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164 CHAPTER 6. ORBITAL CURRENTS IN THE CUPRATES ducting instability in terms of the holes in the three-band Hubbard model. The symmetry that was found in our calculations, by the energy minimization of the RVB wavefunction, is shown in Fig. 6.19. We note that for a reference site i, ∆ ij consists of four strong plaquettes (bold square in Fig. 6.19) around the reference site. The sign of the pairing has a d-wave symmetry for these latter plaquettes, and additionally, inside each of the plaquette the sign is alternating identically to the Zhang-Rice singlet d ↑ (p x↓ − p −x↓ + p y↓ − p −y↓ ) symmetry. 6.11 Role of the Apical oxygens The theoretical challenge is to find the simplest model of the copper-oxygen plane which would contain all the essential physical aspects. The electronic structure calculations suggest that a good starting point is provided by the previously discussed three-band model, including coper 3d x2−y2 orbitals and oxygen 2p σ orbitals. It has been repeatedly argued that the two dimensional plane contains the essential of the low energy physics. Zhang and Rice pointed out that a hole in a copper d x2−y2 orbital and a hole in the oxygen orbital form a local singlet for the realistic parameters of the three-band Hamiltonian, and the three-band model does reduce to an effective single-band t-J model. However, one of the issues related to a breakdown of such a mapping is related to the presence of additional apical oxygens. It was proposed for example that a triplet states could be favored, instead of the singlet state, and stabilized by the occupancy of apical oxygens and copper d 3z 2 −r 2 orbitals. Indeed, since the early days of high-temperature superconductivity, the question of a possible role of apical sites in cuprates superconductors has been controversially discussed. A part of the measurements were consistent with the conjecture that there is a significant influence of the apical site on high-Tc superconductivity. Moreover, further theoretical investigations using a six-band Hubbard model interaction scheme showed that some holes with Cu3d 3z2−r2 orbital character do exist (experimental evidence for this can be found in Ref. [145]), and that a fraction of them is hybridized with the apical oxygen [146]. This can easily be understood, since there is a strong Coulomb repulsion between the holes at Cu sites, the extra holes introduced by doping residing primarily on oxygen sites. Furthermore, it has been pointed out that for a realistic description of the principal features of the cuprates superconductors, like for example the insulating gap in the undoped parent compounds, one has to include also the orbitals of apical oxygens. Several experiments indicate that the out-of-plane apical oxygen orbitals are also involved in accommodating some of the holes doped into the CuO 2 planes. One of the most exciting ones is that there might exist a correlation between the maximal critical temperature T c reached in different cuprates and the copper-toapex bonding, as well as the Madelung potential at the apical oxygen measured
6.11. APICAL OXYGENS 165 a) k b) k Figure 6.19: RVB variational parameters ∆ ij , where a reference site i is located at the site located at the center of the cluster, and j is running through all the site of the lattice. Red (blue) circles denotes positive (negative) ∆ ij ,andthe radius of the circle is proportional to |∆ ij |. Top: the reference site i is located on a copper site. Bottom : the reference site i is located on an oxygen site.
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VARIATIONAL STUDY OF STRONGLY CORRE
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4 Abstract
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6 Version abrégée
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8 Acknowledgments check that our di
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10 Acknowledgments
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12 CONTENTS 3.3.5 Order parameters
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14 CONTENTS
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16 CHAPTER 1. INTRODUCTION c Ba 2+
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18 CHAPTER 1. INTRODUCTION the CuO
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20 CHAPTER 1. INTRODUCTION local Co
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22 CHAPTER 1. INTRODUCTION that the
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24 CHAPTER 1. INTRODUCTION (Haldane
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26 CHAPTER 1. INTRODUCTION This can
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28 CHAPTER 1. INTRODUCTION A(r) by
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30 CHAPTER 1. INTRODUCTION • In C
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32 CHAPTER 2. NUMERICAL METHODS The
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34 CHAPTER 2. NUMERICAL METHODS Sin
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36 CHAPTER 2. NUMERICAL METHODS pai
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38 CHAPTER 2. NUMERICAL METHODS Whe
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40 CHAPTER 2. NUMERICAL METHODS var
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46 CHAPTER 2. NUMERICAL METHODS kno
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48 CHAPTER 2. NUMERICAL METHODS wit
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52 CHAPTER 3. T-J MODEL ON THE TRIA
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86 CHAPTER 4. HONEYCOMB LATTICE B A
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88 CHAPTER 4. HONEYCOMB LATTICE •
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104 CHAPTER 4. HONEYCOMB LATTICE M=
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108 CHAPTER 4. HONEYCOMB LATTICE Or
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110 CHAPTER 4. HONEYCOMB LATTICE
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112 CHAPTER 5. THE FLUX PHASE FOR T
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Page 180 and 181: 180 BIBLIOGRAPHY [17] E. Dagotto. R
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Page 186 and 187: 186 BIBLIOGRAPHY [136] B. Fauqué,
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Page 190 and 191: 190 APPENDIX A. DETERMINANTS AND PF
Page 192 and 193: 192 APPENDIX B. A PAIR OF PARTICLES
Page 198 and 199: Education • Reviewer activity at
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