Zitterbewegung of moir\'e excitons in twisted MoS${}_2$/WSe${}_2$ hetero-bilayers

The moir'e pattern observed in stacked non-commensurate crystal lattices, such as hetero-bilayers of transition metal dichalcogenides, produces a periodic modulation of their bandgap. Excitons subjected to this potential landscape exhibit a band structure that gives rise to a quasi-particle dubbed moir'e exciton. In the case of MoS${}_2$/WSe${}_2$ hetero-bilayers, the moir'e trapping potential has honeycomb symmetry and, consequently, the moir'e exciton band structure is the same as that of a Dirac-Weyl fermion, whose mass can be further tuned down to zero with a perpendicularly applied field. Here we show that, analogously to other Dirac-like particles, moir'e exciton exhibits a trembling motion, also known as zitterbewegung, whose long timescales are compatible with current experimental techniques for exciton dynamics. This promotes the study of the dynamics of moir'e excitons in van der Waals heterostructures as an advantageous solid-state platform to probe zitterbewegung, broadly tunable by gating and inter-layer twist angle.