Physical properties of ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{Ca}}_{\mathit{n}\mathrm{-}1}$${\mathrm{Cu}}_{\mathit{n}}$${\mathrm{O}}_{\mathit{y}}$ (n=1,2,3)

Polycrystalline samples of ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{Ca}}_{\mathit{n}\mathrm{-}1}$ ${\mathrm{Cu}}_{\mathit{n}}$ ${\mathrm{O}}_{\mathit{y}}$ with various hole concentrations were synthesized by substituting La for Sr, Y for Ca, and Pb for Bi. The superconducting properties, magnetic susceptibilities, Hall coefficients, and infrared optical reflection spectra were measured after sufficient characterization of the samples. For the n=1 (2:2:0:1) materials, the antiferromagnetic semiconductor–superconductor–normal-metal transition was observed with increasing hole concentration. In n=1 materials the Hall coefficient deviates strongly from the inverse of the hole concentration with increasing hole concentration. On the other hand, in the n=2 (2:2:1:2) materials the Hall coefficient roughly scales with the inverse of hole concentration even for the samples exhibiting superconductivity above liquid-nitrogen temperature. The edge structure in the infrared reflection spectra shifts to higher frequencies with increasing n, whereas it did not change at all when the hole concentration was varied within the same structure (n value). Together with the result of the magnetic-susceptibility measurement, these results are discussed in terms of the several models describing the normal state of high-${\mathit{T}}_{\mathit{c}}$ oxide superconductors.