Commensurate-incommensurate transition in van der Waals heterostructures : a study based on the one-dimensional Frenkel-Kontorova model

Details

Supervisors

Gonze, Xavier

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] : ingénieur civil physicien

Abstract

This thesis aims at developing and applying a new framework for the prediction of commen- surate or incommensurate phases for the ground state of Van der Waals heterostructures. It builds upon the recent work by B. Van Troeye et al : "First-principles investigation of 2D lattice coherency in van der Waals heterostructures" [1]. In their article the commensurability of different van der Waals heterostructures (vdWHS) was predicted using the mathematical model developed by J. Frenkel and T. Kontorova [2] and then revisited by F. Frank and J. Van der Merwe [3]. In the present work, the analytical solution of Franck and Van der Merwe is first checked for more general situations than in the original proposal of Frenkel and Kon- torova, using a numerical implementation. Then, the same mathematical framework is used to develop more criteria unveiling the possibility to probe more possible ground phases than B. Van Troeye et al, also more accurately. The application of our model to eleven actual vdWHS shows more detailed understanding than the model of B. Van Troeye et al. It is also expected to agree better with experimental results, but the latter are too scarce at the time of writing.