Thermal properties of graphene from path-integral simulations

TL;DR

This study uses path-integral molecular dynamics to analyze the thermal properties of graphene, accounting for quantum vibrational effects and anharmonicity across a wide temperature range, revealing temperature-dependent expansion behaviors.

Contribution

It introduces PIMD simulations to accurately model graphene's thermal properties, including quantum effects and anharmonicity, and compares results with harmonic approximations.

Findings

Harmonic approximation is accurate up to ~400 K.

Thermal expansion coefficient of real area remains positive at all temperatures.

In-plane area expansion coefficient becomes positive above ~1000 K.

Abstract

Thermal properties of graphene monolayers are studied by path-integral molecular dynamics (PIMD) simulations, which take into account the quantization of vibrational modes in the crystalline membrane, and allow one to consider anharmonic effects in these properties. This system was studied at temperatures in the range from 12 to 2000~K and zero external stress, by describing the interatomic interactions through the LCBOPII effective potential. We analyze the internal energy and specific heat and compare the results derived from the simulations with those yielded by a harmonic approximation for the vibrational modes. This approximation turns out to be rather precise up to temperatures of about 400~K. At higher temperatures, we observe an influence of the elastic energy, due to the thermal expansion of the graphene sheet. Zero-point and thermal effects on the in-plane and "real" surface of graphene are discussed. The thermal expansion coefficient $\alpha$ of the real area is found to be positive at all temperatures, in contrast to the expansion coefficient $\alpha_p$ of the in-plane area, which is negative at low temperatures, and becomes positive for $T \gtrsim$ 1000~K.