Sublattice pseudospin in graphene ($⟨\mathbf{\sigma }⟩=(\cos \varphi ,\sin \varphi ,0)$)

At ${\mathbf{K}}_{+}$ and positive energy, a normalized eigenvector for $\mathbf{q}=|\mathbf{q}|(\cos \varphi ,\sin \varphi )$ is $(1,e^{i\varphi })/\sqrt{2}$. Its Pauli matrix expectation values give the displayed direction. This pseudospin records the relative amplitudes and phase on the two sublattices. Real spin supplies another label; confusing these two labels would double-count states and misinterpret the two-band Hamiltonian.