Tuning MoS₂ band structure: How self-intercalation affects screening, interactions and strain

Two-dimensional (2D) materials, especially transition metal dichalcogenides (TMDs), have displayed remarkable physical properties, including 2D superconductivity, magnetism, and layer-dependent bandgaps. At the same time functionalization, strain and substrate interactions were shown to be viable routes to tune their intrinsic properties, bringing them closer to specific applications. In this work we epitaxially grow MoS₂ monolayer islands on graphene on Ir(111) using two different procedures: (i) two-step molecular beam epitaxy (MBE) growth which results in S intercalation between graphene and Ir(111), and (ii) single-step MBE growth resulting in Mo intercalation. Our scanning tunneling microscopy (STM) measurements reveal significant difference in MoS₂ islands morphology, and suggests that S intercalation weakens the interaction in the MoS₂/graphene stack, while Mo intercalation strengthens it. More importantly, our scanning tunneling spectroscopy (STS) measurements show notable shifts of electronic states that goes beyond a rigid band shift. The numerical calculations reveal a strong correlation between substrate screening, intralayer strain and binding energy of MoS₂ per unit cell resulting in changes in the band gap that are in agreement with experiment. We suggest that this elegant and non-invasive technique could be used for altering the band structure of 2D materials in general, especially for 2D semiconductors where it can be utilized to switch the band gap between indirect and direct.