Lattice dynamics and elastic properties of black phosphorus

Abstract

We experimentally determine the lattice dynamics of black phosphorus layered crystals through a combination of x-ray diffuse scattering and inelastic x-ray scattering, and we rationalize our experimental findings using $\textit{ab initio}$ calculations. From the phonon dispersions at terahertz frequencies, we derive the full single-crystal elastic tensor and relate it to the macroscopic elastic response of black phosphorus, described by the elastic moduli. The elastic stiffness coefficients obtained here provide an important benchmark for models of black phosphorus and related materials, such as phosphorene and black phosphorus nanotubes, recently emerged quantum materials, disclosing a huge potential for nanophotonics, optoelectronics, and quantum sensing.