The direction of the $d$-vector in a nematic triplet superconductor

TL;DR

This study explores the orientation and nature of triplet pairing states in nematic superconductors using mean field theory, revealing how lattice distortions and dimensionality influence the $d$-vector and pairing symmetry.

Contribution

It provides a theoretical analysis of how lattice distortions and dimensionality affect the $d$-vector orientation and pairing states in nematic triplet superconductors.

Findings

Weak warping favors chiral fully gapped states.

Stronger warping favors nodal and nematic states with $d$-vector along principal axis.

Lattice elongation can rotate the $d$-vector orthogonal to the elongation axis.

Abstract

We investigate the states of triplet pairing in a candidate nematic superconductor versus typical material parameters, using the mean field theory for two- and three-dimensional tight-binding models with local triplet pairing in the $E_u$ representation. In the two-dimensional model, the system favors the fully gapped chiral state for weaker warping or lower filling level, while a nodal and nematic $\Delta_{4x}$ state is favorable for stronger warping or higher filling, with the $d$-vector aligned along the principle axis. In the presence of lattice distortion, relative elongation along one of the principle axes, ${\bf a}$, tends to rotate the nematic $d$-vector orthogonal to ${\bf a}$, resulting in the nematic $\Delta_{4y}$ state at sufficient elongation. Three-dimensionality is seen to suppress the chiral state in favor of the nematic ones. Our results may explain the variety in the probed direction of the $d$-vector in existing experiments.