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We compare the superconducting phase-diagram under high magnetic fields (upto $H = 45$ T) of Fe$_{1+y}$Se$_{0.4}$Te$_{0.6}$ single crystals originallygrown by the Bridgman-Stockbarger (BRST) technique, which were annealed todisplay narrow superconducting transitions and the optimal transitiontemperature $T_c \gtrsim 14$ K, with the diagram for samples of similarstoichiometry grown by the traveling-solvent floating-zone technique as well aswith the phase-diagram reported for crystals grown by a self-flux method. Wefind that the so-annealed samples tend to display higher ratios $H_{c2}/T_c$,particularly for fields applied along the inter-planar direction, where theupper critical field $H_{c2}(T)$ exhibits a pronounced downward curvaturefollowed by saturation at lower temperatures $T$. This last observation isconsistent with previous studies indicating that this system is Pauli limited.An analysis of our $H_{c2}(T)$ data using a multiband theory suggests theemergence of the Farrel-Fulde-Larkin-Ovchnikov state at low temperatures. Adetailed structural x-ray analysis, reveals no impurity phases but anappreciable degree of mosaicity in as-grown BRST single-crystals which remainsunaffected by the annealing process. Energy-dispersive x-ray analysis showedthat the annealed samples have a more homogeneous stoichiometric distributionof both Fe and Se with virtually the same content of interstitial Fe as thenon-annealed ones. Thus, we conclude that stoichiometric disorder, in contrastto structural disorder, is detrimental to the superconducting phase diagram ofthis series under high magnetic fields. Finally, a scaling analysis of thefluctuation conductivity in the superconducting critical regime, suggests thatthe superconducting fluctuations have a two-dimensional character in thissystem.

Disorder-dependent superconducting phase-diagram at high magnetic fields in Fe$_{1 + y}$Se$_{x}$Te$_{1-x}$ ($x \sim 0.4$)