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A state of matter with a multi-component order parameter can give rise tovestigial order. In the vestigial phase, the primary order is only partiallymelted, leaving a remaining symmetry breaking behind, an effect driven bystrong classical or quantum fluctuations. Vestigial states due to primary spinand charge-density-wave order have been discussed in the context of iron-basedand cuprate materials. Here we present the observation of a partially meltedsuperconductor in which pairing fluctuations condense at a separate phasetransition and form a nematic state with broken Z3, i.e. three-statePotts-model symmetry. High-resolution thermal expansion, specific heat andmagnetization measurements of the doped topological insulator NbxBi2Se3 revealthat this symmetry breaking occurs at Tnem=3.8 K above Tc=3.25 K, along with anonset of superconducting fluctuations. Thus, before Cooper pairs establishlong-range coherence at Tc, they fluctuate in a way that breaks the rotationalinvariance at Tnem and induces a distortion of the crystalline lattice. Similarresults are found for CuxBi2Se3.

$Z_3$-vestigial nematic order due to superconducting fluctuations in the doped topological insulator Nb$_x$Bi$_2$Se$_3$ and Cu$_x$Bi$_2$Se$_3$