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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
1.3. THEORETICAL APPROACHES TO SUPERCONDUCTIVITY 19 T [K] 400 Normal state T* Tc SC AF Pseudogap Phase SC 0.1 0. 0.1 0.2 electron doping hole doping Landau Fermi Liquid QCP Tc x Figure 1.2: Simple Sketch of the phase diagram of the copper oxide superconductors. The system is a Mott insulator at half-filling (x = 0) and the ground-state is antiferromagnetic. The antiferromagnetism is progressively destroyed when additional holes are put in the two dimensional planes (x >0) or when holes are removed from the planes (x
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112 CHAPTER 5. THE FLUX PHASE FOR T
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176 CHAPTER 7. CONCLUSION is the st
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178 CHAPTER 7. CONCLUSION although
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180 BIBLIOGRAPHY [17] E. Dagotto. R
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182 BIBLIOGRAPHY [59] F. F. Assad.
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184 BIBLIOGRAPHY [98] M. Posternak,
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186 BIBLIOGRAPHY [136] B. Fauqué,
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188 BIBLIOGRAPHY
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190 APPENDIX A. DETERMINANTS AND PF
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192 APPENDIX B. A PAIR OF PARTICLES
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Education • Reviewer activity at
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2. Model of strongly correlated ele
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List of publications 1. Ising Trans
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Schools, workshops and conferences
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