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$\require{mhchem}$Misfit phase $\ce{(BiSe)_{$1.10$}NbSe2}$ as the origin of superconductivity in nobium-doped bismuth selenide

$\require{mhchem}$Topological superconductivity is of great contemporary interest and has been proposed in doped $\ce{Bi2Se3}$ in which electron-donating atoms such as Cu, Sr or Nb have been intercalated into the $\ce{Bi2Se3}$ structure. For $\ce{Nb_{x}Bi2Se3}$, with $\text{T}_\text{c} \sim 3 \ \text{K}$, it is assumed in the literature that Nb is inserted in the van der Waals gap. However, in this work an alternative origin for the superconductivity in Nb-doped $\ce{Bi2Se3}$ is established. In contrast to previous reports, it is deduced that Nb intercalation in $\ce{Bi2Se3}$ does not take place. Instead, the superconducting behaviour in samples of nominal composition $\ce{Nb_{x}Bi2Se3}$ results from the $\ce{(BiSe)_{$1.10$}NbSe2}$ misfit phase that is present in the sample as an impurity phase for small $x$ ($0.01 \leq x \leq 0.10$) and as a main phase for large $x$ ($x = 0.50$). The structure of this misfit phase is studied in detail using a combination of X-ray diffraction and transmission electron microscopy techniques.