We have investigated the effects of post-annealing on the Tc of (Hg,Tl)-22(n - 1)n (n =1-5) superconductors synthesized under high pressure. Reducing treatments in Ar, 3% H2/Ar or 5% H2/N2 were found to be effective in increasing the Tc of the n = 2-5 compounds, in particular for the (Hg,Tl)-2212 and (Hg,Tl)-2223 phases. Such enhancement in Tc is considered to be caused by the optimization of the hole concentrations in these compounds. The highest Tc of 120 K in this series was recorded for the n = 3 phase after post-annealing in 5% H2/N2. Though the 2201 sample did not show superconductivity even after the reducing treatments, superconductivity below 36 K was observed by substituting 40 % Nd for Ba. It is considered that our as-synthesized samples with n = 1-3 and n = 4, 5 are highly overdoped and slightly overdoped, respectively.
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