Theory of topological diffusion in a honeycomb lattice

The dynamics of edge states in topological diffusive systems are studied. Concrete calculations are performed using a honeycomb lattice consisting of two sublattices with nonuniform capacities, which is described by the mass term of the Dirac equation. We find that the time evolution of both arm-chair and zig-zag edge states, which are the mass domain walls separating the positive and negative mass regions, give rise to diffusive currents that flow parallel to the edge. From both numerical and analytical calculations, we find that the periodicity of the edge current differs between the zig-zag edge and the arm-chair edge, and the current magnitude decreases as the mass term becomes smaller and the domain wall width grows larger. Finally, these behaviors are verified by simulations of heat diffusion in topological edge states.