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Graphene on transition-metal dichalcogenides (TMDCs) exhibits proximity spin-orbit effects opening new venues for optospintronics [1], and provides route for exploring robust helical edge states [2, 3]. 1T-TaS₂ is a layered TMDC showing metal-insulator transition and the sequence of different charge density wave (CDW) transformations [4]. We present our first-principles results for the electronic band structures of graphene on 1T-TaS₂ in normal state and for periodic lattice distorted David star pattern providing commensurate CDW phase. We discuss the orbital and spin-orbital proximity effects with phenomenological symmetry-based Hamiltonian that we use to fit the first-principles data. The extracted spin-orbit coupling parameters are of the order of meV. A fascinating finding is that induced proximity effects in graphene on 1T-TaS₂ are significantly influenced by the presence of the commensurate CDW in 1T-TaS₂.

[1] M. Gmitra, J. Fabian, Phys. Rev. B 92, 155403 (2015).
[2] M. Gmitra, D. Kochan, P. H\"{o}gl, J. Fabian, Phys. Rev. B 93, 155104 (2016).
[3] T. Frank et al., Phys. Rev. Lett. 120, 156402 (2018).
[4] I. Lutsyk et al., accepted for publication in Phys. Rev. B.