Unexpected symmetries in twisted bilayer MoSe_θ

Spin-orbit interactions lead to a large spin-splitting of the valence band maximum at K in MoSe_² monolayers. However, on stacking a second layer of MoSe₂ in the same manner (2H) as found in the bulk, one finds that there is no spin splitting. This has been attributed to the presence of inversion symmetry. As exploiting the spin splitting at the K valleys allows us to increase the functionality, an obvious route to making the bilayers useful for exploring the coupled spin and valley physics is through breaking inversion symmetry. We examined this by rotating the top layer of the bilayer by an angle θ with respect to the lower layer. The choice of angles was resticted to those for which one had reasonable sized supercells and were otherwise arbitrary. Surprisingly, we found several instances where the spin splitting vanished, though there was no breaking of inversion symmetry. An unusual mechanism behind this is identified. Additionally, we found that while the spin splitting existed for theta, it vanished for 60 - θ. This unusual behavior, we find, is a consequence of the symmetry of the hexagonal Brillouin zone.