Accelerated modes of obtaining Ti(Bi)-HTSC ceramic samples and its record characteristics in the Hubbard model

Accelerated modes of synthesis of thallium-containing samples (tablets) of HTSC ceramics with record superconducting transition temperatures ($T_c$ = 124 K or more) and with critical current densities $(J_c)$ up to thousands of A/cm$^2$ were found. A technology of stable standard (two-stage) accelerated synthesis (less than a day instead of 48 hours) of thallium HTS ceramics has been developed. The synthesis process has been significantly reduced in time (compared to the known two-stage technologies). According to the fractures of the conduction curves $\sigma(T)$ and magnetic susceptibility $\chi(T)$, possible values of $T_c$ up to 205 K are determined. In the Hubbard model, the dependences of $T_c(x)$, magnetic susceptibility $\chi(T)$ and conductivity $\sigma(T)$ on the concentration of $x$ cations Ме$^{2+}_x$, Me = Pb or Bi, and temperature $T$ are determined. The results of the relevant calculations are consistent with the experimental data.