arXiv2026
Anisotropic interactions profoundly affect topological excitations in quantum fluids. Motivated by recent advances in the studies of microwave-shielded polar molecules, we introduce self-trapped modes in the form of pancake-shaped quantum droplets (QDs) with embedded vorticity, which are maintained by strongly anisotropic dipole-dipole interactions. The stability region of singly charged ($S=1$) vortices nearly coincides with that of the ground-state QDs ($S=0$), demonstrating the robustness of the vortex states. The strong anisotropy of the system splits the core (pivot) of vortex QDs with $S=2$ into separated unitary ones. The angular momentum and stability of the state with $S=2$ are affected by the separation between the unitary cores. Higher-charge vortex QDs with $S>2$ are stable too, for sufficiently large particle numbers and inter-core separations. On the other hand, bound vortex-antivortex pairs with $S=\pm 1$ are unstable. Head-on collisions between the vortex QDs exhibit distinct regimes, including rebound, merger, and fragmentation. Tuning the cylindrically symmetric component of the dipolar interaction reveals a pronounced sign-dependent response: positive tuning preserves the self-bound vortex, whereas negative tuning drives expansion and fragmentation. The results demonstrate that the microwave-dressed molecular QDs offer a robust platform for the realization of self-trapped vortex states, demonstrating how the strong anisotropy reshapes their structure, stability, and dynamics.