Pairing at a single Van Hove point

Abstract

We show that an interacting electronic system with a single ordinary or extended Van Hove point, which crosses the Fermi energy, is unstable against triplet superconductivity. The pairing mechanism is unconventional. There is no Cooper instability. Instead, pairing is due to the divergence of the density of states at a Van Hove point, leading to a superconducting quantum critical point at a finite detuning from the Van Hove point. The transition temperature is universally determined by the exponent governing the divergence of the density of states. Enhancing this exponent drastically increases $T_c$. The Cooper pair wave function has a non-monotonic momentum dependence with a steep slope near the gap nodes. In the absence of spin-orbit coupling, pairing fluctuations suppress a $2e$ spin-triplet state, but allow pairs of triplets to condense into a charge-$4e$ singlet state at a temperature of similar order as our result.