Van Hove points are special points in the energy dispersion, where the density of states exhibits analytic singularities. When a Van Hove point is close to the Fermi level, tendencies towards density wave orders, Pomeranchuk orders, and superconductivity can all be enhanced, often in more than one channel, leading to a competition between different orders and unconventional ground states. Here we consider the effects from higher-order Van Hove points, around which the dispersion is flatter than near a conventional Van Hove point, and the density of states has a power-law divergence. We argue that such points are present in intercalated graphene and other materials. We use an effective low-energy model for electrons near higher-order Van Hove points and analyze the competition between different ordering tendencies using an unbiased renormalization-group approach. For purely repulsive interactions, we find that two key competitors are ferromagnetism and chiral superconductivity. For a small attractive interaction, we find an unconventional spin Pomeranchuk order, in wich the spin oder parameter winds around the Fermi surface. The supermetal state, predicted for a single higher-order Van Hove point, is an unstable fixed point in our case.
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We thank D. V. Chichinadze, D. M. Kennes, Y.-P. Lin, R. Thomale, A. M. Tsvelik, and S. Wessel for valuable discussions. M.M.S. was supported by the Deutsche Forschungsgemeinschaft through Sonderforschungsbereich 1238 (projects C02 and C03, Grant No. 277146847), and C.H. was supported through Research Training Group Grant No. 1995. L.C. was supported by the Humboldt foundation during the first part of the project and by the U.S. Department of Energy, Office of Basic Energy Sciences, under Grant No. DE-SC0012704 during the later part of the project. A.V.C. was supported by the Office of Basic Energy Sciences, U.S. Department of Energy, under Grant No. DE-SC0014402.
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