A Review on Flexural Mode of Graphene: Lattice Dynamics, Thermal Conduction, Thermal Expansion, Elasticity, and Nanomechanical Resonance

TL;DR

This review explores the critical role of the flexural mode in graphene's thermal and mechanical properties, including thermal conductivity, expansion, elasticity, and nanomechanical resonance, highlighting recent advances and insights.

Contribution

It provides a comprehensive survey of the flexural mode's influence on various physical properties of graphene, integrating lattice dynamics with experimental and theoretical findings.

Findings

Flexural mode significantly contributes to graphene's thermal conductivity.

Negative thermal expansion in graphene is linked to flexural mode vibrations.

Flexural mode impacts the performance of graphene nanomechanical resonators.

Abstract

Single-layer graphene is so flexible that its flexural mode (also called the ZA mode, bending mode, or out-of-plane transverse acoustic mode) is important for its thermal and mechanical properties. Accordingly, this review focuses on exploring the relationship between the flexural mode and thermal and mechanical properties of graphene. We first survey the lattice dynamic properties of the flexural mode, where the rigid translational and rotational invariances play a crucial role. After that, we outline contributions from the flexural mode in four different physical properties or phenomena of graphene -- its thermal conductivity, thermal expansion, Young's modulus, and nanomechanical resonance. We explain how graphene's superior thermal conductivity is mainly due to its three acoustic phonon modes at room temperature, including the flexural mode. Its coefficient of thermal expansion is negative in a wide temperature range resulting from the particular vibration morphology of the flexural mode. We then describe how the Young's modulus of graphene can be extracted from its thermal fluctuations, which are dominated by the flexural mode. Finally, we discuss the effects of the flexural mode on graphene nanomechanical resonators, while also discussing how the essential properties of the resonators, including mass sensitivity and quality factor, can be enhanced.