Relationship between superconductor and metal-insulator transitions in a large class of tetragonal 1:2:3 cuprates Ca-R-Ba-Cu-O (R=La,Nd)

We report superconductor and transport properties of a large class of tetragonal 1:2:3 cuprates represented by the chemical formula (${\mathrm{Ca}}_{\mathit{xR}1\mathrm{-}\mathit{x}}$)[${\mathrm{Ba}}_{3\mathrm{-}\mathit{z}\mathrm{-}\mathit{x}}$ ${\mathit{R}}_{\mathit{z}\mathrm{-}\left(1\mathrm{}\mathrm{-}\mathit{x}\right)}$]${\mathrm{Cu}}_3$ ${\mathrm{O}}_{\mathit{y}}$, where R=La or Nd and existing as high-purity materials in a large range of z and x. At a given z, these materials maintain, through compensating cosubstitutions, a constant charge Q of the noncopper cations (Q=6+z) independent of x. By accurate control of oxygen content y, both cation and anion charge sources were kept constant. Under these isoelectronic conditions (constant electron concentration n) big changes in transition temperature ${\mathit{T}}_{\mathit{c}}$, resistivity ρ and thermopower (TEP) S occur, suggesting that the microscopic hole density in the ${\mathrm{CuO}}_2$ planes h changes. Having a single ${\mathit{T}}_{\mathit{c}}^{\max }$ (maximal ${\mathit{T}}_{\mathit{c}}$), this material family behaves as a single material. Besides, for all values of Q, x, and y and for each R we show that ${\mathit{T}}_{\mathit{c}}$, ρ, and S can each be represented by a single curve when plotted as a function of y-${\mathit{y}}_{\mathrm{M}\mathrm{-}\mathrm{I}}$(Q,x), where ${\mathit{y}}_{\mathrm{M}\mathrm{-}\mathrm{I}}$ denotes the value of y at the metal-insulator (M-I) transition. Therefore, there exists a one to one correspondence between h and y-${\mathit{y}}_{\mathrm{M}\mathrm{-}\mathrm{I}}$, but there is no straightforward relation between h and n. We found an empirical formula describing the functional dependence of ${\mathit{y}}_{\mathrm{M}\mathrm{-}\mathrm{I}}$ on Q and x. This allows one to estimate ${\mathit{y}}_{\mathrm{M}\mathrm{-}\mathrm{I}}$, ${\mathit{T}}_{\mathit{c}}$, ρ, and S in many materials. Our results are interpreted in terms of a simple band picture which is modified to consider the existence of low-mobility states in the vicinity of ${\mathit{E}}_{\mathit{F}}$. This accounts for the relatively low TEP at the M-I transition.