▎ 摘　　要

We investigate the surface plasmonic lattice solitons (PLSs) in semi-infinite graphene sheet arrays. The surface soliton is formed as the surface plasmon polaritons (SPPs) tunneling is inhibited by the graphene nonlinearity, and meanwhile the incident power should be above a threshold value. Thanks to the strong confinement of SPPs on graphene, the effective width of surface PLSs can be squeezed into deep-subwavelength scale of similar to 0.002 lambda. The influence of the graphene loss on the surface PLSs is also discussed. Based on the stable propagation of surface PLSs, we find that the light propagation can be switched from the array boundary to the inner graphene sheets by reducing the incident power or increasing the chemical potential of graphene. The study may find promising application in optical switches on deep-subwavelength scale.