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In this work, a trial understanding for the physics underling theconstruction of exchange (hopping) matrix $\mathbf{E}$ in Heisenberg model(tight binding model) for 2D materials is done. It is found that the$\mathbf{E}$ matrix describes the particles exchange flow under short range(nearest neighbor) hopping interaction which is effected by the latticegeometry. This understanding is then used to explain the dispersion relationsfor the 2D honeycomb lattice with zigzag and armchair edges obtained forgraphene nanoribbons and magnetic stripes. It is found that the particle flowby hopping in the zigzag nanoribbons is a translation flow and shows$\mathbf{\cos^2}(q_xa)$ dependance while it is a rotational flow in thearmchair nanoribbons. At $q_xa/\pi=0.5$, the particles flow in the edge sitesof zigzag nanoribbons with dependance of $\mathbf{\cos^2}(q_xa)$ is equal tozero. At the same time there is no vertical hopping in those edge sites whichlead to the appearance of peculiar zigzag flat localized edge states.

Understanding of hopping matrix for 2D materials taking 2D honeycomb and square lattices as study cases