Twisted heterobilayers of transition metal dichalcogenides exhibit a moiré pattern that translates into a honeycomb lattice of single-particle gap minima, thus resulting in a superlattice potential for excitons. The quasiparticle associated with the Bloch state of such excitons is known as a moiré exciton, and its band structure corresponds to that of a massive Dirac fermion. Here, we investigate the wavepacket dynamics of such moiré excitons using a momentum-space tight-binding model. Our results demonstrate that wavepackets that populate all the regions of gap minima at the $\mathrm{\Gamma }$-point of the moiré superlattice exhibit an elliptical, cyclotron-like motion, even for zero exciton momentum and in the absence of external forces and/or fields. We show that the period and size of these orbits are controllable via external parameters, such as perpendicularly applied electric fields and the interlayer twist angle. To provide a deeper physical insight, we derive an effective continuum model for the moiré exciton, which reveals a direct analogy to an anisotropic Rashba-like Hamiltonian, thereby explaining the origin of the elliptical trajectories. The analytical solutions for the center-of-mass motion, obtained from the Heisenberg equations of motion, are in excellent agreement with our full numerical simulations. Furthermore, we explore the topological aspects of the system, demonstrating that the anisotropic Berry curvature and the associated nonzero Chern numbers govern the directionality (clockwise or counterclockwise) of the cyclotron-like orbits, linking the exciton's trajectory to the underlying topology of its band structure.

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• Berry curvature
• Excitons
• Quantum transport
• Moire materials
• Twisted bilayers
• van der Waals systems
• Tight-binding model