Spin-orbital dynamics in a system of polar molecules

Spin-orbit coupling (SOC) in solids normally originates from the electron motion in the electric field of the crystal. It is key to understanding a variety of spin-transport and topological phenomena, such as Majorana fermions and recently discovered topological insulators. Implementing and controlling spin-orbit coupling is thus highly desirable and could open untapped opportunities for the exploration of unique quantum physics. Here, we show that dipole-dipole interactions can produce an effective SOC in two-dimensional ultracold polar molecule gases. This SOC generates chiral excitations with a non-trivial Berry phase $2\pi$. These excitations, which we call \emph{chirons}, resemble low-energy quasiparticles in bilayer graphene and emerge regardless of the quantum statistics and for arbitrary ratios of kinetic to interaction energies. Chirons manifest themselves in the dynamics of the spin density profile, spin currents, and spin coherences, even for molecules pinned in a deep optical lattice and should be observable in current experiments.