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We investigate the topological bound modes of surface plasmon polaritons (SPPs) in a graphene pair waveguide array. The arrays are with uniform inter-layer and intra-layer spacings but the chemical potential of two graphene in each pair are different. The topological bound modes emerge when two arrays with opposite sequences of chemical potential are interfaced, which are analogous to Jackiw-Rebbi modes with opposite mass. We show the topological bound modes can be dynamically controlled by tuning the chemical potential, and the propagation loss of topological bound modes can be remarkably reduced by decreasing the chemical potential. Thanks to the strong confinement of graphene SPPs, the modal wavelength of topological bound modes can be squeezed as small as 1/70 of incident wavelength. The study provides a promising approach to realizing robust light transport beyond diffraction limit. [ABSTRACT FROM AUTHOR]

We investigate the exceptional points (EPs) in a non-Hermitian system composed of a pair of graphene sheets with different losses. There are two surface plasmon polaritons (SPPs) modes in the graphene waveguide. By varying the distance between two graphene sheets and chemical potential of graphene, the EPs appear as the eigenvalues, that is, the wave vectors of the two modes coalesce. The cross conversion of eigenmodes and variation of geometric phase can be observed by encircling the EP in the parametric space formed by the geometric parameters and chemical potential of graphene. At the same time, a certain input SPP mode may lead to completely different output. The study paves a way to the development of nanoscale sensitive optical switches and sensors. [ABSTRACT FROM PUBLISHER]