Tight-Binding Superconducting Phases in the Unconventional Compounds Strontium-Substituted Lanthanum Cuprate and Strontium Ruthenate

Abstract

We use the idea of the Wigner probability distribution (WPD) in a reduced scattering phase space (RPS) for the elastic scattering cross-section, with the help of a Tight-Binding (TB) numerical procedure allowing us to consider the anisotropic quantum effects, to phenomenologically predict several phases in these two novel unconventional superconductors. Unlike our previous works with pieces of evidences that these two compounds are in the unitary strong scattering regime and that superconductivity is suppressed by the atoms of strontium in both materials, several phases are built. In the case of the strontium-substituted lanthanum cuprate, it was found three phases from one family of Wigner probabilistic distributions, one corresponding to the antiferromagnetic compound La 2 CuO 4 another one which consists of a coalescing metallic phase for very lightly doped La 2-x Sr x CuO 4 , and finally a strong self-consistent dependent strange metal phase with optimal levels of doping. In the case of a triplet superconductor strontium ruthenate, three phases can be differentiated from two families of Wigner distribution probabilities, one family of WDP with point nodes where Cooper pairs and dressed scattered normal quasiparticles are mixed for the whole range of frequencies and which correspond to a FS γ-flat-sheet in the ground metallic state, and two phases from another WPD family, where, in one of then, the Miyake-Narikiyo quasinodal tiny gap model allows the unique presence of Cooper pairs in a tiny interval of frequencies near the superconducting transition T C , the other phase corresponds to the mixed phase with Cooper pairs and dressed by stoichiometric strontium non-magnetic atoms, where strong self-consistent effects are noticeable. This approach allows comparing experimental results for samples in both compounds with numerical analysis studies.

A Tale of the Scattering Lifetime and the Mean Free Path

“…One of the peculiarities with the compound La2-xSrxCuO4 is that Tc depends on both the concentration of doped ions and the number of CuO2 layers and makes the use of this procedure a computational challenge where the initial frequency values are not always stable to obtain the hidden self-consistency. Similitudes and differences of the two compounds using this approach with a small frequency window is given in [34,35]. We think of a model composed by a gas of fermionic dressed quasiparticles which obey the Fermi liquid behavior [36].…”

A Tale of the Scattering Lifetime and the Mean Free Path

“…One of the peculiarities with the compound La 2x Sr x CuO 4 is that T c depends on both the concentration of doped ions and the number of CuO 2 layers and makes the use of this procedure a computational challenge where the initial frequency values are not always stable to obtain the hidden self-consistency. Similitudes and differences of the two compounds using this approach with a small frequency window is given in [36,37]. We think of a model composed by a gas of fermionic dressed quasiparticles which obey the Fermi liquid behavior [38].…”