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

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 remaining nonsuperconducting. This has been suggested as an explanation for the observed normal state nematicity of nematic ${M}_{x}{\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$. We examine condition this to occur within Ginzburg-Landau theory parameter fluctuations, on both and chiral sides theory. Contrary prior theoretical results, we rule out large portion space possible order. argue that very extreme anisotropy is one prerequisite formation stable via mechanism, which likely not met in real materials.