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DopedCuprate< Superconductivity.ResistivityVsTemperature | Index | Superconductivity.FeSe > The t-J model The full d-p Hamiltonian contains d electrons and ligand electrons. In the hole picture it contains d holes and ligand holes. First of all double electron occupancy on d sites is too costly and it is projected out of possible final states, although they are taken into account perturbatively (as virtual states). The d and p orbitals of the charge transfer insulator give rise to a model where the injection of one hole stabilizes the Zhang-Rice singlet. This state is obtained as the symmetrized superposition of Wannier states of holes in p orbitals next-neighbour to a given Cu d electron. The singlet antisymmetric orbital as well as the triplet states are all more than 5 eV above the singlet symmetric state, and they are ignored. The cretion operator {$c_{i,\sigma}$} for the hole in such a state consists of a suitable superposition of {$ p_{l,\sigma}$} creators. The hopping integral for the ZR singlet may be evaluated in terms of the same intergals appearing in the d-p Hamiltonian and it corresponds to the exchange of a hole and a localized spin. Since {$d$} hopping as such is neglected because it would lead to double occupancy, whose virtual state effects are taken into account perturbatively to second (up to fourth) order, the effective Hamiltonian may be rewritten in terms of the {$c_{i\sigma}$} alone {$ {\cal H} = - \sum_{(i,j),\sigma} P_G(t_{ij}c^\dagger_{i\sigma}c_{j\sigma}+h.c.)P_G + J \sum_{(i,j)}\mathbf{S}_i\cdot\mathbf{S}_j $} where {$\mathbf{S}_i= {1 \over 2} \sum_{\alpha\beta} c^\dagger_{i\alpha} \mathbf{\sigma}_{\alpha\beta} c_{i\beta}$} is the spin operator associated with the hole delocalizes over the symmetric net of oxygen sites ({$\mathbf{\sigma}$} are usual the Pauli matrices) and {$P_G=\prod_i(1-n_{i\uparrow}n_{i\downarrow}),$} This t-J Hamiltonian is similar but not perfectly equivalent to the Hubbard model. It requries further constraints, such as, for example {$U\approx 12t$}, strong coupling, etc. the Gutzwiller projection operator, guarantees the exclusion of doubly occupied hole states. Standard values are {4t=0.4$} eV, {$J=0.13$} eV, and the second nearest neighbor hopping, {$t^\prime=-0.12$} eV. The latter is negative(!) and, according to Pavarini, the higher absolute value, the higher Tc. < Superconductivity.ResistivityVsTemperature | Index | Superconductivity.FeSe > |