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In this paper we present a paradigmatic tight-binding model for single-layeras well as for multi-layered semiconducting MoS$_2$ and similar transitionmetal dichalcogenides. We show that the electronic properties of multilayersystems can be reproduced in terms of a tight-binding modelling of thesingle-layer hopping terms by simply adding the proper interlayer hoppingsruled by the chalcogenide atoms. We show that such tight-binding model permitsto understand and control in a natural way the transition between a direct-gapband structure, in single-layer systems, to an indirect gap in multilayercompounds in terms of a momentum/orbital selective interlayer splitting of therelevant valence and conduction bands. The model represents also a suitableplayground to investigate in an analytical way strain and finite-size effects.

Tight-binding model and direct-gap/indirect-gap transition in single-layer and multi-layer MoS$_2$