Superconductivity at T_c ~ 14 K in Single Crystalline FeTe$_{0.61}$Se$_{0.39}$

Single crystalline FeTe$_{0.61}$Se$_{0.39}$ with a sharp superconducting transition at $T_{textrm{c}} sim$ 14 K is synthesized via slow furnace cooling followed by low-temperature annealing. The effect of annealing on the chemical and superconducting inhomogeneities is carefully characterized. We also report resistivity, magnetization, and magneto-optical images of this crystal. Based on the Bean model, critical current density is estimated to exceed $1 times 10^5$ A/cm$^2$ below 5 K under zero field. Weak fish-tail effect is identified at lower temperatures.