Dynamical Jahn-Teller effect in a spin-orbital coupled system

Dynamical Jahn-Teller (DJT) effect in a spin-orbital coupled system on a honeycomb lattice is examined, motivated from recently observed spin-liquid behavior in Ba₃CuSb₂O₉. An effective vibronic Hamiltonian, where the superexchange interaction and the DJT effect are taken into account, is derived. We find that the DJT effect induces a spin-orbital resonant state where local spin-singlet states and parallel orbital configurations are entangled with each other. This spin-orbital resonant state is realized in between an orbital-ordered state, where spin-singlet pairs are localized, and an antiferromagnetic ordered state. Based on the theoretical results, a possible scenario for Ba₃CuSb₂O₉ is proposed.