Local Strong Coupling Pairing in $D$-Wave Superconductor with Inhomogeneous Bosonic Modes

TL;DR

This paper develops a local strong coupling model for d-wave superconductors, linking nanoscale inhomogeneities in the superconducting gap and bosonic modes, and explains experimental tunneling spectra and isotope effects.

Contribution

It introduces a local model connecting inhomogeneous bosonic modes with superconducting gap variations, advancing understanding of nanoscale inhomogeneity effects.

Findings

Local gap increases with electron-boson coupling strength.

Local gap decreases with boson mode energy.

Isotope substitution effects are complex and differ from BCS predictions.

Abstract

Recent local tunneling data indicate strong nanoscale inhomogeneity of superconducting gap in high temperature superconductors. Strong local nanoscale inhomogeneity in the bosonic scattering mode has also been observed in the same samples. We argue that these two inhomogeneities directly related to each other. To address local boson scattering effects, we develop a local strong coupling model of superconducting pairing in a coarse grained superconducting state. Each patch is characterized by local coupling to the bosonic mode as well as by local mode energy. We find that local gap value on each patch grows with the local strength of electron-boson interaction. At the same time local gap value decreases with the local boson mode energy, an observation consistent with the tunneling experiments. We argue that features in the tunneling spectrum due to boson scattering are consistent with experimentally observed spectra. We also address the $^{16}O$ to $^{18}O$ isotope substitution. Since both coupling constant and boson energy could change upon isotope substitution, we prove that interplay between these two effects can produce results that are very different from conventional BCS model.