- Main

## Thermal Conductivity and Phonon Properties of Twisted Bilayer Graphene

- Author(s): Li, Chenyang
- Advisor(s): Lake, Roger K
- et al.

## Abstract

Misorientation of two layers of bilayer graphene leaves distinct signatures in the electronic properties and the phonon modes. The effect on the thermal conductivity has received the least attention and is the least well understood.

In this work, the in-plane thermal conductivity of twisted bilayer graphene (TBG) is investigated as a function of temperature and interlayer misorientation angle using nonequilibrium molecular dynamics (NEMD). The central result is that with rotation angles larger than 13 degrees, the calculated thermal conductivities decrease approximately linearly with the increasing lattice constant of the commensurate TBG unit cell. Comparisons of the phonon dispersions show that misorientation has a negligible effect on the low-energy phonon frequencies and velocities. However, the larger periodicity of TBG reduces the Brillouin zone size to the extent that the zone edge acoustic phonons are thermally populated. This allows Umklapp scattering to reduce the lifetimes of the phonons contributing to the thermal transport, and consequently, to reduce the thermal conductivity. This explanation is supported by direct calculation of reduced phonon lifetimes in TBG based on density functional theory (DFT) for larger rotation angles.

Nothing was previously known about the questions about how small twist angles (< 13 degrees) affect the thermal conductivity of TBG, and how it approaches its aligned value as the twist angle approaches 0 degrees. To provide insight into these questions, we perform large scale NEMD calculations on commensurate TBG structures with angles down to 1.87 degrees. The results show a smooth, non-monotonic behavior of the thermal conductivity with respect to the commensurate lattice constant. As the commensurate lattice constant increases, the thermal conductivity initially decreases by 50%, and then it returns to 90% of its aligned value as the angle is reduced to 1.89 degrees. These same qualitative trends are followed by the trends in the shear elastic constant, the wrinkling intensity, and the out-of-plane ZA2 phonon frequency. The picture that emerges of the physical mechanism governing the thermal conductivity is that misorientation reduces the shear elastic constant; the reduced shear elastic constant enables greater wrinkling, and the greater wrinkling reduces the thermal conductivity. The small-angle behavior of the thermal conductivity raises the question of how do response functions approach their aligned values as the twist angle approaches 0 degrees. Is the approach gradual, discontinuous, or a combination of the two?

Much attention has been given recently to the material data science. A particular emphasis is placed on low dimensional materials exhibiting novel electrical and thermal properties. An improved dimension classifier model has been created to identify the quasi-1D materials that are often classified within the 2D material family. The algorithm is based on the fact that quasi-1D materials contain different bond lengths within the unit cell. The model can identify known quasi-1D material based on the structural data from Material Project Database. Using the optimized distributed gradient boosting model (XGBoost), both the band gap and the magnetization properties can be predicted from structural and elemental features. By fitting the XGBoost model with 15,000 kinds of materials, the accuracy of the predictions on the 5000 testing samples is greater than 91%. The mean absolute error of the band gap prediction is only 0.148 eV. Additionally, 1,025 kinds of magnetic materials have been identified among 5000 kinds of materials. According to the feature importance analysis, the most correlated feature for band gap prediction is the number of the valence electrons. While, for the magnetic material classification, it is the elemental period.