Phonon anharmonicity and thermal expansion in two-dimensional graphene/MoS2 and graphene/WS2 heterostructures: DFT and Raman study

Anharmonicity is a crucial feature of solid-state systems, affecting phenomena such as thermal expansion and temperature-dependent heat conductivity. Here, phonon anharmonicity in monolayer MoS 2 , WS 2 , and their heterostructures with graphene is comprehensively investigated, using ab-initio calculations and Raman spectroscopy. The presented theoretical approach yields exceptionally accurate predictions of temperature-dependent phonon frequencies in these systems. It is demonstrated that the friction regime between monolayers strongly affects thermal expansion in heterostructures – resulting in a tenfold difference in in-plane expansion coefficients. Furthermore, significant impact of four-phonon processes is unveiled, contributing to approximately 1/3 of temperature-dependent frequency slopes (d ω /d T ) in MoS 2 and WS 2 monolayers, although this factor has been commonly ignored in state-of-the-art theoretical works. This effect changes noticeably if a graphene cap layer is present, which, combined with the evolved thermal expansion, can flatten the d ω /d T slopes by 20%. Our work introduces a novel approach to calculating phonon anharmonicity in complex, multi-layered two-dimensional structures, which might also support determining their macroscopic thermal properties.