Abstract

In this paper, we investigate the possibility of the Anderson transition for polarons, different dopants, and impurities in doped cuprates. We have developed the continuum theory of carrier self-trapping in a deformable lattice and near different dopants (impurities), the appropriate variational methods and tight-binding model for studying the formation of the localized hole states and the narrow energy bands of large polarons and dopants (impurities) in hole-doped cuprates $$\mathrm{La}_{2-x}\mathrm{Sr}_{x}\mathrm{CuO}_{4}$$ (LSCO) and $$\mathrm{YBa}_{2}\mathrm{Cu}_{3}\mathrm{O}_{7-\delta }$$ (YBCO). To develop the quantitative theory of the Anderson localization and derive the adequate quantitative criteria for the Anderson metal–insulator transition (MIT) in doped materials, we have studied localized states of non-interacting hole carriers in crystalline solids and metal–insulator transitions (MITs) caused by disorder in distribution of large polarons, dopants (or impurities). It is suggested that the large polarons, dopants, and impurities from different superlattices with different degrees of disorder. We have considered a crystalline array of potential wells with the depth $$U = U_{0}$$ in the absence of disorder and developed the approximate methods for the quantitative estimation of the possible changes (or fluctuations) of the depth U of these potential wells between the limits $$U_{0}-V_{0}/2<U<U_{0}+V_{0}/2$$ in the presence of disorder, where $$V_{0}$$ is a random potential which is determined as the amplitude of the change of U due to random distribution of large polarons and dopants (impurities). Using the uncertainty principle, we have obtained the new and more adequate criteria for the Anderson transition in doped polar materials and analyzed the applicability of these criteria to the hole-doped cuprates both in the absence and in the presence of polaronic effects. We have shown that our theoretical results on Anderson MIT obtained by taking into account polaronic effects are in quantitative agreement with the well-established experimental results on MITs in hole-doped cuprates LSCO and YBCO.

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