The absence of Ginzburg-Landau mechanism for vestigial order in the normal phase above a two-component superconductor

TL;DR

This paper investigates the possibility of vestigial order in two-component superconductors above the transition temperature and finds that such order is unlikely under realistic conditions, challenging previous theoretical suggestions.

Contribution

The study demonstrates that Ginzburg-Landau theory with fluctuations does not support vestigial order in most realistic scenarios, contrary to prior claims.

Findings

Vestigial order is unlikely in typical parameter regimes.

Extreme anisotropy is required for vestigial phase stability.

Most of the parameter space for vestigial order is ruled out.

Abstract

A two-component superconductor may hypothetically support a vestigial order phase above its superconducting transition temperature, with rotational or time-reversal symmetry spontaneously broken while remain non-superconducting. This has been suggested as an explanation to the observed normal state nematicity of the nematic superconductor $M_x$Bi$_2$Se$_3$. We examine the condition for this vestigial order to occur within Ginzburg-Landau theory with order parameter fluctuations, on both the nematic and chiral sides of the theory. Contrary to prior theoretical results, we rule out a large portion of parameter space for possible vestigial order. We argue that very extreme anisotropy is one prerequisite for a stable vestigial phase, which is likely not met in real materials.