Unusual dynamic charge-density-wave correlations in HgBa${}_2$CuO${}_{4+\delta }$

Abstract

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 CDW correlations are still in their infancy. We report a high-resolution resonant inelastic X-ray scattering (RIXS) study of the underdoped cuprate superconductor HgBa${}_2$CuO${}_{4+\delta }$ ($T_c=70$ K). At $T=250$ K, above the CDW order temperature $T_{\mathrm{CDW}}\approx 200$ K, we observe significant dynamic CDW correlations at about 40 meV. This energy scale is comparable to both the superconducting gap and the previously reported low-energy pseudogap. At $T=T_c$, a strong elastic CDW peak appears, but the dynamic correlations around 40 meV remain virtually unchanged. In addition, we observe a new feature: dynamic correlations at significantly higher energy, with a characteristic scale of about 160 meV. A similar scale was previously identified in other experiments as a high-energy pseudogap. The existence of three distinct features in the charge response is highly unusual for a CDW system, and suggests that charge order in the cuprates is closely related to the pseudogap phenomenon and more complex than previously thought. We further observe the paramagnon dispersion along [1,0], across the two-dimensional CDW wavevector ${\mathbf{q}}_{\mathrm{CDW}}$, which is consistent with magnetic excitations measured by inelastic neutron scattering. Unlike for some other cuprates, our results point to the absence of a discernible coupling between CDW and magnetic excitations.