and quenched disorder12, 13 arising from dopants and strain14, 15, 16, 17. This complex, multiscale phase separation18, 19, 20, 21 invites the development of theories of high-temperature superconductivity that include complexity22, 23, 24, 25. The nature of the spatial interplay between charge and dopant order that provides a basis for nanoscale phase separation remains a key open question, because experiments have yet to probe the unknown spatial distribution at both the nanoscale and mesoscale (between atomic and macroscopic scale). Here we report micro X-ray diffraction imaging of the spatial distribution of both short-range charge-density-wave 'puddles' (domains with only a few wavelengths) and quenched disorder in HgBa2CuO4 + y, the single-layer cuprate with the highest Tc, 95 kelvin (refs 26, 27, 28). We found that the charge-density-wave puddles, like the steam bubbles in boiling water, have a fat-tailed size distribution that is typical of self-organization near a critical point19. However, the quenched disorder, which arises from oxygen interstitials, has a distribution that is contrary to the usually assumed random, uncorrelated distribution12, 13. The interstitial-oxygen-rich domains are spatially anticorrelated with the charge-density-wave domains, because higher doping does not favour the stripy charge-density-wave puddles, leading to a complex emergent geometry of the spatial landscape for superconductivity.