Pairing at a single Van Hove point

TL;DR

This paper demonstrates that systems with a Van Hove point crossing the Fermi energy are prone to unconventional triplet superconductivity driven by density of states divergence, leading to a quantum critical point and potential charge-4e pairing.

Contribution

It reveals a novel pairing mechanism at Van Hove points causing triplet superconductivity without a Cooper instability, and predicts a charge-4e condensate possibility.

Findings

Superconductivity is driven by density of states divergence at Van Hove points.

Transition temperature scales with the divergence exponent.

Charge-4e pairing may occur due to pairing fluctuations.

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.