Abstract
The (111) surface of SnTe hosts one isotropic Γ[over ¯]-centered and three degenerate anisotropic M[over ¯]-centered Dirac surface states. We predict that a nematic phase with spontaneously broken C_{3} symmetry will occur in the presence of a perpendicular magnetic field when the N=0 M[over ¯] 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[over ¯] Landau-level degeneracy, yielding a ground state energy with 2π/3 periodicity as a function of Zeeman-field orientation angle.
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