Origin of the Higher-$T_\rm{c}$ Phase in the K$_x$Fe$_{2-y}$Se$_2$ System

Single crystals of K$_x$Fe$_{2-y}$Se$_2$ are prepared by quenching at various temperatures. The crystals obtained at higher quenching temperatures have a surface morphology with mesh-like texture. They show a sharp superconducting transition at $T_\rm{c}$ ~32 K with a large shielding volume fraction. On the other hand, the crystals prepared without quenching show an onset superconducting transition at ~44 K and a zero resistivity around ~33 K, and they possess island-like regions on the surface with a larger amount of Fe incorporation. In-situ high-temperature single crystal X-ray diffraction measurements tell us the Fe-vacancy ordered phase is generated at a temperature region around 270 {\deg}C via iron diffusion. The creation of this Fe-vacancy ordered phase may become a driving force of the growth of the higher $T_\rm{c}$ phase. The superconductivity at ~44 K is attributed to a metallic phase with no Fe-vacancy.