Momentum dependence of spin-orbit interaction effects in single-layer and multi-layer transition metal dichalcogenides

One of the main characteristics of the new family of two-dimensional crystals of semiconducting transition metal dichalcogenides (TMDs) is the strong spin–orbit interaction, which makes them very promising for future applications in spintronics and valleytronics devices. Here we present a detailed study of the effect of spin–orbit coupling (SOC) on the band structure of single-layer and bulk TMDs, including explicitly the role of the chalcogen orbitals and their hybridization with the transition metal atoms. To this aim, we combine density functional theory (DFT) calculations with a Slater–Koster tight-binding (TB) model. Whereas most of the previous TB models have been restricted to the K and K' points of the Brillouin zone (BZ), here we consider the effect of SOC in the whole BZ, and the results are compared to the band structure obtained by DFT methods. The TB model is used to analyze the effect of SOC in the band structure, considering separately the contributions from the transition metal and the chalcogen atoms. Finally, we present a scenario where, in the case of strong SOC, the spin/orbital/valley entanglement at the minimum of the conduction band at Q can be probed and be of experimental interest in the most common cases of electron-doping reported for this family of compounds.RR, MPL-S and FG acknowledge financial support from MINECO, Spain, through grant FIS2011-23713, and the European Union, through grant 290846. RR acknowledges financial support from the Juan de la Cierva Program (MINECO, Spain). EC acknowledges support from the European project FP7-PEOPLE-2013-CIG 'LSIE_2D' and Italian National Miur Prin project 20105ZZTSE. JAS-G and PO ackowledge support from Spanish MINECO (Grants No. FIS2012-37549-C05-02 with joint financing by FEDER Funds from the European Union, and No. CSD2007-00050). JAS-G was supported by an FPI Fellowship from MINECO. RR and FG acknowledge the financial support of FCT-Portugal through grant no. EXPL/FIS-NAN/1720/2013.Peer Reviewe