Odd-parity superconductivity near inversion breaking quantum critical point in one dimension

TL;DR

This paper investigates how an inversion-breaking quantum critical point influences a one-dimensional electronic system, revealing that critical fluctuations induce a spin gap and lead to a form of spin triplet superconductivity.

Contribution

It demonstrates that quantum critical fluctuations near inversion-breaking points induce a spin gap and promote odd-parity superconductivity in one-dimensional systems.

Findings

Critical fluctuations cause a spin gap regardless of interaction strength.

The spin-gapped state is a one-dimensional analog of spin triplet superconductivity.

Ferromagnetic critical points do not lead to superconductivity due to opposite renormalization effects.

Abstract

We study how an inversion-breaking quantum critical point affects the ground state of a one-dimensional electronic liquid with repulsive interaction and spin-orbit coupling. We find that regardless of the interaction strength, the critical fluctuations always lead to a gap in the electronic spin-sector. The origin of the gap is a two-particle backscattering process, which becomes relevant due to renormalization of the Luttinger parameter near the critical point. The resulting spin-gapped state is a one-dimensional version of spin triplet superconductivity. Interestingly, in the case of a ferromagnetic critical point the Luttinger parameter is renormalized in the opposite manner, such that the system remains non-superconducting.