Temperature dependence of positron annihilation parameters in Tl-Ba-Ca-Cu-O superconductors

The results of positron lifetime and Doppler broadened line-shape parameter measurements as a function of temperature, across ${\mathit{T}}_{\mathit{c}}$, in the Tl-Ba-Ca-Cu-O superconductors are presented. The bulk lifetime in the normal state is found to decrease with the increase in the number of ${\mathrm{CuO}}_2$ layers. Different temperature dependencies of the annihilation parameters are observed in the various Tl systems containing different numbers of ${\mathrm{CuO}}_2$ layers. In the ${\mathrm{Tl}}_2$${\mathrm{Ba}}_2$${\mathrm{Ca}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{10}$ system, an increase in lifetime is observed below ${\mathit{T}}_{\mathit{c}}$, whereas in ${\mathrm{Tl}}_2$${\mathrm{Ba}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$, a decrease in lifetime is seen below ${\mathit{T}}_{\mathit{c}}$. In the ${\mathrm{Tl}}_2$${\mathrm{Ba}}_2$${\mathrm{CuO}}_6$ system, the lifetime is observed to be temperature independent. The different temperature variations of positron annihilation parameters are discussed in the light of the positron density distribution, obtained with use of the results of the self-consistent orthogonalized linear combination of atomic orbitals band-structure calculations. It is argued that the different temperature dependencies of the annihilation parameters is related to the positron density distribution within the unit cell and arise due to local charge transfer in the vicinity of the ${\mathrm{CuO}}_2$ layer in the superconducting state.