Observation of Correlations Up To the Micrometer Scale in Sliding Charge-Density Waves

A high resolution coherent x-ray diffraction experiment has been performed on the charge-density wave (CDW) system ${\mathrm{K}}_{0.3}{\mathrm{MoO}}_3$. The $2k_F$ satellite reflection associated with the CDW has been measured with respect to external dc currents. In the sliding regime, the $2k_F$ satellite reflection displays secondary satellites along the chain axis which corresponds to correlations up to the micrometer scale. This super long-range order is 1500 times larger than the CDW period itself. This new type of electronic correlation seems inherent to the collective dynamics of electrons in charge-density wave systems. Several scenarios are discussed.

Figure 1

3D diffraction patterns of (a) the $Q_s=(6,\overline{0.252},\overline{3.5})$ satellite and (b) the $(6,0,\overline{3})$ fundamental Bragg reflection for two current values at $T=75\mathrm{K}$. Each isosurface has been fixed at $I_{\max }/18$ for the $(6,0,\overline{3})$ and $I_{\max }/7$ for $Q_s$. For clarity, the reflections with and without current have been shifted along ${\mathbf{b}}^{*}$. The total size of the boxes is $40\times (\delta \theta ={10}^{-3}\mathrm{degree})$ (vertical axis) by $50\times 60$ pixels (horizontal plane). Each 3D acquisition lasted less than 15 mn. 2D patterns corresponding to integration of the Fig. 1a over the $\theta$ axis, without (c) and with current (d). The secondary satellites are indicated by arrows.

Figure 2

2D diffraction patterns ($30\times 40$ pixels) of the $2k_F$ reflection in the ($2{\mathbf{a}}^{*}\mathrm{\text{−}}{\mathbf{c}}^{*};{\mathbf{b}}^{*}$) plane for $I=0\mathrm{mA}$ (a), $I=12$ $I_s$ (b), and $I=16$ $I_s$ (c). The secondary satellites are indicated by arrows. Corresponding profiles along $2{\mathbf{a}}^{*}\mathrm{\text{−}}{\mathbf{c}}^{*}$ in (d) and ${\mathbf{b}}^{*}$ in (e). The profiles have been rescaled.