Phase separation instabilities and pairing modulations in $Bi_2Sr_2CaCu_2O_{8+\delta}$

TL;DR

This paper investigates how phase separation instabilities near quantum critical points lead to unconventional pairing and inhomogeneities in high-Tc superconductor Bi-2212, supported by exact diagonalization and microscopic modeling.

Contribution

It provides a microscopic explanation for observed supermodulation of the pairing gap and charge density variations in Bi-2212 based on phase separation near quantum critical points.

Findings

Supermodulation of the pairing gap observed in STM experiments.

Sign change of the energy gap related to apical oxygen vibrations.

Correlation between phase separation and superconducting inhomogeneities.

Abstract

There is growing evidence that the unconventional spatial inhomogeneities in the doped high-Tc superconductors are accompanied by the pairing of electrons, subsequent quantum phase transitions (QPTs), and condensation in coherent states. We show that these superconducting states can be obtained from phase separation instabilities near the quantum critical points. We examine electron coherent and incoherent pairing instabilities using our results on exact diagonalization in pyramidal and octahedron Hubbard-like clusters under variation of chemical potential (or doping), interaction strength, temperature and magnetic field. We also evaluate the behavior of the energy gap in the vicinity of its sign change as a function of out-of-plane position of the apical oxygen atom, due to vibration of apical atom and variation of inter-site coupling. These results provide a simple microscopic explanation of (correlation induced) supermodulation of the coherent pairing gap observed recently in the scanning tunneling microscopy experiments at atomic scale in $Bi_2Sr_2CaCu_2O_{8+\delta}$. The existence of possible modulation of local charge density distribution in these materials is also discussed.