A state of matter with a multi-component order parameter can give rise to vestigial order. In the vestigial phase, the primary order is only partially melted, leaving a remaining symmetry breaking behind, an effect driven by strong classical or quantum fluctuations. Vestigial states due to primary spin and charge-density-wave order have been discussed in iron-based and cuprate materials. Here we present the observation of a partially melted superconductivity in which pairing fluctuations condense at a separate phase transition and form a nematic state with broken Z 3 , i.e., three-state Potts-model symmetry. Thermal expansion, specific heat and magnetization measurements of the doped topological insulators Nb x Bi 2 Se 3 and Cu x Bi 2 Se 3 reveal that this symmetry breaking occurs at T nem ' 3:8 K above T c ' 3:25 K, along with an onset of superconducting fluctuations. Thus, before Cooper pairs establish long-range coherence at T c , they fluctuate in a way that breaks the rotational invariance at T nem and induces a crystalline distortion.

With the recent discovery of the quantum anomalous Hall insulator (QAHI), which exhibits the conductive quantum Hall edge states without external magnetic field, it becomes possible to create a novel topological superconductor by introducing superconductivity into these edge states. In this case, two distinct topological superconducting phases with one or two chiral Majorana edge modes were theoretically predicted, characterized by Chern numbers (N ) of 1 and 2, respectively. We present spectroscopic evidence from Andreev reflection experiments for the presence of chiral Majorana modes in a Nb / (Cr0.12Bi0.26Sb0.62)2Te3 heterostructure with unique signatures attributed to two different topological superconducting phases. The results are consistent with the theoretical predictions.

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