Select the low-temperature state of the two-dimensional E representation

Determine whether the low-temperature superconducting state of the two-dimensional E representation in the noncentrosymmetric two-orbital triangular-lattice model with Rashba, Ising, and orbital spin-orbit coupling is nematic or chiral by evaluating the quartic Ginzburg–Landau free energy or performing a self-consistent nonlinear gap calculation.

Background

The linearized Eliashberg equation identifies the twofold-degenerate E-representation pairing instability but does not determine how its two basis components combine below the superconducting transition. A real combination may produce a nematic nodal state, whereas a complex combination may produce a chiral state that spontaneously breaks time-reversal symmetry and can gap some or all of the nodal structure.

The paper therefore restricts its analysis to the pairing instability and dominant spin-orbital structure. Resolving the actual low-temperature order requires information beyond the linearized theory, specifically the quartic Ginzburg–Landau coefficients or a fully self-consistent nonlinear solution of the superconducting gap equation.

References

A remaining issue concerns the internal order-parameter selection within the two-dimensional $E$ representation. The linearized theory determines the instability at $$ but not whether the low-temperature state is nematic or chiral. This requires a quartic Ginzburg-Landau analysis or a self-consistent nonlinear gap calculation and is left for future work.

— Pairing-channel reconstruction by Ising spin-orbit coupling in a multiorbital triangular-lattice model  (2610.21369 - Wang et al., 15 Oct 2026) in Section 4, Discussion and conclusions; related discussion in Section 3.1, “E representation: Ising-triplet sector”