The results of positron lifetime and Doppler broadened line-shape parameter measurements as a function of temperature, across Tc, 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 CuO2 layers. Different temperature dependencies of the annihilation parameters are observed in the various Tl systems containing different numbers of CuO2 layers. In the Tl2Ba2Ca2Cu3O10 system, an increase in lifetime is observed below Tc, whereas in Tl2Ba2CaCu2O8, a decrease in lifetime is seen below Tc. In the Tl2Ba2CuO6 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 CuO2 layer in the superconducting state.
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