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A nematic superconductor can in principle support a vestigial order phaseabove its superconducting transition temperature, with rotational symmetryspontaneously broken while remain nonsuperconducting. We examine the conditionfor this vestigial nematic order to occur, within a Ginzburg-Landau theory withorder parameter fluctuations included. Contrary to prior theoretical results,we found that this vestigial order actually requires very stringent conditionsto be met: the material must be sufficiently deep in the nematic regime (i.e.far away from the boundary separating the nematic and chiral superconductingphases) to possibly exhibit a vestigial nematic order.

Criterion for Vestigial Order above a Nematic Superconductor