Topological Odd-Parity Superconductivity at Type-II 2D Van Hove Singularities

We study unconventional superconductivity induced by weak repulsive interactions in 2D electronic systems at Van Hove singularity (VHS) where density of states is logarithmically divergent. We define two types of VHS. For systems at type-I VHS, weak repulsive interactions generically induce unconventional singlet pairing. However and more interestingly, for type-II VHS renormalization group (RG) analysis shows that weak repulsive interactions favor triplet pairing (e.g. p-wave) when the Fermi surface is not sufficiently nested. For type-II VHS systems respecting tetragonal symmetry, topological superconductivity (either chiral p+ip pairing or time-reversal invariant $Z_2$ p+ip pairing) occurs generally. We shall also discuss relevance of our study to materials including recently discovered superconductors LaO$_{1-x}$F$_x$BiS$_2$ which can be tuned to type-II VHS by doping.