Thermal expansion behavior of two-dimensional (2D) nitrides and graphene were studied by ab initio molecular dynamics (MD) simulations as well as quasiharmonic approximation (QHA). Anharmonicity of the acoustic phonon modes are related to the unusual negative thermal expansion (NTE) behavior of the nitrides. Our results also hint that direct ab initio MD simulations are a more elaborate method to investigate thermal expansion behavior of 2D materials than the QHA. Nevertheless, giant NTE coefficients are found for $h$-GaN and $h$-AlN within the covered temperature range 100–600 K regardless of the chosen computational method. This unusual NTE of 2D nitrides is reasoned with the out-of-plane oscillations related to the rippling behavior of the monolayers.

• Received 24 July 2020
• Accepted 27 January 2021

DOI:https://doi.org/10.1103/PhysRevB.103.085430