## 1 Introduction  
Surface plasmon polaritons (SPPs), the surface waves supported at the interface of metal and dielectric, have attracted enormous attention as they are able to propagate beyond diffraction limit and realize strong field enhancement [1; 2; 3; 4]. In searching for new plasmonic material, graphene, a two-dimensional material composed of carbon atoms, has emerged as a promising candidate instead of noble metal [5; 6; 7; 8; 9; 10]. Graphene shows stable mechanical properties thanks to the stability of the sp2 bonds that form the hexagonal lattice and oppose a variety of in-plane deformations [5; 11]. The chemical properties of graphene are quite stable and will not be easily oxidized. The optical properties of graphene change with the change of the dielectric environment in contact with it. For example, air components such as different concentrations of oxygen and water vapor may affect the chemical potential of graphene [5]. The unique electronic, thermal, mechanical, and chemical characteristics of graphene, along with the intrinsic benefits of a carbon material, make it a promising candidate for many applications, such as supercapacitor [11; 12; 13; 14]. Graphene based plasmonic devices have many new advantages when compared with metal. The SPPs in graphene are confined more than two orders smaller than that of free-space wavelength [8]. The surface conductivity of graphene can be dynamically controlled by tuning chemical potential via electrostatic and chemical doping [5]. The high carrier mobility in graphene makes it suitable for ultra-fast switching [15; 16; 17; 18]. Graphene is also convenient to integrate with other optical nanodevices thanks to its dimensionless and flexible properties [6]. Moreover, graphene is utilized to investigate nonlinear optics due to its high nonlinear coefficient [19; 20; 21; 22; 23]. Many schemes are proposed to manipulate the optical property and control the propagation of SPPs, such as coupled graphene waveguides [24; 25; 26], graphene metamaterials [7; 27], and dynamic modulation [28; 29; 30; 31]. The graphene waveguide arrays have also been utilized to demonstrate optical analogues of semiclassical electron dynamics [32; 33; 34]. On the other hand, topology, a new freedom that characterizes the collective behavior of the wave functions on the photonic band structure, is demonstrated to reveal new states of light and provide robust way to control light flows [35; 36; 37; 38]. One important feature of topological theory is that topologically-protected bound states emerge when two structures with different topologies are interfaced [35; 39; 40]. Such topological bound modes are usually located at the middle of band gap and rather robust against certain structure disorder. For example, the Su-Schriffer-Heeger (SSH) model, which studies the topology of a binary periodic array, can possess two distinct topological phases determined by the relative strength of inter-layer and intra-layer couplings [41; 42; 43; 44]. The structure is topologically nontrivial as inter-layer coupling is stronger than intra-layer coupling, while it is topologically trivial as inter-layer coupling is weaker than intra-layer coupling [41]. The SSH model is demonstrated using graphene sheets [45; 46; 47; 48; 49]. However, the optical properties of topological bound modes in these systems are mostly determined by the spatial spacing between different graphene sheets, which cannot be flexibly adjusted after manufacturing. In this work, we propose another scheme to investigate the topological bound modes in the binary graphene sheet arrays. The arrays are with uniform inter-layer and intra-layer spacings but the chemical potential of two graphene in each unit cell is different. The topological bound mode emerges when two arrays with opposite sequence of chemical potential are interfaced, which is analogous to Jackiw-Rebbi mode at the interface where the mass term changes sign in a Dirac equation with position dependent mass [50; 51; 52; 53; 54].