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Results are presented from a theoretical study of the possibility of hole carrier localization and metal-insulator transitions which show up in the temperature dependences of the magnetic susceptibility χ(T) of doped copper-oxide (cuprate) compounds. The criteria for metal-insulator transitions owing to strong hole-lattice interactions and the formation of very narrow polaron bands in these materials with reduced doping level x are analyzed. It is shown that these kinds of metal-insulator transitions occur in underdoped La2-xSrxCuO4 and YBa2Cu3O6+x cuprates (i.e., for x ranging from 0.04 to 0.12). The characteristic temperature dependences χ(T) of the HTSC cuprates are found for different doping levels. These results are in good agreement with experimental data on metal-insulator transitions and the magnetic susceptibility of the HTSC cuprates.

We study the distinctive features of the metal-insulator transitions, multiscale phase separation, and evolution of coexisting insulating and metallic/superconducting phases in hole-doped cuprates. We show how these interrelated phenomena and related effects manifest themselves in a wide doping range from the lightly doped to optimally doped regime in these systems, where the localized and mobile hole carriers reside in hole-poor (insulating) and hole-rich (metallic or superconducting) regions. We argue that small hole-rich regions (i.e. narrow nanoscale metallic islands or stripes) can persist in the insulating phase of the lightly doped cuprates, while the competing insulating, metallic, and superconducting phases would coexist in the under-doped cuprates. When the doping level is increased further, the hole-poor regions (or insulating zones) gradually narrow from macroscale to nanoscale insulating stripes and disappear in the optimally doped cuprates. We demonstrate clearly that the metal-insulator transitions and the coexisting insulating and metallic/superconducting phases are manifested in the suppression of superconductivity in underdoped cuprates and in the different temperature-dependent behaviors of the magnetic susceptibility and c-axis resistivity of lightly to optimally doped cuprates.

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