# Spin-nematic order induced superconductivity

## TL;DR

This paper investigates how spin-nematic order can induce p-wave superconductivity through fermion-spin interactions, revealing quantum critical transitions influenced by chemical potential and interaction strength.

## Contribution

It introduces a spin-fermion model linking spin-nematic order to superconductivity, highlighting the role of fermion-spin-quadrupolar interactions in phase transitions.

## Key findings

- Positive coupling leads to p-wave, spin-parallel superconductivity.
- Negative coupling results in p-wave, spin-antiparallel pairing.
- Quantum critical transition occurs with non-zero chemical potential.

## Abstract

We explore a spin-fermion model with fermion-spin-quadrupolar interaction. In a nematic phase, this interaction reduces to a four-fermion interaction that is a basis of superconductivity. When the coupling constant is positive the superconductivity is p-wave with spin-parallel paired fermions. When it is negative the superconductivity is p-wave and fermions are spin-antiparallel paired. For a system with zero chemical potential, even a very small coupling can bind fermions into bound state that leads to the superconductivity. When the chemical potential is non-zero the system possesses quantum critical transition from normal spin-nematic phase to phase where superconductivity coexists with spin-nematicity. The value of the quantum critical fermion-spin-nematicity coupling constant depends on the chemical potential.