The electronic $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}U\text{\ensuremath{-}}J$ model for the
CuO2 plane in high-
Tc superconducting cuprates is elaborated. It incorporates both charge transfer
U and exchange correlation
J with direct
t and diagonal ${t}^{\ensuremath{'}}$ hopping. Making use of the Yang concept of the off diagonal long range order (ODLRO) in the reduced density matrix of the electronic system we study the loss of quantum wave coherence (and thereby superconductivity) due to the Coulomb interaction. To this aim the second-quantized Hamiltonian of the model is translated to the phase representation with the help of the topologically constrained path integral formalism. As a result the electrons emerge as composite particles consisting of of spin-carrying neutral fermions and charged topological bosons in a form of ``flux tubes'' with the quantum phase variable dual to the local electron density. The charge carrying bose field forms a collective variable representing the correlated ``sliding'' motion of the entire electronic system. We found that the spin gap $\ensuremath{\Delta}$ which appears in one-particle spectrum is the result of valence bond pairing of neutral fermions without ODLRO and deduce the solution for $\ensuremath{\Delta}$ with ``
d-wave'' symmetry. In the bosonic sector we derive the effective quantum rotor model along with microscopic phase stiffnesses setting the energy scale for superconductivity and point out the special role played by the diagonal hopping ${t}^{\ensuremath{'}}$. We explore the relationship of the quantum rotor phase model and the Bose-Hubbard system emphasizing the ring topology of quantum phase variable. Furthermore, we obtain the ground state phase diagrams which facilitate the Mott insulator-superconductor transition scenario. We elucidate the role of the chemical potential (doping) and the huge degeneracy of the effective bosonic system in achieving ODLRO with long-range phase coherence in the presence of large Coulomb repulsion. Finally, we discuss a number of relevant issues pertaining to the the present work which include: theoretical aspects of the hierarchy of the energy scales in cuprates, ``spin-charge separation'' concepts, ``local-pair'' and ``phase-fluctuation'' scenarios as well as experimental findings related to the role of the ``
d-wave'' symmetry of the spin gap and diagonal hopping ${t}^{\ensuremath{'}}$ in cuprates.
The Emery model is the quintessential model for cuprate superconductors. In his eponymous paper, Emery only considered the next-nearest-neighbor oxygen-copper hopping. Later, also the relevance of nearest- and next-nearest oxygen-oxygen hoppings has been pointed out. Using dynamical vertex approximation, we find a superconducting dome consistent with cuprates. However, long-range hoppings beyond the three conventional hopping parameters are necessary for the quantitatively correct phase diagram and for a proper d-wave order parameter.
Abstract The nature of the spin excitations in superconducting cuprates is a key question toward a unified understanding of the cuprate physics from long-range antiferromagnetism to superconductivity. The intense spin excitations up to the over-doped regime revealed by resonant inelastic X-ray scattering bring new insights as well as questions like how to understand their persistence or their relation to the collective excitations in ordered magnets (magnons). Here, we study the evolution of the spin excitations upon hole-doping the superconducting cuprate Bi2Sr2CaCu2O8+δby disentangling the spin from the charge excitations in the experimental cross section. We compare our experimental results against density matrix renormalization group calculations for at-J-like model on a square lattice. Our results unambiguously confirm the persistence of the spin excitations, which are closely connected to the persistence of short-range magnetic correlations up to high doping. This suggests that the spin excitations in hole-doped cuprates are related to magnons—albeit short-ranged.