Competing orders at high-order Van Hove points: doped graphene

Van Hove points are special points in the energy dispersion, where the density of states exhibits singularities. When a Van Hove point is close to the Fermi level, tendencies towards density wave, Pomeranchuk, and superconducting orders can all be enhanced leading to unconventional ground states. Here we consider effects from high-order Van Hove points, around which the dispersion is exceptionally flat 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 high-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 exchange interaction, we find a new type of spin Pomeranchuk order, in which the spin order parameter winds around the Fermi surface. The supermetal state, predicted for a single high-order Van Hove point, is an unstable fixed point in our case.