Phonon Engineering of the Specific Heat of Twisted Bilayer Graphene: The Role of the Out-of-Plane Phonon Modes

TL;DR

This study theoretically analyzes how out-of-plane phonon modes influence the specific heat of twisted bilayer graphene, revealing deviations from traditional models and highlighting the role of phonon dispersion in thermodynamic properties.

Contribution

It provides a detailed phonon dispersion analysis and demonstrates the significant impact of out-of-plane phonons on the specific heat of twisted bilayer graphene, challenging conventional assumptions.

Findings

ZA phonons deviate from parabolic dispersion starting at ~100 1/cm

ZA phonons dominate specific heat below 200 K

Optical and acoustic phonons contribute equally above 1000 K

Abstract

We investigated theoretically the specific heat of graphene, bilayer graphene and twisted bilayer graphene taking into account the exact phonon dispersion and density of states for each polarization branch. It is shown that contrary to a conventional believe the dispersion of the out-of-plane acoustic phonons - referred to as ZA phonons - deviates strongly from a parabolic law starting from the frequencies as low as ~100 1/cm. This leads to the frequency-dependent ZA phonon density of states and the breakdown of the linear dependence of the specific heat on temperature T. We established that ZA phonons determine the specific heat for T<200 K while contributions from both in-plane and out-of-plane acoustic phonons are dominant for 200 K < T < 500 K. In the high-temperature limit, T>1000 K, the optical and acoustic phonons contribute approximately equally to the specific heat. The Debye temperature for graphene and twisted bilayer graphene was calculated to be around ~1861 - 1864 K. Our results suggest that the thermodynamic properties of materials such as bilayer graphene can be controlled at the atomic scale by rotation of the sp2-carbon planes.