Single Spin Superconductivity: Formulation and Ginzburg-Landau Theory

TL;DR

This paper introduces a new type of superconductivity arising from a pairing instability in half-metallic antiferromagnetic states, with a detailed symmetry-based Ginzburg-Landau theory and phase diagram analysis.

Contribution

It formulates the Ginzburg-Landau theory for single spin superconductivity and classifies possible phases based on symmetry considerations.

Findings

Identifies the least symmetric normal phase allowing zero momentum pairing.

Constructs a symmetry-consistent Ginzburg-Landau free energy for various crystal point groups.

Predicts gap nodes leading to power-law thermodynamic behavior at low temperatures.

Abstract

We describe a novel superconducting phase that arises due to a pairing instability of the half-metallic antiferromagnetic (HM AFM) normal state. This single spin superconducting (SSS) phase contains broken time reversal symmetry in addition to broken gauge symmetry, the former due to the underlying magnetic order in the normal state. A classification of normal state symmetries leads to the conclusion that the HM AFM normal phase whose point group contains the inversion operator contains the least symmetry possible which still allows for a zero momentum pairing instability. The Ginzburg-Landau free energy for the superconducting order parameter is constructed consistent with the symmetry of the normal phase, electromagnetic gauge invariance and the crystallographic point group symmetry including inversion. For cubic, hexagonal and tetragonal point groups, the possible symmetries of the superconducting phase are classified, and the free energy is used to construct a generalized phase diagram. We identify the leading candidate out of the possible SSS phases for each point group. The symmetry of the superconducting phase is used to determine the cases where the gap function has generic zeros (point or line nodes) on the Fermi surface. Such nodes always occur, hence thermodynamic properties will have power-law behavior at low temperature.