SU(3) Quantum Hall Ferromagnetism in SnTe

The (111) surface of SnTe hosts one isotropic Γ¯-centered and three degenerate anisotropic M¯-centered Dirac surface states. We predict that a nematic phase with spontaneously broken C₃ symmetry will occur in the presence of a perpendicular magnetic field when the N=0 M¯ Landau levels are 1/3 or 2/3 filled. The nematic state phase boundary is controlled by a competition between intravalley Coulomb interactions that favor a valley-polarized state and weaker intervalley scattering processes that increase in relative strength with magnetic field. An in-plane Zeeman field alters the phase diagram by lifting the threefold M¯ Landau-level degeneracy, yielding a ground state energy with 2π/3 periodicity as a function of Zeeman-field orientation angle.