Spin-momentum locking

Spin-momentum locking means that a state's spin direction is constrained by its momentum and its energy branch. In the isotropic Weyl Hamiltonian with $v>0$, the upper and lower branches have mean spin parallel and antiparallel to the momentum. Their textures in an equatorial momentum plane are radial outwards and inwards. Other Hamiltonians can lock spin transverse to momentum, so radial locking is an example rather than the general definition. In an effective model one must check whether its Pauli matrices represent physical spin or pseudospin before interpreting the texture as a measured spin.

For $H=c(p_x{\sigma }_x+p_y{\sigma }_y)$ with $c>0$ and physical spin matrices, $⟨\mathbf{S}{⟩}_s=s(\hslash /2)\hat{\mathbf{p}}$. The positive-energy branch is parallel and the negative-energy branch antiparallel to momentum. Both are collinear; no preferred spin direction is defined at zero momentum.