Lattice dynamics and elastic properties of black phosphorus

TL;DR

This study combines experimental techniques and ab initio calculations to analyze the lattice dynamics and elastic properties of black phosphorus, providing valuable data for future nanomaterial applications.

Contribution

It offers the first comprehensive experimental and theoretical analysis of black phosphorus's lattice dynamics and elastic tensor, serving as a benchmark for related quantum materials.

Findings

Determined phonon dispersions at terahertz frequencies.

Derived the full elastic tensor of black phosphorus.

Provided elastic moduli relevant for nanophotonics and quantum sensing.

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.