Low bending rigidity and large Young's modulus drive strong flexural phonon renormalization in two-dimensional monolayers

TL;DR

This study uses first-principles calculations to show how bending rigidity influences the anharmonic renormalization of flexural phonons in 2D monolayers, affecting their stability and vibrational properties.

Contribution

It provides a detailed first-principles analysis of how bending rigidity controls ZA phonon renormalization and stability in 2D materials, highlighting the importance of anharmonic effects.

Findings

Bending rigidity ($7$) controls ZA phonon renormalization across the Brillouin zone.

Low-$7$ materials like germanene exhibit stronger phonon renormalization.

ZA phonons at long wavelengths are stabilized by a balance of bending rigidity and Young's modulus.

Abstract

Many intriguing phenomena such as the wave-like hydrodynamic heat flow, the logarithmic divergence of electrical resistivity at low temperatures and microscale kirigami are driven by flexural acoustic (ZA) phonons in two-dimensional (2D) materials. Yet, a definitive first-principles description of their dispersion, with explicit consideration of the crystal anharmonicity and the stability of large 2D monolayers against thermal fluctuations, is lacking in the literature. Using first-principles calculations, we show that the bending rigidity ($\kappa$) controls the anharmonic renormalization of the ZA phonons throughout the Brillouin zone in 2D monolayers, with stronger renormalization in low-$\kappa$ materials like germanene and weaker effects in high-$\kappa$ materials like molybdenum disulphide. Furthermore, the ZA phonons at long wavelengths undergo an additional renormalization to stabilize the flat phase of the 2D monolayers against thermal fluctuations, which is modulated by the competing influence of the bending rigidity and the in-plane Young's modulus in all materials. The resulting renormalized ZA phonon dispersions are qualitatively and quantitatively different from those commonly used by the first-principles community, thus motivating a re-examination of the ZA phonon-driven unconventional thermal and electronic phenomena in 2D as well as lower-dimensional systems. Our work provides new insights into the role of nanoscale crystal anharmonicity and macroscale elasticity in shaping the vibrational properties of 2D materials and will inform novel engineering applications that are exclusive to low dimensions such as kirigami, with materials beyond graphene.