Research master thesis: Using Machine Learning Interatomic Potentials to Investigate Charge Density Waves in Monolayer Transition Metal Dichalcogenides

Abstract

Charge Density Waves (CDWs) are characterized by an instability of the electronic structure, that is coupled with a distortion in the atomic arrangement in a metal, leading to a decrease in energy (lower than the high symmetry phase) along with the appearance of an unstable phonon mode. CDWs in Transition Metal Dichalcogenides (TMDs) have been researched for the past four decades. Aided by the advancement of computational power and the development of computational methods, there have been successful attempts at simulating these CDWs using first principle methods [Nano Lett. 2020, 20, 7, 4809–4815; Phys. Rev. B 92, 094107]. Although these methods are quite accurate, they are computationally very expensive, and hence there is a need for faster alternatives like classical Molecular Dynamics (MD) simulations. As a solution, we propose the use of Machine Learning Interatomic Potentials (MLIPs), fit to first principles calculations, in order to reduce simulation times and costs, while achieving near ab initio accuracy. In this study, we compared two types of MLIPs - Spectral Neighbor Analysis Potential (SNAP) and Moment Tensor Potential (MTP), trained on a set of Density Functional Theory (DFT) that are ab initio calculations. They were then tested to investigate if they can reproduce the CDW distortion in two monolayer TMDs - 1T-TiSe2 and 1T-TiS2 . The Python package ‘MLACS’ [Phys. Rev. B 106, L161110] is used for the ML training. The results of this thesis show that the chosen MLIPs are orders of magnitude faster than ab initio calculations, but might not be accurate enough. Phonons calculated using finite-difference approximation clearly show an unstable mode at the M point for monolayer 1T-TiS2 , indicating the CDW state as found in the literature [EPL (2016) 115 47001]. Yet, no instability was found for the monolayer 1T-TiSe2 . The phonon modes were then calculated at finite temperatures using a theory of anharmonic vibrations called the Temperature Dependent Effective Potential (TDEP) [Phys. Rev. B 88, 144301]. TDEP is a method to calculate the free energy of a system and not just the potential energy. It renormalizes all orders of anharmonicity as well and makes it perfect for our research. Phonons calculated using TDEP do not show an instability, which could be a limitation caused by the potential’s accuracy or even the DFT “ground truth” calculations. This study hence demonstrates that MLIPs calculated can be used for MD simulations, but have certain limitations.