Van Hove exciton-cageons and high-Tc superconductivity XA. Role of spin-orbit coupling in generating a diabolical point

Abstract

Spin-orbit coupling plays a large role in stabilizing the low-temperature orthorhombic phase of La 2−x Sr x CuO 4 . It splits the degeneracy of the van Hove singularities (thereby stabilizing the distorted phase) and completely changes the shape of the Fermi surfaces, potentially introducing diabolical points into the band structure. The present paper gives a detailed account of the resulting electronic structure.A slave boson calculation shows how these results are modified in the presence of strong correlation effects. A scaling regime, found very close to the metal-insulator transition, allows an analytical determination of the crossover, in the limit of zero oxygen-oxygen hopping, t OO → 0. Extreme care must exercised in chosing the parameters of the three-band model. In particular, t OO is renormalized from its LDA value. Furthermore, it is suggested that the slave boson model be spin-corrected, in which case the system is close to a metal-insulator transition at half filling.

A survey of the Van Hove scenario for high-tc superconductivity with special emphasis on pseudogaps and striped phases

“…Spin-orbit coupling, by splitting the VHS, can produce an incommensurate diffraction pattern of the observed form, and can explain the doping dependence (since the spin-orbit splitting is suppressed by correlation effects near half filling) [136]. However, the observed splitting is larger than expected for the estimated magnitude of the spin-orbit coupling.…”

“…1, above.) However, spin-orbit scattering leads to a coupling between these bands, opening gaps and strongly modifying the topology of the Fermi surface [136]. Since spin-orbit coupling can split the VHS degeneracy, it was originally thought that it might play an important role in structural phase transitions, but the energy involved seems to be too small.…”

“…[136], I attempted to derive an effective value of t OO from a five-band model of the CuO 2 planes, including the Cu d z 2 and apical O orbitals [137]. I found a reduction by more than a factor of two, but due to uncertainties in the parameter values, I do not believe that the final results are quantitatively correct.…”

“…47 and 48 are valid for a hole picture, so f h (E k ) = 1 for E k > E F , and = 0 otherwise. An equivalent electron picture can be constructed, but some care must be taken, since the above sums are then over all three occupied bands [136]. The sums are normalized per Cu atom, so for example…”

Time Reversal Breaking Superconducting State in the Phase Diagram of the Cuprates

“…For typical values of the particle density in the HTCS, the Van Hove singularity (VHS) of the two-dimensional DOS strongly favors the d x 2 −y 2 symmetry, which thus represents the principal component of the superconducting gap, in agreement with the phenomenology [15]. We take henceforth η = d + in Eqs.…”