Large-scale atomistic computations of the phonons in twisted bilayer graphene

Abstract

To help explore new combinations of techniques not available in existing software, a new code is written specialized to meet the unique demands of this problem. Details of the implementation are discussed in depth, particularly in the context of other existing software solutions. In broad, the structures are relaxed using the conjugate gradient method, and then phonon normal modes are computed in the harmonic approximation using a new code optimized for large structures, modeling energy with the classical second-generation reactive empirical bond order potential (REBO) with a Kolmogorov/Crespi registry-dependent term. The structure can then be further optimized as necessary using a novel technique based on the computed phonon modes. With this, a database is constructed with the vibrational normal mode frequencies and non-resonant Raman spectra for all of the structures. When nonlinear machine learning models are applied to the dataset to predict twist angle from Raman spectra, they are found to be robust to noise and make successful predictions during cross-validation despite the spectra lacking many of the key features that have previously been identified as possible fingerprints of twist angle. This is promising evidence for the viability of creating a black box model mapping experimental spectra to twist angle using supervised machine learning.

Additionally, by unfolding the phonon modes onto the first Brillouin zone (FBZ) of a single layer, it becomes viable to track the evolution of the phonon modes as a function of twist angle, and splitting of bands around the M and K points is observed which is attributed to phonon scattering by the network of solitons that arises during relaxation. The standalone Python script written to perform this unfolding will be suitable for other future work involving band structures on extremely large supercells.

The vibrational modes of twisted bilayer graphene (tBLG) are computed and analyzed for a series of 692 twisting angle values in the [0, 30°] range.