Soliton signature in the phonon spectrum of twisted bilayer graphene

TL;DR

This study investigates how twisting bilayer graphene affects its phonon spectrum, revealing soliton-related features and angle-dependent phonon modes through a detailed spectral analysis and modeling.

Contribution

It introduces a nearly-free-phonon model that emphasizes the role of solitons in the phonon spectrum of twisted bilayer graphene, especially at small twist angles.

Findings

Emergence of well-defined side-bands in phonon spectra due to twist angle.

Pronounced soliton-related phonon features below a 3.75° twist angle.

Structural relaxation influences phonon mode evolution.

Abstract

The phonon spectra of twisted bilayer graphene (tBLG) are analyzed for a series of 692 twisting angle values in the $[0,30{\degree}]$ range. The evolution of the phonon bandstructure as a function of twist angle is examined using a band unfolding scheme where the large number of phonon modes computed at the $\Gamma$ point for the large moir\'e tBLG supercells are unfolded onto the Brillouin Zone (BZ) of one of the two constituent layers. In addition to changes to the low-frequency breathing and shear modes, a series of well-defined side-bands around high-symmetry points of the extended BZ emerge due to the twist angle-dependent structural relaxation. The results are rationalized by introducing a nearly-free-phonon model that highlights the central role played by solitons in the description of the new phonon branches, which are particularly pronounced for structures with small twist angles, below a buckling angle $\theta_{\rm B}\sim {3.75}{\degree}$.