Massive two-dimensional Dirac Hamiltonian ($H=c(p_x{\sigma }_x+p_y{\sigma }_y)+V{\sigma }_z$)

The two-component model $H=c(p_x{\sigma }_x+p_y{\sigma }_y)+V{\sigma }_z$ has energies $E_s=s\sqrt{c^2{p}^2+V^2}$. The sign of $V$ changes eigenstates and spin polarization but not the uniform energy dispersion at fixed $|V|$. The Pauli matrices may represent actual spin or an effective pseudospin, depending on the physical realization.