Stacking of charge-density waves in 2H-NbSe₂ bilayers

We employ ab-initio electronic-structure calculations to investigate the charge-density waves and periodic lattice distortions in bilayer 2⁢H-NbSe₂. We demonstrate that the vertical stacking can give rise to a variety of patterns that may lower the symmetry of the charge-density waves exhibited separately by the two composing 1⁢H-NbSe₂ monolayers. The general tendency to a spontaneous symmetry breaking observed in the ground state and the first excited states is shown to originate from a non-negligible interlayer coupling. Simulated images for scanning tunneling microscopy as well as geometric structure factors show signatures of the different stacking orders. This may not only be useful to reinterpret past experiments on surfaces and thin films, but it may also be exploited to devise ad hoc experiments for the investigation of the stacking order in 2H-NbSe₂. We anticipate that our analysis not only applies to the 2H-NbSe₂, but is also relevant for thin films and bulk, whose smallest centrosymmetric component is indeed the bilayer. Finally, our results illustrate clearly that the vertical stacking is not only important for 1T structures, as exemplified by the metal-to-insulator transition observed in 1⁢T-TaS₂, but seems to be a general feature of metallic layered transition metal dichalcogenides as well. The dataset includes the fully relaxed atomic positions of the most favorable charge-density waves, as well as the main output files of the electronic structure calculations. Selected files for the charge densities are also included.