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?


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

| cite | improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.