Interplay between atomic fluctuations and charge density waves in La${}_{2-x}$Sr${}_x$CuO${}_4$

Abstract

In the cuprate superconductors, the spatial coherence of the charge density wave (CDW) state grows rapidly below a characteristic temperature $T_{\mathrm{CDW}}$, the nature of which is debated. We have combined a set of x-ray scattering techniques to study La${}_{1.88}$Sr${}_{0.12}$CuO${}_4$ ($T_{\mathrm{CDW}}$~$\approx$~80\,K) to shed light on this discussion. We observe the emergence of a crystal structure, which is consistent with the CDW modulation in symmetry, well above $T_{\mathrm{CDW}}$. This global structural change also induces strong fluctuations of local atomic disorder in the intermediate temperature region. At $T_{\mathrm{CDW}}$, the temperature dependence of this structure develops a kink, while the atomic disorder is minimized. We find that the atomic relaxation dynamics cross over from a cooperative to an incoherent response at $T_{\mathrm{CDW}}$. These results reveal a rich interplay between the CDWs and atomic fluctuations of distinct spatio-temporal scales. For example, the CDW coherence is enhanced on quasi-elastic timescales by incoherent atomic relaxation.