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As I have seen it in the Fu-Kane-Mele model context of a bipartite lattice, it is represented as a coupling between second-nearest neighbors $\langle\langle i,j\rangle\rangle$, like so:

$i \lambda \sum\limits_{\langle\langle i,j\rangle\rangle}(c_i^\dagger~\mathbf{e}_{ij}\cdot\mathbf{s}~c_j-H.c.)$,

where $\mathbf{e}_{ij}=\frac{\mathbf{e}_{i}\times\mathbf{e}_{i}}{|\mathbf{e}_{i}\mathbf{e}_{j}|}$, and the $\mathbf{e}_{i}$ are vectors connecting second nearest neighbors. $\mathbf{s}=(s_x,s_y,s_z)$ are Pauli Matrices acting on spin.

I just wanted to know why it is not nearest neighbor? Is it connected to the physical origin of Dresselhaus SOC?

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Because the nearest neighbor bond is inversion symmetric, on which the Dresselhaus SOC is forbidden by the inversion symmetry.

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