Possible mechanisms of carrier localization, metal–insulator transitions and stripe formation in inhomogeneous hole-doped cuprates

Abstract

Possible mechanisms of carrier localization, metal–insulator transitions (MITs) and stripe formation in inhomogeneous hole-doped cuprates have been studied theoretically. Three distinctly different scenarios are proposed for the carrier localization in three-dimensional (3D) lightly doped cuprates in which the self-trapping and pairing of hole carriers (i) near the small-radius dopants and (ii) in a defect-free deformable lattice lead to the formation of the extrinsic and intrinsic (bi)polaronic states in the charge-transfer gap of the cuprates, and (iii) the self-trapping of carriers away from the large-radius dopants results in the formation of the in-gap hydrogenic impurity states. The binding energies and radii of the extrinsic and intrinsic large (bi)polarons in cuprates are calculated variationally using the continuum model and adiabatic approximation. We have shown that the extrinsic and intrinsic 3D large bipolarons exist in lightly doped cuprates at η = ε ∞ / ε 0 < 0.127 and η < 0.138 , respectively, where ε ∞ ( ε 0 ) is the optic (static) dielectric constant. While the optical bipolarons can exist if η < 0.134 and the Fröhlich coupling constants α are greater than 5.8. The dopant- and carrier-driven inhomogeneities favor the specific charge ordering in the form of a 3D network of carrier-rich and carrier-poor stripes and the formation of different superlattices and in-gap bands of dopants and large polarons. The localized in-gap states develop into metallic states at some critical doping levels. We use the uncertainty relation to obtain the specific conditions for the Mott, Anderson and new MITs in cuprates. The applicability limits of these MITs in cuprates are clarified. We argue that the new MITs in the cuprates caused by the strong carrier–defect–phonon and carrier–phonon interactions are accompanied by the formation of a 3D self-organized network of carrier-poor (insulating) and carrier-rich (metallic) stripes, which coexist in a wide range of doping x ≃ 0.02 − 0.20 , and the suppression of superconductivity observed in underdoped region near the x=1/8 is caused by the formation of insulating stripes on a global scale and by the preponderance of insulating phase compared with the metallic one. Our results are in good agreement with the existing experiments on La-based and other cuprates.