Title: Single-Crystal Growth and Characterization of Cuprate Superconductor (Hg,Re)Ba$_2$Ca$_2$Cu$_3$O$_{8+δ}$

Abstract: We grew (Hg,Re)Ba$_2$Ca$_2$Cu$_3$O$_{8+\delta}$ ((Hg,Re)1223) single crystals with good reproducibility via the single-step flux method using monoxides as raw materials. A double-sealing method using a thick-walled quartz tube and a stainless-steel container was adopted for explosion protection. The maximum crystal size was approximately 1 mm x 1 mm in the ab plane and 0.04 mm in thickness. The crystal was square-shaped, reflecting the tetragonal crystal structure of (Hg,Re)1223. Magnetic susceptibility measurements indicated a critical temperature of 130 K. The in-plane resistivity exhibited a linear temperature dependence, indicating that the sample was close to optimal doping level. The out-of-plane resistivity was also measured, and the anisotropy parameter was 250-650 at 300 K.