Generating spin-mixed edge states with hybridized spin-up and spin-down components and clarifying their transport mechanisms are critical to topological spintronic and valleytronic devices. In this work, we propose two types of spatially modulated Haldane-Rashba models that incorporate spatial variation of both the Haldane term and the extrinsic Rashba effect, aiming at generating spin-mixed edge states. For one model type with modulation directed inward from the system boundaries, two chiral edge states (CESs) and four antichiral edge states (AESs) can be induced, which are attributed to the coupling between bulk states of pristine graphene and inner edge states characterized by the Chern number difference between the two adjacent topological domains. Based on a similar mechanism, the other model type with modulation directed outward from the central system interface, yields two valley-dependent CESs and two valley-dependent AESs. To explore the transport behavior of these states and the underlying mechanism, we derive the corresponding expressions for conductance and local bond current of these edge states in zigzag graphene nanoribbons. Our results demonstrate that the general expressions of conductance and local bond current enable the calculation of spin-conserved and spin-flipping transport properties involving valley scattering, applicable to both these spin-mixed edge states and other types of edge states. In this work, we not only provide a theoretical foundation for exploring the transport properties of spin-mixed edge states but also offer a promising platform for their realization and engineering, thereby jointly advancing the design of topological spintronic and valleytronic device technologies.

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• Edge states
• Electrical conductivity
• Topological insulators