Observation of van der Waals phonons in the single-layer cuprate ( Bi , Pb ) 2 ( Sr , La ) 2 CuO 6 + δ
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,Pb) 2 (Sr,La) 2 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. Here, 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.