Jahn-Teller effect in quasi-two-dimensional doped cuprate antiferromagnets and underdoped high-Tc superconductors (Review)

The theoretical aspects of research on the role of Jahn-Teller interactions in quasi-two-dimensional cuprate antiferromagnets and high-T-c superconductors (HTSCs) are analyzed. An analysis is made of results that permit one to establish a link between the quasi-two-dimensional character of the properties of underdoped cuprate HTSCs in the normal and superconducting states and the Jahn-Teller (JT) nature of the divalent copper ions. It is shown that the combination of these two features leads to the existence of a pseudogap state. In underdoped cuprate HTSCs with JT lattice distortions the quasi-two-dimensionality gives rise to two-dimensional local and quasilocal states of the charge carriers. This is manifested in substantial temperature dependence of the number of components of the localized and delocalized states of the charge carriers and in repeated dynamical reduction of the dimensionality of underdoped cuprate HTSCs as the temperature is lowered. Such a HTSC, with doping concentrations less than optimal, is found in a quasi-two-dimensional state in the greater part of its phase diagram, both in the normal and superconducting states. This means that the superconducting state of underdoped cuprate HTSCs differs from the BCS state and is closer in its properties to the state of a two-dimensional Berezinskii-Kosterlitz-Thouless (BKT) superconductor without off-diagonal long-range order (ODLRO). It is shown that the difference primarily consists in the mechanism of superconductivity. In spite of the fact that a strong JT electron-phonon interaction in underdoped cuprate HTSCs plays a key role and leads to the formation of two-site JT polarons, the attraction between holes and such polarons and the formation of a superfluid two-site JT polaron with an antiferromagnetic core are due to compensation of the Coulomb repulsion by the polaron energy shift. The hypothesis that the superconducting state in overdoped cuprate HTSCs is a consequence of the establishment of ODLRO in the three-dimensional BCS model with nonconserved total number of charge carriers and nonzero quantum fluctuations of the number of charge carriers is discussed. (C) 2004 American Institute of Physics.