▎ 摘　　要

In this work, a mechanism of achieving phonon heat current between distant graphene sheets inserted into a cavity with two reflectors at different temperatures are presented. The photon-mediated pseudospin interaction between two graphene sheets and electron-phonon interaction in each graphene sheet lead to the generation of this phonon heat current. We calculate the phonon heat current, thermal conductivity, and current-current correlation functions between distant graphene sheets. This phonon heat current can be manipulated by the energy flow density and frequency of photons. The giant heat current and thermal conductivity of phonons induced by intense photon field indicate that this mechanism has potential applications on the chip cooling, and far-range heat transfer.