Effect of hydrostatic pressure on ${\mathrm{HgBa}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{8+\delta }$ superconductor doped with Re

Samples of the ${\mathrm{Hg}}_{1-x}{\mathrm{Re}}_x{\mathrm{Ba}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{8+\delta }$ superconductor (Hg, Re-1223), with varying rhenium (Re) content $\mathrm{}(0.00<x<\mathrm{}0.30\mathrm{})\mathrm{}$ were produced with the help of a thermobaric analysis, which can monitor the total pressure inside the quartz tube during the synthesis at high temperatures. The sample quality was verified by means of Rietveld analysis of the x-ray-diffraction data, ac susceptibility, and by ac resistance measurements. The same procedure was used to prepare all the samples with different Re content (reduction of oxygen content in the precursor ${\mathrm{Re}}_x{\mathrm{Ba}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7+\delta }$ and the increase of the mercury partial pressure inside the quartz tube). The Re atoms lead to a reduction of the lattice parameter along the c axis with a decrease of the lattice volume which is equivalent to an applied hydrostatic pressure of 1 GPa. The aim of this work is a comparative and quantitative study of the chemical and external hydrostatic pressure on the Hg, Re-1223 system. The samples with $0.10<x<\mathrm{}0.25\mathrm{}$ showed strong magnetic shielding effects and low residual resistance. Resistance measurements as a function of temperature display an increase of the superconducting transition temperature $T_C$ with applied hydrostatic pressure. The $\partial T_C/\partial P$ value depends strongly on the Re doping and the sample with the Re content $x=0.18\mathrm{}$ showed the largest measured $\partial T_C/\partial P=6.8\mathrm{}\left(2\right)\mathrm{}\mathrm{K}/\mathrm{G}\mathrm{P}\mathrm{a}.$ We argue that the Re concentration does not increase $T_C$ in the same way as external hydrostatic pressure but provides a strong influence on the intrinsic term proposed by Almasan et al. [Phys. Rev. Lett. 69, 680 (1992)].