# Superconducting and density-wave instabilities of low dimensional conductors with a Zeeman coupling to a magnetic field

## TL;DR

This paper investigates how magnetic fields influence superconducting and density-wave instabilities in low-dimensional conductors, revealing transitions from singlet to triplet superconductivity and the emergence of FFLO states, with implications for Bechgaard salts.

## Contribution

It provides a detailed theoretical analysis of magnetic field effects on superconducting states in quasi-one-dimensional conductors, including the transition mechanisms and critical field behavior.

## Key findings

- Transition from singlet d-wave to FFLO state under magnetic field
- Weak interchain interactions promote triplet f-wave superconductivity
- Anomalous increase of upper critical field near quantum critical point

## Abstract

In the framework of the weak coupling renormalization group technique we examine the possible instabilities of the extended quasi-one-dimensional electron gas model with both intrachain and interchain electron-electron interactions, including the influence of umklapp scattering and the coupling of spins to a magnetic field. In the limit of purely repulsive intrachain interactions, we confirm the passage from singlet d-wave like superconductivity to an inhomogeneous FFLO state under magnetic field. The passage is accompanied by an anomalous increase of the upper critical field that scales with the antinesting distance from the quantum critical point joining superconductivity to antiferromagnetism in the phase diagram, as well as the strength of interactions. Adding weak repulsive interchain interactions promotes the passage from singlet to triplet $f$-wave superconductivity which is expanded under field by the development of a triplet FFLO state with zero angular momentum projection for the Cooper pairs. The connection between theory and experiments on the anomalous upper critical field in the Bechgaard salts is discussed.