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18 CHAPTER 1. INTRODUCTION
the CuO 2 planes. Since none of this is accompanied by any major structural
change of the materials, it is quite natural to expect electronic correlations to
play a significant role in these systems. The notion of overdoped or underdoped
cuprates is frequently used to define the region of doping above, or below the
so-called optimal doping concentration at which the superconducting transition
temperature T c is highest. Obviously, holes and electrons doped into the antiferromagnetic
insulators are very efficient in destroying the magnetic order. In
La 2−x Sr x CuO 4 only 2% of holes are sufficient to achieve this. Therefore, the
charge carriers seem to couple strongly to the spin systems. However, there is an
apparent asymmetry between the electron and the hole-doped systems regarding
the stability of antiferromagnetism as well as that of superconductivity, since
the magnetic order is stable up to 30% in the electron doped side of the phase
diagram.
1.3 Theoretical approaches to superconductivity
Regarding theory, despite the huge research efforts and tremendous scientific
activity, the current understanding of both the normal state properties of the
cuprates as well as the nature of the superconducting phase remains incomplete.
Early on, it has been argued that many of the unusual properties of the
cuprates are related to the electronic structure of the CuO 2 planes. It is widely
believed that this structural unit supplies the carriers which form the superconducting
condensate. At present time, it is commonly accepted that the relevant
degrees of freedom in the perovskites are confined to the two dimension plans,
though the role of the out-of-plane oxygens, the so called apical oxygens, remains
unclear. Therefore, low dimensionality is one of the challenging aspects of the
carrier dynamics in the cuprates which is directly related to their layered crystal
structure.
Another challenging aspect from the theoretical point of view is that the electron
correlations constitute the key issue in the description of the elementary
excitations in the cuprates. Ab initio LDA calculations (Local Density Approximations)
corroborate the picture of strong local Coulomb correlations and give
an onsite electronic repulsion of about 10eV in the d x2−y2 orbitals [4], which are
located in the copper-oxide planes.
More importantly, the Fermi level in La 2 CuO 4 is located such that at halffilling
we get one hole per unit cell, which would exactly satisfy the valencies
of La + 2 ,O− 2 ,andCu+ 2 . Therefore, any picture within a simple band structure
theory would predict that at half-filling the cuprates have a metallic ground
state and fail to reproduce the insulating behavior of undoped La 2 CuO 4 . The
inconsistency of LDA is a direct consequence of an improper treatment of strong