Schematic diagram of two nanoscale plasmonic waveguide structures and optical gradient force in such waveguide structures: (a) structure A, (b) structure B. Both structures A and B are constructed by two semi-infinite HMM cladding layers and one nanoscale gap core. The semi-infinite HMMs are composed of alternating insulator (grey) and metal (yellow) thin layers. The coordinate origin is placed at the middle of the gap, and the SPP modes propagate along the z direction. (c) The optical gradient force from mutual coupling of the symmetric SPP mode (black solid line) and the antisymmetric SPP mode (red dashed line). (d) A unit planar surface A parallel to the interface of the waveguide for calculating the optical gradient force.