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The idea of employing non-Abelian statistics for error-free quantum computing ignited interest in recent reports of topological surface superconductivity and Majorana zero modes (MZMs) in FeTe$_{0.55}$Se$_{0.45}$. An associated puzzle is that the topological features and superconducting properties are not observed uniformly across the sample surface. Understanding and practical control of these electronic inhomogeneities present a prominent challenge for potential applications. Here, we combine neutron scattering, scanning angle-resolved photoemission spectroscopy (ARPES), and microprobe composition and resistivity measurements to characterize the electronic state of Fe$_{1+y}$Te$_{1-x}$Se$_{x}$. We establish a phase diagram in which the superconductivity is observed only at sufficiently low Fe concentration, in association with distinct antiferromagnetic correlations, while the coexisting topological surface state occurs only at sufficiently high Te concentration. We find that FeTe$_{0.55}$Se$_{0.45}$ is located very close to both phase boundaries, which explains the inhomogeneity of superconducting and topological states. Our results demonstrate the compositional control required for use of topological MZMs in practical applications.
Single crystals of Fe(1+x)Te(1-y)Se(y) have been grown with a controlled Fe excess and Se doping, and the crystal structure has been refined for various compositions. The systematic investigation of magnetic and superconducting properties as a functi
The iron chalcogenide Fe$_{1+y}$Te$_{1-x}$Se$_{x}$ on the Te-rich side is known to exhibit the strongest electron correlations among the Fe-based superconductors, and is non-superconducting for $x$ < 0.1. In order to understand the origin of such beh
We compare the superconducting phase-diagram under high magnetic fields (up to $H = 45$ T) of Fe$_{1+y}$Se$_{0.4}$Te$_{0.6}$ single crystals originally grown by the Bridgman-Stockbarger (BRST) technique, which were annealed to display narrow supercon
We report the achieving of depairing current limit along $c$-axis in Fe$_{1+y}$Te$_{1-x}$Se$_x$ single crystals. A series of crystals with $T_{rm{c}}$ ranging from 8.6 K to 13.7 K (different amount of excess Fe, $y$) were fabricated into $c$-axis bri
Neutron scattering has played a significant role in characterizing magnetic and structural correlations in Fe$_{1+y}$Te$_{1-x}$Se$_x$ and their connections with superconductivity. Here we review several key aspects of the physics of iron chalcogenide