Synthesis and superconducting properties of FeTe1-xSe Single Crystals under high magnetic fields

Single crystals of superconductor FeTe$_{1-x}$Se$_{x}$ (0.1 $\le $ x $\le $ 0.5) were synthesized using optical floating zone, Bridgeman technique, and solid stat reaction. The samples were synthesized under various temperature gradients and cooling rates. Crystals were characterized via EDX, X-ray scattering, magnetization and transport measurements. Upper critical fields Hc$_{2 }$as estimated through the Werthamer-Hohenberg-Helfand (WHH) formalism indicate that these materials strongly surpass the weak coupling Pauli limiting field indicating that the shape of their phase diagram under field is essentially controlled by the Pauli effect. Annealing, leads to a metallic temperature dependence of the resistivity, and to sharper superconducting transitions. Despite the relatively small increase in single crystallinity, as quantified by single crystal x-ray diffraction measurements, we observe a different phase diagram under high magnetic fields when compared to non-annealed samples.