Interlayer van der Waals (vdW) coupling is generic in two-dimensional materials such as graphene and transition-metal dichalcogenides, which can induce very low-energy phonon modes. Using high-resolution inelastic hard x-ray scattering, we uncover the ultralow energy phonon mode along the Cu-O bond direction in the high-$T_c$ cuprate (Bi,${\mathrm{Pb})}_2$(Sr,${\mathrm{La})}_2{\mathrm{CuO}}_{6+\delta }$ (Bi2201). The energy and full-width half-maximum (FWHM) of these modes are independent of temperature, while their intensity decreases with doping in accordance with an increasing $c$-axis lattice parameter. We compare the experimental results to first-principles density functional theory simulations and identify the observed mode as a van der Waals phonon, which arises from the shear motion of the adjacent Bi-O layers. This shows that Bi-based cuprate has vibrational properties similar to graphene and transition-metal dichalcogenides, which can be exploited to engineer novel heterostructures.

中文翻译：

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单层铜酸盐(Bi,Pb)2(Sr,La)2CuO6+δ中范德华声子的观测

层间范德华 (vdW) 耦合在石墨烯和过渡金属二硫属化物等二维材料中很常见，它可以诱导非常低能量的声子模式。利用高分辨率非弹性硬 X 射线散射，我们揭示了高能谱中沿 Cu-O 键方向的超低能声子模式。${\mathrm{时间}}_C$铜酸盐（Bi，${铅）}_2$（先生，${拉）}_2{\mathrm{氧化铜}}_{6+\delta }$（Bi2201）。这些模式的能量和半峰全宽 (FWHM) 与温度无关，而它们的强度随着掺杂的增加而降低。$C$-轴晶格参数。我们将实验结果与第一性原理密度泛函理论模拟进行比较，并将观察到的模式识别为范德华声子，它是由相邻 Bi-O 层的剪切运动产生的。这表明铋基铜酸盐具有与石墨烯和过渡金属二硫属化物类似的振动特性，可用于设计新型异质结构。