Depressions of T$_C$ in the superconducting dome of La-Bi2201 and PbLa-Bi2201

In the generic phase diagram of the hole-doped cuprates, the superconducting transition temperature (T$_C$) versus hole-doping is typically illustrated as a flipped parabola which exhibits the maximum at around 16\% of hole doping. But there is also the possibility of a generic existence of depressions within this superconducting dome: At certain hole-dopings, the TC drops. For La$_{2-x}$Ba$_x$CuO$_4$, the famous 1/8 depression [1] is widely accepted. La$_{2-x}$Sr$_x$CuO$_4$ also exhibits this 1/8 depression, but other fractional depressions (``magic doping fractions'') are suggested for this material [2]. We will show that for two structurally quite different single-layered Bi cuprates, namely La-Bi2201 and PbLa-Bi2201, also depressions at certain hole dopings exist. Possible consequences of the assumed generality of these depressions will be discussed.\\[4pt] [1] A. R. Moodenbaugh et al., Phys. Rev. B 38, 4596 (1988).\\[0pt] [2] S. Komiya et al., Phys. Rev. Lett. 94, 207004 (2005).