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

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.

Journal of Physics: Condensed Matter, topical review, published

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• Collective Excitations in 2D Materials
• Heisenberg's uncertainty principle in the PTOLEMY project: a theory update
• Topological continuum charges of acoustic phonons in 2D
• Bending mode and thermal expansion of graphene
• Phonon anharmonicity and thermal conductivity of two-dimensional van der Waals materials: A review
• Phonons in MoSe2/WSe2 van der Waals heterobilayer
• ${\sigma }_h$ symmetry and electron-phonon interaction in two-dimensional crystalline systems
• Vibrations and tunneling of strained nanoribbons at finite temperature
• Temperature effects in topological insulators of transition metal dichalcogenide monolayers
• Multifractal wave functions of charge carriers in graphene with folded deformations, ripples or uniaxial flexural modes: analogies to the quantum Hall effect under random pseudomagnetic fields
• Apparent rippling with honeycomb symmetry and tunable periodicity observed by scanning tunneling microscopy on suspended graphene
• Perturbative renormalization and thermodynamics of quantum crystalline membranes
• Study of Thermal Expansion Coefficients of 2D Materials via Raman Micro-spectroscopy: Revisited