On Valence-Band Splitting in Layered MoS₂

Abstract

As a representative two-dimensional semiconducting transition-metal dichalcogenide (TMD), the electronic structure in layered MoS₂ is a collective result of quantum confinement, interlayer interaction, and crystal symmetry. A prominent energy splitting in the valence band gives rise to many intriguing electronic, optical, and magnetic phenomena. Despite numerous studies, an experimental determination of valence-band splitting in few-layer MoS₂ is still lacking. Here, we show how the valence-band maximum (VBM) splits for one to five layers of MoS₂. Interlayer coupling is found to contribute significantly to phonon energy but weakly to VBM splitting in bilayers, due to a small interlayer hopping energy for holes. Hence, spin–orbit coupling is still predominant in the splitting. A temperature-independent VBM splitting, known for single-layer MoS₂, is, thus, observed for bilayers. However, a Bose–Einstein type of temperature dependence of VBM splitting prevails in three to five layers of MoS₂. In such few-layer MoS₂, interlayer coupling is enhanced with a reduced interlayer distance, but thermal expansion upon temperature increase tends to decouple adjacent layers and therefore decreases the splitting energy. Our findings that shed light on the distinctive behaviors about VBM splitting in layered MoS₂ may apply to other hexagonal TMDs as well. They will also be helpful in extending our understanding of the TMD electronic structure for potential applications in electronics and optoelectronics