Z3-vestigial nematic order due to superconducting fluctuations in the doped topological insulators NbxBi2Se3 and CuxBi2Se3

Abstract

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.

Misfit phase (BiSe)1.10NbSe2 as the origin of superconductivity in niobium-doped bismuth selenide

“…report a slight expansion in c on Nb doping, but do not report the estimated standard deviation and Cho et al 20 report a c lattice parameter of 28.4633(7) Å, which is much smaller than what we and Wang et al 19 find for pure Bi 2 Se 3 . Our previous work on Li 1-x Fe 1+x As samples showed that trends in lattice parameters arising from very small compositional changes could only be monitored by synchrotron radiation 27 .…”

“…In this paper and particularly in the supporting information we describe the structure in detail and show how (BiSe) 1.10 NbSe 2 compares with related misfit layered chalcogenides. This misfit phase corresponds to the peaks previously assigned to the BiNbSe 3 impurity 18 (which is of fairly similar composition) by Kobayashi et al 11 and by Cho et al 20 We observe that the amount of the phase present with the Bi 2 Se 3 structure (assumed to be the superconducting phase Nb x Bi 2 Se 3 in the literature 11,12,17,19,20,[22][23][24][25][26] , including very recent literature 19,20,24,25 ) in the samples decreases with increasing Nb content in the synthesis mixture and completely vanishes for x = 0.50 while the superconducting volume fraction of the sample is directly proportional to the Nb content of the sample. In addition we do not observe, with synchrotron resolution, a measurable caxis expansion of the Bi 2 Se 3 -structure phase upon Nb doping, suggesting that it is pure and undoped Bi 2 Se 3 .…”

“…Since the scanning electron microscopy (SEM) data of Supplementary Fig. S4 reveal that this Several papers report the presence of BiNbSe 3 impurities, but do not regard these impurities as relevant for the reported physical properties 11,19,20 . Wang et al 19 attempted to make this impurity as a pure phase, but no structure or physical properties were given.…”

“…This is in contrast to the variations stated in literature reports. However, these reports either do not refine the lattice parameters from the whole pattern 11 , or do not present any uncertainties on the refined values 19 , or do not make a comparison using the same measurement conditions with a pure Bi 2 Se 3 phase 20 . Wang et al 19 Supplementary Fig.…”

“…These impurities increased in fraction with increasing x and indeed they showed that the phase fraction of the proposed Nb x Bi 2 Se 3 phase with the Bi 2 Se 3 structure reaches zero (within the uncertainty) at x = 0.50. Work by Wang et al 19 and recent work by Cho et al 20 also show that Nb x Bi 2 Se 3 samples are multiphase in the bulk. Nevertheless, all these reports assign the superconductivity evident in these samples to a Nb-doped Bi 2 Se 3 -type phase.…”