Narrow carrier concentration range of superconductivity and critical point of pseudogap formation temperature in Pb-substituted Bi ₂Sr ₂CuO _6+δ

We have determined the precise T-p phase diagram of Pb-substituted Bi ₂Sr ₂CuO _6+δ by using the hole concentration p estimated from the Hall coefficient, and found that the superconducting region of Pb-substituted Bi ₂Sr ₂CuO _6+δ is rather narrow as compared with other Bi-based high-T _c cuprates. In Bi-based single-layer high-T _c cuprates, the width of the superconducting region becomes more narrow as the maximum T _c (T _c,max) gets smaller. This is different from other high-T _csuperconductors, in which T _c/T _c,max is described by a universal function of p. Furthermore, we have found that the p dependence of the pseudogap formation temperature T _*projects to zero at the critical point p _cr < 0.205{0.21, which is outside the superconducting region of Pb-substituted Bi ₂Sr ₂CuO _6+δ. Taking into account that p _cr of high-T _c cuprates is commonly located around p ∼ 0.19{0.21, it is concluded that whether p _cr is inside or outside the superconducting region simply depends on the width of the superconducting region.