Criterion for vestigial order above two-component superconductors from Ginzburg-Landau theory*

MxBi2Se3 displays nematic superconductivity, where the two-component superconducting order parameter breaks both the U(1) symmetry and the lattice rotational symmetry. More recent experiments [1, 2] seem to have shown that the rotational symmetry breaking occurs at a temperature slightly higher than the superconducting Tc. In the so-called "vestigial order" [3] scenario, the rotational symmetry breaking is driven by the fluctuation of the same superconducting order parameter. By studying the Ginzburg Landau theory with fluctuation, we rule out this scenario for a very large portion of the parameter space: the existence of this vestigial order phase requires some extreme choice of the parameters, that seems exceedingly unlikely for the case of MxBi2Se3. The same GL theory can be easily generalized to describe a p-wave chiral superconductor. For the chiral case, the possibility of a vestigial phase, where the time-reversal symmetry breaking occurs in the normal state above TC, has been discussed theoretically [4] but found little experimental support in Sr2RuO4 [5], the most prominent candidate material. Our result also helps to clarify the non-observation of the vestigial phase there. The present result has implication on any two-component superconductors.

1. Sun et al, Phys. Rev. Lett. 123, 027002 (2019)

2. Cho et al, Nat. Comm. 11, 3056 (2020)

3. Hecker and Schmalian, npj Quantum Material 3, 26 (2018)

4. Fischer and Berg, Phy. Rev. B 93, 054501 (2016)

5. Grinenko et al, Nat. Comm. 12:3920 (2021)