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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Mott, N.F.: Metal-insulator transitions. Taylor and Francis, London (1990)
Fink, J., Nicker, N., Alexander, M., et al.: High-energy spectroscopy studies of high-\(\text{ T }_{{\rm c}}\) superconductors. Physica C 185–189, 45 (1991)
Boebinger, G.S., Ando, Y., Passner, A., et al.: Insulator-to-metal crossover in the normal state of \(\text{ La }_{2-{\rm x}}\text{ Sr }_{{\rm x}}\text{ CuO }_{4 }\) near optimum doping. Phys. Rev. Lett. 77, 5427 (1996)
Kastner, M.A., Birgeneau, R.J., Shirane, G., Endoh, Y.: Magnetic, transport, and optical properties of monolayer copper oxides. Rev. Mod. Phys. 70, 897 (1998)
Lavrov, A.N., Gantmakher, V.F.: Low-temperature resistivity of underdoped cuprates. Phys. Usp. 41, 223 (1998)
Abrikosov, A.N.: Resonant tunneling in high-\(\text{ T }_{{\rm c}}\) superconductors. Phys. Usp. 41, 605 (1998)
Imada, M., Fujimori, A., Tokura, Y.: Metal-insulator transitions. Rev. Mod. Phys. 70, 1039 (1998)
Matchetti, P.A., Su, Z.-B., Lu, Yu.: Metal-insulator crossover in superconducting cuprates in strong magnetic fields. Phys. Rev. Lett. 86, 3831 (2001)
Konstantinovic, Z., Li, Z.Z., Raffy, H.: Evolution of the resistivity of single-layer \(\text{ Bi }_{2}\text{ Sr }_{1.6}\text{ La }_{0.4}\text{ CuO }_{{\rm y}}\) thin films with doping and phase diagram. Physica C351, 163 (2001)
Stojkovic, B.P., Pines, D.: Theory of the longitudinal and Hall conductivities of the cuprate superconductors. Phys. Rev. B 55, 8576–8595 (1997)
Emin, D.: Disorder effects on small-polaron formation and hopping. Int. J. Mod. Phys. B 8, 819 (1994)
Quemerias, P.: Crystallization of Polarons in Doped Ionic Materials. Mod. Phys. Lett. B 9, 1665 (1995)
Dzhumanov, S.: Possible insulating, metallic and superconducting states in doped high-\(\text{ T }_{{\rm c}}\) superconductors. Solid State Commun. 115, 155 (2000)
Ando, Y., Ono, S., Sun, X.F., Takeya, J., Balakirev, F.F., Betts, J.B., Boebinger, G.S.: Quantum Phase Transitions in the Cuprate Superconductor \(\text{ Bi }_{2}\text{ Sr }_{2-{\rm x}}\text{ La }_{{\rm x}}\text{ CuO }_{6+\delta }\). Phys. Rev. Lett. 92, 247004 (2004)
Dzhumanov, S., Kurbanov, U.T., Kurmantayev, A.: Possible quantitative criteria for the mott and anderson transitions in doped uncompensated systems. Int. J. Mod. Phys. B 2, 12 (2007)
Finkel, B.A.: Low-temperature electric conductivity of \(\text{ YBa }_{2}\text{ Cu }_{3}\text{ O }_{7-\delta }\) ceramic high-\(\text{ T }_{{\rm c}}\) superconductors with different oxygen concentrations. Fiz. Nizk. Temp 28, 687 (2002)
Tsendin, K.D., Denisov, D.V., Popov, B.P.: Unified model of pseudogap features of conductivity in HTSCs. Pisma v Zh. Eksp. Teor. Fiz. 80, 277 (2004)
Ridley, B.: Quantum Processes in Semiconductors. Mir, Moscow (1986)
Toyozawa, Y.: Electron induced lattice relaxations and defect reactions. Physica B 116, 7 (1983)
Dzhumanov, S., Baratov, A.A.: Rep. of Uzbek Academy of Sciences. 4, 16 (1995)
Dzhumanov, S., Baratov, A.A., Abboudy, S.: Pairing theory of polarons in real and momentum space. Phys. Rev. B 54, 13121 (1996)
Lu, J.P., Si, Q.: Spin polarons in high-\(\text{ T }_{{\rm c}}\) copper oxides: Differences between electron- and hole-doped systems. Phys. Rev. B 42, 950 (1990)
Verbist, G., Peeters, F.M., Devreese, J.T.: Possible (bi)polaron effects in the high-\(\text{ T }_{\rm c}\) superconductors. Phys. Scripta. T39, 66 (1991)
Emin, D., Hillery, M.S.: Formation of a large singlet bipolaron: Application to high-temperature bipolaronic superconductivity. Phys. Rev. B 39, 6575 (1989)
Baetzold, R.C.: Atomistic study of defects in \(\text{ YBa2Cu }_{3}\text{ O }_{7 }\). Phys. Rev. 42, 56 (1990)
Ino, A., Mizokawa, T., Kobayashi, K., Fujimori, A., Sasagawa, T., Kimura, T., Kishio, K., Tamasaku, K., Eisaki, H., Uchida, S.: Doping dependent density of states and pseudogap behavior in \(\text{ La }_{2-{\rm x}}\text{ Sr }_{{\rm x}}\text{ CuO }_{4}\). Phys. Rev. Lett. 81, 2124 (1998)
Walz, F.: The Verwey transition—a topical review. J. Phys.: Condens. Matter. 14, R285 (2002)
Dzhumanov, S.: Theory of conventional and unconventional superconductivity in the high-\(\text{ T }_{\rm c}\) cuprates and other systems. Nova Science, New York (2013)
Mott, N.F., Davis, E.A.: Electronic processes in noncrystalline materials. Mir, Moskow (1974)
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Dzhumanov, S., Khudayberdiev, Z.S. Anderson metal–insulator transition in doped polar cuprates. Quantum Stud.: Math. Found. 5, 75–81 (2018). https://doi.org/10.1007/s40509-017-0134-x
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DOI: https://doi.org/10.1007/s40509-017-0134-x