The charge-density-wave (CDW) instability in the underdoped, pseudogap part of the cuprate phase diagram has been a major recent research focus, yet measurements of dynamic, energy-resolved charge correlations are still in their infancy. Such information is crucial in order to help discern the connection between CDW and pseudogap phenomena, and to understand the extent to which charge correlations in general shape the phase diagram}. We report a resonant inelastic X-ray scattering study of the underdoped cuprate superconductor HgBa${}_2$CuO${}_{4+\delta }$ ($T_c=70$ K). At 250 K, above the previously established temperature $T_{C}DW\approx 200$ K that signifies the onset of quasistatic short-range CDW order}, we observe significant dynamic correlations that are {broadly peaked} at about 40 meV and centered at the two-dimensional wavevector ${𝐪}_{C}DW$.} This energy scale is comparable to both the superconducting gap and the low-energy pseudogap. At 70 K, we observe a quasistatic CDW peak at ${𝐪}_{C}DW$}, but the dynamic correlations around 40 meV remain virtually unchanged, and we identify a new featuredynamic correlations well above the optic phonon range that are broadly peaked in the 150-200 meV range}. A similar energy} scale was previously identified in other experiments as a high-energy pseudogap. The observation} of three distinct features in the charge response is highly unusual for a CDW system and suggests that charge order in the cuprates is complex. We demonstrate that other single-layer cuprates exhibit approximately the same relative strength of high- to low-temperature energy-integrated} charge signal, which} points to the universal existence of significant dynamic correlations. } Intriguingly, the two energy scales identified here are also comparable to those of the superconducting glue function extracted from other spectroscopic techniques, consistent with a dual charge and magnetic nature of the pairing glue.} We further determine} the paramagnon dispersion along [1,0], across ${𝐪}_{C}DW$, and find it to be} consistent with magnetic excitations measured by inelastic neutron scattering. Unlike for some other cuprates, our result points to the absence of a discernible coupling between charge and magnetic excitations.

中文翻译：

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简单四边形HgBa2CuO4 +δ中异常的动态电荷相关性

铜酸盐相图中欠掺杂伪间隙部分的电荷密度波（CDW）不稳定性一直是最近的主要研究重点，但动态，能量分辨电荷相关性的测量仍处于起步阶段。为了帮助辨别CDW和伪间隙现象之间的联系，并了解电荷相关性在多大程度上影响相位图，这些信息至关重要。我们报告了掺杂不足的铜酸盐超导体HgBa的共振非弹性X射线散射研究${}_2$氧化铜${}_{4+\delta }$ （${Ť}_C=70$K）。在250 K，高于先前确定的温度${Ť}_{C}d\mathrm{w\; ^}\approx 200$ K表示准静态短程CDW阶的发生}，我们观察到了显着的动态相关性，这些动态相关性在40 meV处{广泛地达到峰值}，并以二维波矢为中心 ${𝐪}_{C}d\mathrm{w\; ^}$。}该能级可与超导间隙和低能伪间隙相媲美。在70 K时，我们观察到一个准静态CDW峰${𝐪}_{C}d\mathrm{w\; ^}$}，但40 meV附近的动态相关性实际上保持不变，并且我们确定了一个新的特征动态相关性，该相关性远高于光学声子范围，该声子范围在150-200 meV范围内普遍达到峰值。之前在其他实验中已将相似的能级定为高能假间隙。电荷响应中三个不同特征的观察对于CDW系统是非常不寻常的，并且表明铜价中的电荷顺序很复杂。我们证明了其他单层铜酸盐表现出大约相同的高温到低温能量集成的电荷信号的相对强度，这表明普遍存在显着的动态相关性。有趣的是，${𝐪}_{C}d\mathrm{w\; ^}$，并且发现它与通过非弹性中子散射测量的磁激发一致。与其他某些铜酸盐不同，我们的结果表明电荷和磁激励之间没有可辨别的耦合。