Observation of van der Waals phonons in the single-layer cuprate (Bi,Pb)2(Sr,La)2CuO6+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-𝑇𝑐 cuprate (Bi,Pb)2(Sr,La)2⁢CuO6+𝛿 (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.