  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 (SPP) 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.
