Twisted Bilayer Dirac Spin Liquid

When two layers of two-dimensional materials are assembled with a relative twist, moiré patterns can arise, giving rise to a tremendous wealth of exotic phenomena. In this work, we consider twisting two triangular lattices hosting Dirac quantum spin liquids. The single-layer parent state is stable, since the proliferation of monopole operators, inducing conventional long-range magnetic or valence bond solid order, is symmetry forbidden. Conversely in the bilayer system, interlayer monopole tunneling is a symmetry-allowed relevant perturbation and can lead to ordered bilayer states. Adding a relative twist between the two layers reduces the stability of the ordered phases compared with the untwisted case and results in tunable moiré modulations of antiferromagnetic and valence bond solid order parameters.